Jenaro Guisasola - Eilish McLoughlin

General Editors

Connecting Research in Physics Education

with Teacher Education 3

I.C.P.E. Book

General Editors

Jenaro Guisasola

Department of Applied Physics,

University of the Basque Country (UPV/EHU),

San Sebastian, Spain

Eilish McLoughlin

School of Physical Sciences & CASTeL,

Dublin City University,

Dublin, Ireland

Published by The International Commission on Physics Education in cooperation with

University of the Basque Country (UPV/EHU) and Dublin City University.

An I.C.P.E. Book © International Commission on Physics Education 2022

ISBN 978-1-911669-33-3

DOI: 10.5281/zenodo.5792968

Contents

Foreword ...................................................................................................................................6

Roberto Nardi

Introduction -- Making the results of research

in Physics Education available to teacher educators .....................................................8

Jenaro Guisasola and Eilish McLoughlin

Part I -- Insights from Physics Education Research ............................. 12

Chapter 1 -- Preparing Physics Students for 21st Century Careers .................................13

Paula Heron and Laurie McNeil

Chapter 2 -- Using history of physics to teach physics? .....................................................22

Ricardo Karam and Nathan Lima

Part II -- Contemporary Physics topics in the curriculum .................. 39

Chapter 3 -- Quantum Mechanics in Teaching and Learning physics:

Research-based educational paths for secondary school ............................................40

Marisa Michelini and Alberto Stefanel

Chapter 4 -- Introducing Einsteinian Physics in High School and College ......................76

Irene Arriassecq and Ileana M. Greca

Part III -- Students and teachers as learners in Physics ...................... 93

Chapter 5 -- Research-guided physics teaching:

Foundations, enactment, and outcomes ........................................................................94

Stamatis Vokos, Lane Seeley and Eugenia Etkina

Chapter 6 -- The educational implications of the relationship

between Physics and Mathematics .............................................................................. 111

Mieke De Cock

Chapter 7 -- Physics Teachers’ Professional Knowledge and Motivation .......................129

Stefan Sorge, Melanie M. Keller and Knut Neumann

Part IV -- Experimentation and Multimedia in Physics Education..... 144

Chapter 8 -- Experimentation in Physics Education ........................................................145

Elizabeth J. Angstmann and Manjula D. Sharma

Chapter 9 -- Multimedia in Physics Education .................................................................163

David Sokoloff

Part V -- Designing and evaluating classroom practices .................... 174

Chapter 10 -- Research-based design of teaching learning sequences:

Description of an iterative process ..............................................................................175

Jenaro Guisasola, Jaume Ametller, Kristina Zuza and Paulo Sarriugarte

Chapter 11 -- Designing curriculum to introduce contemporary

topics to physics lectures ..............................................................................................191

Mojca Čepič

Chapter 12 -- Inquiry approaches in Physics Education ..................................................209

Eilish McLoughlin and Dagmara Sokolowska

Part VI -- Learning in informal context and

inclusion in Physics Education ........................................................ 222

Chapter 13 -- An Overview of Informal Physics Education ............................................223

Michael Bennett, Noah Finkelstein and Dena Izadi

Chapter 14 -- Science Education in the Post-Truth Era ...................................................240

N. G. Holmes, Anna McLean Phillips and David Hammer

Biographical Sketches ..........................................................................................................255

An I.C.P.E. Book © International Commission on Physics Education 2021

All rights reserved under International and Pan-American Copyright Conventions

I.S.B.N. (English Edition)

The ICPE wishes to make the material in this book as widely available to the physics

education community as possible. Therefore, provided that appropriate acknowledgement is

made to the source and that no changes are made to the text or graphics, it may be freely

used and copied for non-profit pedagogical purposes only. Any other use requires the written

permission of the International Commission on Physics Education and the authors of the

relevant sections of the book.

6

Foreword

As Chair of the International Commission on Physics Education (ICPE) set up by the

International Union of Pure and Applied Physics (IUPAP), I am delighted to present the third

volume of the ICPE book series entitled “Connecting Research in Physics Education with

Teacher Education”. The first, published in 1997 was edited by Professors Tiberghien, Jossem

and Barojas and the second, published in 2008 was edited by Professors Vicentini and Sassi.

This third volume has been edited by Professors Jenaro Guisasola, of the University of Basque

Country, Spain, and Eilish McLoughlin, of Dublin City University, Ireland, researchers in

Physics Education, recognized not only in their respective countries, but worldwide.

This publication is very important in terms of meeting IUPAP objectives, especially as the

book launch coincides with this esteemed institution celebrating its Centenary in 2022. IUPAP

is known to be the only international physics organization that is organized by, and has

members who are identified by, physics communities in countries or regions around the world.

It has the ultimate goal of promoting the worldwide development of physics, to foster

international cooperation among physicists, and mobilize physics toward solving problems that

concern humanity. IUPAP was set up in Brussels in 1922 with 13 member countries: Belgium,

Canada, Denmark, France, Holland, Japan, Norway, Poland, Spain, Switzerland, United

Kingdom, United States of America and the Union of South Africa. As part of its Centennial

celebrations, the IUPAP Executive Council has launched the project entitled “One Hundred

Years of IUPAP: A History”, which involves digitalization of the Union’s institutional archival

documents.

As one of the basic sciences, physics relates to all branches of natural science. Many of

today’s most exciting scientific developments take place on the frontiers between different

disciplines. To cover interdisciplinary activities, IUPAP liaises closely with other similar

unions. IUPAP endorses and sponsors international conferences and workshops, promoting

diversity and inclusion among participants, speakers and committee members.

The International Commission on Physics Education, one of the 20 IUPAP commissions,

was set up by IUPAP in 1960 to promote exchange of information and views among the

members of the international scientific community in Physics Education. ICPE, with support

from IUPAP, promotes, organizes and endorses international conferences, meetings, workshops

and other activities aiming to improve physics teaching worldwide, mainly in the sixty

countries associated with IUPAP.

It is important to highlight that this book is based on communications presented at one of

the last in-person conferences, held in partnership with the International Research Group in

Physics Education – GIREP, and the Multimedia in Physics Teaching and Learning - MPTL,

prior to the pandemic that devastated humanity and led to widespread lockdowns throughout

the world.

This Covid-19 pandemic made us reflect on the role and importance of science in solving

multidisciplinary issues, where Physics played an important role, alongside sciences such as

Biology, Mathematics, Chemistry, Environment, plus Medicine and other fields of study. It also

demanded that scientists and the whole world address problems by working together, to swiftly

resolve this threat to countries around the world. At the same time, teachers and students were

suddenly faced with the need to change how they communicated, switching to remote teaching

and seeking new teaching methodologies to teach and learn virtually in schools and

universities. Research and the lessons learnt, as presented in this book, have led the way in the

switch to remote teaching and learning.

Foreword | 7

This period was important for us to think about how scientists have dealt with the economic

and social inequalities that divide nations across this planet’s different continents. This brought

to light the importance of thinking collectively about problems that afflict humanity, not only

on issues such as health, environment and the economy, but on several other themes, such as

education and, particularly, Physics teaching.

In this sense, it is important to reflect on how teaching Physics and Science, more

generally, can help to change our students’ worlds. I would like to take this opportunity to

reflect on and stress the words of an influential educator who celebrated the centenary of his

birth in 2021, my compatriot, Paulo Freire (1921-1997), author of the foundational text on

critical pedagogy and amongst the most frequently cited authors in social sciences. To Professor

Freire, education [like science] should not be neutral, but rather a tool for 'practicing freedom'

in which people, being critically educated, could transform their reality and participate in the

construction of the world. In a way, “Connecting Research in Physics Education with Teacher

Education” is envisioned to share the knowledge generated at University (Physics Education

Research) with knowledge originating from teaching practice among teachers. Certainly, this

role can be fulfilled by the themes explored in the chapters of this book, developed by renowned

researchers from various countries. The themes discussed here are important and essential

reading for physicists working in higher education, teachers working in basic education, and

for anyone interested in improving teaching of physics and other natural sciences around the

world. It captures IUPAP’s vision by celebrating physics education and sharing understanding

through an open-access, freely-available resource. The series highlights and chronicles trends

and developments in physics education, hopefully transforming learners’ worlds.

We are immensely grateful for the financial support from the University of Basque Country

and Dublin City University, and especially the IUPAP, for providing the opportunity to publish

this book. Of course, it will be added to the collection of books already authored by colleagues

who have been working in partnership with International Commission on Physics Education to

improve Physics teaching around the world.

Last, but not least, ICPE would like to thank Professors Guisasola and McLoughlin for

championing the idea of the book and ensuring its completion in such challenging times. The

book clearly demonstrates their meticulous attention to detail and intellectual insights, which

have produced a book that ICPE is proud to showcase.

Professor Roberto Nardi: Chair - International Commission on Physics Education - ICPE

International Union of Pure and Applied Physics - IUPAP

São Paulo State University, UNESP, São Paulo, Brazil, December 2021.

8

Introduction

Making the results of research in Physics Education

available to teacher educators

Jenaro GUISASOLA Department of Applied Physics & DoPER-STEMER,

University of the Basque Country (UPV/EHU), San Sebastian, Spain

Eilish MCLOUGHLIN

School of Physical Sciences & CASTeL, Dublin City University (DCU), Dublin, Ireland

One of the principal aims of the IUPAP Commission for Physics Education (ICPE) is to

disseminate Physics Education Research findings and promote their relevance to physics

teacher education and classroom practice. In particular, suggesting ways in which physics

learning and teaching at all levels might be improved and publishing handbooks, where

feasible. In accordance with these objectives, the ICPE published a handbook in 1998 entitled

“Connecting Research in Physics Education with Teacher Education 1”[1]. The editors of this

handbook, A. Tiberghien, E. L. Jossem and J. Barojas, commented that “research results in any

field, their transfer into practice is not necessarily straightforward. We consider this book as a

starting point of an international cooperative effort to transfer the results of research in physics

education to teacher educators”. In 2008, ICPE decided to continue this project and edit a

second handbook, “Connecting Research in Physics Education with Teacher Education 2” [2].

The Commission observed that research in physics education had evolved over the ten-year

period and many new findings had been reported on the learning and teaching of physics. The

editors of the second volume, M. Vicentini and E. Sassi, addressed the objectives of the initial

project and commented that “The overall goal is to gather significant experiences and

viewpoints from different areas around the world that are expressed in plain language, in order

also to encourage the implementation of innovative class practices and the starting of PER

initiatives”. Both ICPE handbooks have been made freely available online and have been

widely read and cited by the physics education community. In 2020, the project was continued

by the Commission and a third handbook was proposed that would reflect on significant

developments of research in physics education and their implications for educational

innovation. ICPE considered it important to inform the international community of physics

teachers about research findings and innovations over the preceding decade. The Commission

appointed J. Guisasola and E. McLoughlin to edit the third volume of this handbook.

The purpose of this handbook, “Connecting Research in Physics Education with Teacher

Education 3”, is to provide a structured, documented and critical review of extant Physics

Education Research (PER) and serve as an important platform for discussion and debate on

appropriate strategies and innovations in physics education. Reflecting on reported research

and initiatives in learning and teaching physics is also the central theme of the third ICPE

Handbook. Facilitating student learning in physics is complex and requires teachers to have

knowledge and understanding from across the disciplines of physics and its epistemology, to

cognitive theory of learning and to design of pedagogical approaches. Some of these aspects

were already covered in the two previous volumes: i.e., knowledge of physics and its

epistemology, student learning difficulties, challenges faced by teachers of physics, appropriate

teaching strategies in physics. Handbook 3 highlights novel and innovative approaches that

Introduction | 9

have emerged in the past decade to improve physics teacher professional learning and their

classroom practice. This handbook examines the role of student knowledge in the learning and

teaching of physics and explores innovative approaches to learning and teaching physics in the

laboratory and reflects on the use of multimedia tools. The opportunities and experiences of

learning and teaching physics across formal, informal and non-formal contexts reviewed in this

handbook share successful strategies for widening participation and engagement in physics and

enhancing scientific literacy.

Book structure

Handbook 3 reflects the fact that the Physics Education globally is currently in a process of

development and change, as evidenced by contributions at different International Forums and

Conferences. One of the main reasons for these changes is the realization as a Physics teacher

- whether at primary, secondary or university level - of a mismatch between what we teach our

students and how they perceive Physics. Research findings report on several different factors

that influence the learning and teaching of Physics – thus making this task complex enough to

warrant its own field of research. In this handbook we present a review and discussion of

research findings over six sections that represent different aspects of Physics teaching-learning

processes.

Part I “Insights from Physics Education Research” begins with a reflection on the

objectives of learning physics in the 21st century. P. Heron and L. McNeil in Chapter 1, analyze

key aspects that should be emphasized more explicitly in future physics programmes. In

Chapter 2, R. Karam and N. Lima consider how advances in the interpretation of the nature of

physics, findings in the history of science and epistemology of science in recent decades, have

influenced how we teach physics. In Part II "Contemporary Physics topics in the curriculum"

focuses on issues relating to learning and teaching contemporary physics topics that have been

incorporated into curricula across most countries, due to the fundamental role these topics play

in addressing physical phenomena and building new knowledge. M. Michelini and A. Stefanel,

in Chapter 3, discuss teaching and learning approaches in Quantum Mechanics from the

perspective of fundamental nuclei. I. Arriassecq and I.M. Greca, Chapter 4, review various

proposals for teaching special and general relativity in introductory physics courses and

provide examples of inquiry-based learning approaches.

Part III “Students and teachers as learners in Physics”, highlights that PER studies and

findings on the knowledge of students and teachers have a crucial influence on the learning and

teaching of Physics. In Chapter 5, S. Vokos, L. Seeley, and E. Etkina discuss research findings

and provide recommendations for what physics teachers need to know and do, so that they may

engage their students in learning physics by practicing it and may improve their students' well-

being in the process. M. De Cock in Chapter 6, reviews the important role, not only technical,

but also communicative and structural, of mathematics in teaching and learning of physics. She

also reviews research on the role of teachers in developing student’s understanding of the

meaning of mathematics and its interrelationship with the physical world. In Chapter 7, S.

Sorge, M. Keller, and K. Neumann discuss a novel aspect of physics teacher education by

addressing the relationship between teacher professional knowledge and motivation. They

review research findings that highlight the importance of the teacher's motivational

characteristics in his/her planning and behavior in the classroom, and ultimately, impact on

student learning outcomes.

In Part IV "Experimentation and Multimedia in Physics Education", research findings

focused on the learning and teaching of physics in the "laboratory" are discussed. "Laboratory"

is used as a general term for activities based on observations, tests, experiments and

10 | Guisasola J., McLoughlin E.

investigations carried out by students. Multimedia, similarity is considered as important tool

for learning and teaching physics. Indeed, in today’s world, it is hard to imagine how we might

learn or teach physics without the use of laboratory or multimedia tools. In Chapter 8, E. J.

Angstmann and M. D. Sharma describe how the approach to physics experimentation has

changed over time, and they discuss different investigations and findings from different

approaches, e.g. the role and assessment of inquiry based learning in school settings. D.

Sokoloff in Chapter 9, reflects on the rapid development of computer-based multimedia over

the past century, and introduces a range of exciting multimedia materials that have been made

available to physics educators. He describes the current state of research in this field, examines

the main multimedia tools available and presents examples of their applications to active

learning in physics.

In recent decades, a wide range of strategies have been proposed for teaching specific

physics topic without any attention devoted to evaluating the design process or impact of such

strategies, i.e., present a methodology for systematic development of curriculum , justify the

design choices, provide a detailed description of the design process (including integrated

evaluation). Part V includes three chapters that describe the current state of “Designing and

Evaluating classroom practices”. In Chapter 10, J. Guisasola, K. Zuza, P. Sarriugarte and J.

Ametller analyse the process of constructing teaching-learning sequences as a research activity.

They present an example of a study to design and evaluate teaching-learning sequences and

they substantiate it in the design-based research methodology. M. Čepič, in Chapter 11,

discusses the prerequisites and design of activities necessary to introduce contemporary physics

in introductory physics courses and considers topic-related module design issues. In Chapter

12, E. McLoughlin and D. Sokolowska present an overview of inquiry-based learning and

discusses how an inquiry approach can be utilised to develop both student and teacher learning

in physics. An inquiry approach that involves teachers conducting their own practitioner

inquiry in the context of inquiry-based learning in physics is recommended.

Science and technology have become a fundamental aspect of contemporary culture and

the value of learning outside of formal institutions has been recognised. There is substantial

evidence that participation in out-of-school and extracurricular activities influences

educational attainments of students. Scientific literacy, learning in non-formal and informal

contexts and ‘experience outside the classroom’ is as an important element of promoting

interest, motivation and identity in science. These topics are discussed in Part VI “Learning in

informal context and inclusion in Physics Education”. In Chapter 13, M. Bennett, N.

Finkelstein and D. Izadi, provide a review of informal physics education initiatives with an

emphasis on research and design approaches. They analyse programmes that intentionally

focus on partnerships and provide examples of successful approaches. In Chapter 14, NG

Holmes, A. McLean Phillips and D. Hammer analyse science education taking into account the

societal phenomenon of "post-truth”. They argue there is an urgent need for science education

to respond to the societal phenomenon of "post-truth," and they need to do more to support

students understanding of how science constructs and reconstructs "truth". Students must

understand how science arrives at and refines ideas, as well as the complexity of the process of

establishing laws and models scientists.

Concluding Remarks

Research activity in the learning and teaching of physics has accelerated in recent decades with

the incorporation of PER into University physics departments in several countries. This trend,

already consolidated in countries such as the United States, is growing in countries such as

Australia, South Africa and across Europe. Recent growth makes it foreseeable that in the next

Introduction | 11

decade the findings of PER will increase in quantity and quality, addressing new issues that are

not yet considered or not widespread. For example, Part VI of this third handbook was barely

considered or discussed in the previous two handbooks. However, this does not mean that the

results of this handbook and the previous ones are not relevant. The three handbooks

collectively have a common goal to enhance the learning and teaching of physics across all

levels. Each handbook reviews and discusses research findings, critiques pedagogical

practices, and challenges existing theories and strategies. In this sense, the findings and

conclusions from each handbook are transferable to other disciplines or can serve as a starting

hypotheses for new research.

We hope this book provides the physics teaching community with a platform to share and

discuss their own research findings and educational practices. In closing, we want to thank all

the contributing authors of this handbook for their collaboration and commitment to this

handbook, and all those whose assistance and encouragement have made this publication

possible.

[1] A. Tiberghien, E. L. Jossem and J.Barojas, Connecting Research in Physics Education with Teacher

Education 1, An I.C.P.E. Book © International Commission on Physics Education, 2008.

[2] M. Vicentini and E. Sassi, Connecting Research in Physics Education with Teacher Education 2, An

I.C.P.E. Book © International Commission on Physics Education, 2018.

Part I

Insights from Physics Education Research

13

Chapter 1

Preparing Physics Students for 21st Century Careers

Paula HERON University of Washington, Department of Physics, 98195-1560. Seattle, USA

Laurie MCNEIL Univ. of North Carolina at Chapel Hill, Dept. of Physics & Astronomy,

27599-3255 Chapel Hill, USA

Abstract: Physics programs have traditionally focused on the potential for intellectual growth

offered by the discipline; providing a foundation for future employment has been a secondary

concern at best. Nevertheless, physics graduates are sought after for their flexibility, problem

solving skills, and exposure to a wide range of technologies, and are successful in many

different careers. They would be even more successful if additional technical skills,

professional skills, and communication skills were more explicitly emphasized in our

programs. These skills would also benefit graduate students, postdocs and faculty, and

potentially result in broader participation in the discipline.

1. Introduction

Physics courses and programs have traditionally focused on the potential for intellectual growth

offered by the discipline. In parallel, physics teacher education has focused on cultivating

teacher knowledge of the discipline, of student thinking, and of teaching techniques. That the

study of physics could offer a solid foundation for future employment has been, at best, a

secondary concern. Even students don’t perceive career preparation as a reason to study physics

at the university level. [1] What little professional development is provided is almost always

directed at the one career that is tacitly approved: professor.

To the extent that broader career preparation is considered, the tacit assumption appears to

be that the standard coursework will help students develop certain skills and knowledge – from

mastery of specific concepts to “thinking like a physicist” – and that those are adequate

preparation for all students. While our study of the topic finds some support for this assumption,

and we certainly believe these fundamental skills and knowledge are what makes a physics

degree special, there are many aspects of career preparation that are frequently neglected,

leaving physics degree holders less prepared than necessary. In this article we argue that these

aspects can be incorporated in ways that complement, rather than compete with, traditional

learning goals. Our goal is to provide physics teachers, teacher educators and physics faculty

in general with information and suggestions that can inform course and program design aimed

at preparing students for the broad spectrum of professional challenges they will face after

graduation.

We start by emphasizing the diversity of career paths open to students who study physics.

We then point out how current physics instruction leaves students well-prepared to meet some

of the demands of those careers, but ill-prepared for others. Then we briefly describe strategies

that physics programs have adopted to help prepare students to pursue their career goals.

Finally, we argue that strengthening career preparation has many benefits to the school,

college, or university. Much of this article draws on a report we co-authored that contains the

findings of a task force convened by the American Physical Society and the American

Association of Physics Teachers. [2, 3] While the report, Phys21: Preparing Physics Students

for 21st Century Careers, was aimed at informing university-based physics programs, we

14 | Heron P., McNeil L.

believe the insights and suggestions are useful for physics educators more broadly. Moreover,

despite the fact that most data were drawn from the experience of students, professors and

employers in the United States, the experience of our colleagues in Europe, Asia and elsewhere

suggests the fundamental issues are universal. The growing need for a technical workforce that

includes physics specialists is well-documented [4], however studies in Europe demonstrate

that students do not necessarily view the study of physics as useful for employability [5].

European projects have also identified similar competencies that are useful, or even necessary,

for physics students to be well-prepared for success after university [6].

2. Employment paths for physics students

Many of us who teach physics at the university level followed the traditional path to get where

we are: undergraduate and graduate degrees in physics, perhaps a postdoctoral position (or

two), and then a faculty position. It is tempting to assume that most of our students will follow

in our footsteps, and that we best serve them by preparing them to do so. However, in the

United States, the American Institute of Physics’ (AIP) Statistical Research Center reports that

fewer than 5% of students who earn undergraduate physics degrees end up employed as physics

professors.[2] The overwhelming majority of graduates are employed outside academia for all

or part of their careers and are engaged in a wide variety of work. This is equally true for

recipients of Ph.D. degrees in physics, almost half of whom occupy positions outside academia

one year after receiving their degrees, and more of whom move to private-sector or government

positions after completing a postdoc.

In the United States, slightly less than half of recent university graduates with a degree in

physics enter graduate school (in physics, astronomy, or other fields); most of the rest enter the

private sector with employment in engineering and computing most common.[7] However

about a third of graduates are employed outside of STEM and even they typically report that

solving technical problems is a regular part of their jobs.

The ultimate pathways pursued by our graduates are strikingly diverse. The Phys21 Report

features profiles of entrepreneurs, financial analysts, engineers, writers, software developers

and others who used their physics degree as a springboard. The Institute of Physics website

features profiles of bankers, artists, policy researchers, managers, and teachers, among others.

[8] All discuss how their study of physics helped them succeed in their chosen careers.

One of the more traditional paths for a physics graduate, teaching at the secondary school

level, is an option pursued by a small number. There are significant national differences in the

degree to which physics departments offer special preparation for these students; in the US,

national organizations have been urging greater engagement for several decades.[9] In many

cases, preparation is essentially the same, if not identical, to that provided to graduate-school

bound students.

3. Skills and knowledge needed by physics students

Physics graduates working outside academia report that they regularly need to use skills that

go beyond their knowledge of physics, such as working in teams, technical writing,

programming, applying physics to solve interdisciplinary problems, designing and developing

products, managing complex projects, and working with clients. Our task force commissioned

a set of interviews with recent graduates in a variety of positions. They appreciated the

foundations they obtained in problem-solving and cited experiences in research, teaching and

programming as valuable. However, they also unanimously wished they had acquired more

programming skills and more exposure to industrial and applied settings. They also wished

Chapter 1 | 15

they had been better able to identify jobs for which they were qualified (few jobs available to

physics graduates contain the word “physics”) and that they had been better able to articulate

what they could offer to employers. Interviews with those responsible for hiring the graduates

emphasized that physics graduates bring broad training and valuable skills such as the ability

to tackle ill-defined problems but pointed out some shortcomings. Hiring managers generally

expressed a wish that graduates had obtained more research and industry experience, were

better able to work in teams, and had stronger communication skills.

To further assess the needs of graduates, our task force also drew on documents from other

disciplinary societies, education associations, business and government groups, our own

interviews with a selection of physicists in non-academic careers, developers of innovative

university-based programs, and representatives of other disciplines that have tackled similar

issues. In surveying this data, we developed a clear picture of the knowledge and skills that,

ideally, a physics graduate should have in order to be successful in a wide range of careers.

We formulated our findings into a set of learning goals to assist educators in identifying

explicitly what specific knowledge and skills they want to help students acquire and in

developing ways to verify that they are providing the necessary opportunities. While some of

them are unique to physics, others are equally relevant for other STEM disciplines. A well-

articulated set of student learning goals and a means of measuring success in providing

opportunities for students to attain those goals are fundamental to the design of an effective

program. We organized these goals into four categories: physics-specific knowledge, scientific

and technical skills, communication skills, and professional and workplace skills. The

Educating Physicists for Impactful Careers report has an even broader scope. [1]

3.1. Physics-specific knowledge

Physics programs have traditionally paid the closest attention to ensuring that students graduate

with physics-specific knowledge, including core physics concepts (energy, fundamental nature

of the physical world, conservation principles, etc.) that are generally taught in the canon of

physics topics: mechanics, electricity and magnetism, thermodynamics and statistical

mechanics, quantum mechanics, and their application in areas such as optics, nuclear physics,

condensed matter physics, and other subdisciplines. Physics students also gain skills in

numerical, analytical, and experimental methods. It is less common, however, for physics

programs to explicitly consider knowledge and skills associated with the application of physics

in interdisciplinary contexts and in the wide variety of non-academic career settings in which

graduates may find themselves. The best-prepared graduates will have acquired the ability to

represent basic physics concepts in multiple ways, including mathematically (including

through estimations), conceptually, verbally, pictorially, computationally, by simulation, and

experimentally. They will also have experience in solving problems that involve multiple areas

of physics or multidisciplinary problems that link physics with other disciplines and to applying

basic physics concepts to the solution of applied problems.

3.2. Scientific and technical skills

Educators can also serve their students well by providing their students with opportunities to

acquire a variety of scientific and technical skills that are not necessarily specific to physics.

These include problem solving; generic experimental skills in optics, vacuum technology,

electronics, etc.; coding and software use; and data processing and analysis. While some

aspects of these skills (especially certain kinds of problem solving, and electronics at the

component level) are explicit components of traditional coursework, faculty often assume that

other such skills will be acquired as part of advanced laboratory classes or through participation

in research. However, without an explicit goal of inculcating such skills and including specific

16 | Heron P., McNeil L.

activities to enable all students to acquire them, it is easy for many of these skills to fall through

the cracks, or for students to fail to recognize which marketable skills they have acquired.

When a physics graduate enters the workplace (or, for that matter, when she undertakes a

dissertation project), she is likely to face the challenge of solving complex, ambiguous

problems in real-world contexts. She will need to define and formulate the question or problem,

perform literature studies (print and online) to determine what is known about the problem and

its context and manage scientific and engineering information so that it is actionable. Based on

that information, she will need to identify appropriate approaches to the question or problem,

such as conducting an experiment, performing a simulation, developing an analytical model,

and develop one or more strategies to solve the problem and iteratively refine the approach. To

carry out the strategy she will need to identify resource needs and make decisions or

recommendations for beginning or continuing a project based on the balance between

opportunity cost and progress made, determine follow-on investigations, and place the results

in a larger perspective. It is likely that she will have had little or no experience in most of these

actions unless her undergraduate program has provided her with specific opportunities to

develop such skills.

There are also more focused skills that physics graduates need to make use of. Competency

in instrumentation, software, computation, and data analysis is vital to success in the types of

workplaces where physics graduates typically find themselves. Physics graduates are expected

to be capable of using basic experimental technologies, including vacuum, electronics, optics,

sensors, and data acquisition equipment. Such capability extends beyond operating the

apparatus to knowing equipment limitations; understanding and using manuals and

specifications; building, assembling, integrating, troubleshooting, and repairing equipment;

establishing interfaces between apparatus and computers; and calibrating laboratory

instrumentation. Students most often are introduced to such skills by participation in

undergraduate research or in advanced laboratory classes, but unless these experiences are

designed specifically to foster them, students may miss out.

Another example of a technical skill that many graduates need but typically do not acquire

in a standard program is software competency. It is rare for academic activities in physics,

whether in a class or in research experiences, to include the use of industry-standard

computational, design, analysis, and simulation software. Computational tools for optics,

electrical systems, mechanics, and physics are widely used in the private sector, and experience

with learning and using such software is important for a physics graduate. Coding competency,

i.e., writing and executing software programs using a current software language to explore,

simulate, or model physical phenomena, is also vital—graduates we interviewed were

unanimous in their desire for more programming skills. Competency in analyzing data (with

statistical and uncertainty analysis), distinguishing between models, and presenting results with

appropriate tables and charts (data analytics competency) is important in many careers pursued

by physics graduates. The omission of these types of preparation from their programs puts them

at a disadvantage compared to their peers with engineering degrees, who are more likely to

have had such experience.

3.3. Communication Skills

Members of the broader physics community are well aware of graduates’ need for good

communication skills, but often a physics program will focus primarily on the preparation of

refereed publications. This is only one form of communication in the discipline, and one that

may be of limited importance for many physics graduates. A physicist in an industrial or

government setting is likely to need the ability to communicate science content and outcomes

to individuals who may not be trained in science, including managers, sponsors, members of

Chapter 1 | 17

Congress, marketing personnel, technicians, and members of the public. She will need to

articulate her own state of understanding and be persuasive in communicating the worth of her

own ideas and those of others using words, mathematical equations, tables, graphs, pictures,

animations, diagrams, and other visualization tools. She may need to teach a complex idea or

method to others, use feedback to evaluate the learning achieved, and develop revised strategies

for improved learning. A physics graduate teaching at the K-12 level needs these skills and

others. Most physics programs include no specific opportunities to develop these kinds of

communication skills, even if students have the opportunity to co-author scientific publications

and present their research at professional conferences.

3.4. Professional and Workplace Skills

Beyond this wide range of skills and knowledge that are often not explicitly fostered, most

physics programs short-change their students in another way: they rarely help their students

learn about career opportunities in physics, how to find a job (e.g., by developing résumé

writing and interview skills), and how to assess one’s skill set and its relevance to a job. This

can make physics graduates’ transitions to the workforce more challenging than necessary. The

fact that many physics faculty members are only vaguely aware of careers outside academia

makes this doubly challenging.

4. What can physics teachers, courses and programs do?

The long list of skills and knowledge that physics graduates need may seem daunting to both

students and faculty members. How can a program provide a student with all that career

preparation and still make sure she can solve Schrödinger’s equation? To find examples of

strategies that other departments could adopt, we commissioned a set of case studies of

departments that have modified their programs to enhance graduates’ career readiness. (We

refer here to the “Physics Department” as the primary unit in charge of curricular decisions,

but depending on the region, such decisions might be taken in collaboration with a School,

Faculty or College.)

Fortunately, most of the learning goals can be pursued through more than one channel, and

there are examples of different kinds of institutions that have found creative and effective ways

to address the challenges. Depending on the local conditions, the resources available, the size

and aspirations of the student body, industries in the region, and other factors, departments can

choose different strategies. They may be ready to redesign their programs entirely; or choose

to infuse the development of new skills into their current course offerings or rely primarily on

enhanced co-curricular activities. In our report we provide many examples of different

approaches that have been adopted by physics departments.

Most physics faculty members will feel that their standard courses already provide a firm

foundation of physics knowledge, and rightly so (although physics education research is

increasingly addressing advanced coursework). But why stop there? The content of virtually

any of these courses can be related to career-relevant applications (even general relativity has

a practical use in GPS technology), while maintaining a focus on fundamentals. Faculty can

also cultivate students’ scientific and technical skills by modifying existing courses or labs to

incorporate the application of physics principles to industrial processes and commercial

devices, without reducing the learning of fundamental physics content. Commercial products

can be incorporated into laboratory courses to help ensure that students are familiar with

industry-standard software packages.

Looking beyond individual courses, students’ communication skills can be addressed at

many points in the curriculum. For example, students can produce oral reports on topics

18 | Heron P., McNeil L.

relevant to a standard class or as part of a seminar. They can give presentations on their research

to the general public, perhaps as part of outreach efforts. And not all the skill development

needs to take place in physics classes--general writing and editing skills can be cultivated in

classes taught in language and communication departments, and basic business concepts can

be incorporated through courses taught in engineering departments or in business schools. By

guiding students to fulfill requirements outside the physics major by enrolling in appropriate

business, economics, law, ethics, organizational effectiveness, graphic design, and other

courses that fulfill these requirements, it may be possible to achieve some of the learning

outcomes without adding to the physics program or increasing the academic load the students

bear. Campus-wide career placement offices can partner with physics departments to help

students learn how to conduct a successful job search by hone their résumé-writing and

interview skills and giving them practice in describing their skill sets and articulating what they

have to offer to potential employers.

Academic activities outside the classroom provide often-overlooked opportunities to

develop professional knowledge and skills. Departments can host talks and other events that

feature physics graduates in diverse careers, engage their alumni/ae who have pursued diverse

careers, and support student organizations in activities such as industrial site visits and

educational outreach. Many national professional organizations offer professional development

activities at conferences.

Engaging students in teaching is another way to help them gain needed skills without

expanding the number of required courses. In many universities, more advanced students can

serve as teaching assistants in introductory level courses. Such opportunities can help develop

professional skills taken for granted in industry but often not required by students, such as

punctuality, a professional appearance, and providing polite and constructive feedback in a

timely manner.

A department that is prepared to make significant changes can pursue collaborative efforts

with other units on campus and with employers of physics graduates, creating immersive

experiences in the workplace through co-op stages or internships, or intensive interdisciplinary

programs on themes such as innovation and entrepreneurship. The EPIC report contains many

recommendations and examples. [1] Such options provide unmatched opportunities for

students to pursue multiple learning goals in a single coherent program. Internships or co-op

stages, which have been used in engineering for decades, allow students to spend a significant

amount of time in an off-campus workplace. In addition to providing direct exposure to product

development and manufacturing, internships can help students focus on nontechnical aspects

of science, such as documentation, communication, and business development. Students placed

at scientific service companies will be exposed to proposal preparation, project cost tracking,

corporate structures, and project execution. Technology transfer offices at national laboratories

offer opportunities to learn about patents, licensing, and commercialization. Internships often

lead to job opportunities for students, and students interested in a particular industry would do

well to intern with a leading firm. In designing such programs, departments should work

closely with other campus groups that may have relevant connections and expertise, such as

career services offices, engineering departments, and business schools. These linkages may

also provide opportunities that may be more diverse than traditional physics positions—exactly

the type of experience that will expose students to the full breadth of applications of their

knowledge and expertise.

Interdisciplinary programs are another efficient way to capitalize on expertise not found

in the physics department. Programs that offer a minor or certificate may be especially

appealing to students. Moreover, the opportunity to work with students from a variety of

disciplines can provide an excellent opportunity to develop professional and workplace skills.

Such programs are also very well suited to introducing students to key principles and practices

Chapter 1 | 19

related to entrepreneurship and innovation. These programs can be staffed by individuals who

have the academic, industrial, and economic development background to link students and

departments with opportunities in the private sector. The goals of these programs are to create

graduates who are particularly skilled in innovation and the entrepreneurial mindset, with

grounding in a breadth of professional and business skills applicable in any career pathway.

A department that does not choose to make major changes may nevertheless benefit its

students by making the degree program more flexible to allow students to tailor their course

selections to specific career paths. Some students may be better served by replacing a few of

the traditional core physics courses with physics electives that address practical topics with

industrial applications, such as condensed matter physics and optics. Some traditional core

courses could also be with replaced with courses from disciplines such as engineering, biology,

statistics, computer science, speech, business, technical and creative writing, philosophy

(especially ethics/reasoning skills), and pedagogy. These substitutions can be made on a

student-by-student basis or can be organized into pre-determined “tracks,” or recommended

packages of electives, designed to offer a coherent experience and prepare students for specific

types of careers, especially those relevant to the region in which the institution is located.

Another program modification that can enhance students’ career preparation is a relevant

“capstone” experience: a thesis, senior seminar, or other substantial integrating experience.

Often students will intern in a research laboratory and write up their work, conduct book

research on a historical or major scientific breakthrough, or carry out a model experiment of

their own under faculty guidance. These activities could be tailored to address one or more of

the learning goals we have identified and bring industry-standard skills into an existing part of

the program. For example, students could use commercial graphics software packages to

analyze data and prepare charts and use CAD software for diagrams and design.

At an even more modest level, individual courses can be modified to use commercial

applications to illustrate basic concepts, incorporate career-relevant technical skills (such as

software competency) in standard laboratory activities, and introduce problem definition and

project management skills into the lab experience. New courses can be designed around

specific applications that involve important physics concepts. For example, a course designed

around solar cells can encompass quantum mechanics, thermal physics, optics, electricity and

magnetism, solid state physics, etc., either concentrating on one of these subdisciplines or

covering more than one in an integrated fashion. Physics also plays a central role in

understanding challenges and solutions associated with clean energy, clean water, and the

environment, and courses with such emphases could prove very attractive to students as well

as provide them with the broader experience that fosters workplace success.

Clearly the development of many of the skills and competencies needed for career success

can be begun in primary and secondary education. In particular, while pupils are making

decisions that will affect their long-term prospects, they should be made aware of the

opportunities that await if they choose to pursue physics at the post-secondary level. The need

for teacher education programs to address career preparation is thus vitally important.

5. How can we get started?

The starting point for any effort to improve career preparation is to assess the needs and goals

of your own students, to assess the jobs available in your region, and to select learning goals

accordingly. You will find that many of the learning goals are already addressed in your

program, but many others are not. (You may also find that some elements of your program are

there for historical reasons and don’t address contemporary learning goals or are redundant

with other elements.) Deciding on the scale of change requires engagement of the entire unit,

20 | Heron P., McNeil L.

regardless of who will do most of the implementation work. Assessing the outcomes is essential

but may not be appropriate right away – often new courses, projects or experiments need time

to be refined. National physics organizations may provide resources, especially those aimed at

helping students recognize what sorts of future paths are available to them.

6. What are the benefits of enhancing career preparation?

Even the most minor changes that we recommend to enhance graduates’ career preparedness

will require some sustained effort on the part of physics faculty members. So, what would be

the reward for you and your department? First, if you investigate the employment outcomes of

your program’s recent graduates and the career aspirations and prospects of your current and

future students, you will better know your students and be able to help them achieve their full

potential after graduation. Second, doing so will enhance the reputation of your department and

attract a talented and diverse group of students who might otherwise have chosen different

disciplines or institutions that appear to offer better employment prospects or greater

opportunities to serve society. Enhancing your students’ engagement with applied research will

result in access to new resources and new, interesting research questions. Third, those few

students who go to graduate school will have developed skills that are every bit as useful in a

research group as they are in the workforce. But ultimately, we believe that you and your

department should choose to follow our recommendations because you desire two things. One

is to prepare 21st-century graduates as effectively as possible for the diverse careers that they

can be expected to have—in other words, to do right by all of your students. The other is for

your department to obtain the many benefits that will follow from fulfilling the first desire—

in other words, to pursue enlightened self-interest.

7. Conclusion

Few physics programs are explicitly designed to prepare students for the most likely careers

they enter. Indeed, both graduates and their employers report that physics graduates could be

better prepared for positions available to those with physics training. Despite these

shortcomings, physics graduates are largely remarkably successful in the career paths they

choose. Physics graduates are sought for their flexibility, problem solving skills, and exposure

to a wide range of technologies. However, graduates would benefit from a wider and deeper

knowledge of computational analysis tools, particularly industry-standard packages; a broader

set of experiences that engage them with industry-type work, such as internships and applied

research projects; and closer connections between physics content and applications and

innovation. Graduates would also be more successful in the workplace if opportunities to

develop professional skills such as teamwork, communications, and basic business

understanding were added the undergraduate physics program. If these skills were more

explicitly emphasized in undergraduate physics programs, we could better prepare physics

graduates for all of the career paths available to them.

It is also important to note that while this article and the reports it cites contain practical

information, there are broader cultural issues that need to be addressed. In particular, a common

attitude, tacit in many cases, but often quite explicit, is that employment as a professor

represents the pinnacle of achievement and an ambition shared by all students; other career

paths are for those lacking in ability or drive. A shift toward respecting non-academic careers

and those who pursue them could play an important role in making our discipline more

attractive to students and ensuring their success.

Chapter 1 | 21

Acknowledgements

This article draws heavily from the work of the Joint Task Force on Undergraduate Physics

Programs (J-TUPP), which was convened by the American Physical Society (APS) and the

American Association of Physics Teachers (AAPT) in 2014 to answer the following question:

What skills and knowledge should the next generation of undergraduate physics degree holders

possess to be well prepared for a diverse set of careers? J-TUPP’s members were drawn from

the academic and industrial physics communities, and the Task Force was asked to provide

guidance for physicists who wish to revise their department’s undergraduate curriculum to

better prepare students for diverse careers. The report of the Task Force, entitled Phys21:

Preparing Physics Students for 21st Century Careers, is available for download at

http://www.compadre.org/JTUPP. In this article, “we” generally refers to the entire

membership of task force, but the two authors take responsibility for any errors or omissions.

References

[1] Arion, D. (2021). Educating Physicists for Impactful Careers. American Physical Society.

https://epic.aps.org/

[2] Heron, PRL. & McNeil, L. (2016). Phys21: Preparing Physics Students for 21st Century Careers.

American Physical Society. https://www.compadre.org/jtupp/report.cfm

[3] McNeil, L. & Heron, P. (2017). Preparing physics students for 21st-century careers. Phys. Today, 70 (11)

38 https://doi.org/10.1063/PT.3.3763

[4] Hazelkorn, E., Ryan, C., Beernaert, Y., Constantinou, C. P., Deca, L., Grangeat, M., & Welzel-Breuer, M.

(2015). Science education for responsible citizenship. Report to the European Commission of the expert

group on science education.

https://www.academia.edu/14816833/Science_Education_for_Responsible_Citizenship

[5] Levrini, O., De Ambrosis, A., Hemmer, S., Laherto, A., Malgieri, M., Pantano, O., & Tasquier, G. (2016).

Understanding first-year students’ curiosity and interest about physics—lessons learned from the HOPE

project. European Journal of Physics, 38(2) 025701.

[6] TUNING Educational Structures in Europe Physics. Specific Competences –

Physics.http://www.unideusto.org/tuningeu/competences/specific/physics.html

[7] American Institute of Physics. (2020). Employment and Careers in Physics.

https://www.aip.org/statistics/reports/employment-and-careers-physics

[8] Institute of Physics (2021). Careers with physics. https://www.iop.org/careers-physics

[9] Meltzer, D.E., Plisch, M., & Vokos, S. (2012). Transforming the Preparation of Physics Teachers: A Call to

Action. A Report by the Task Force on Teacher Education in Physics (T-TEP). American Physical Society

https://www.aps.org/about/governance/task-force/upload/ttep-synopsis.pdf

22

Chapter 2

Using history of physics to teach physics?

Ricardo KARAM Department of Science Education, University of Copenhagen, Denmark

Nathan LIMA Department of Physics, Federal University of Rio Grande do Sul, Brazil

Abstract: For over a hundred years we have been teaching and learning physics through

textbooks. To members outside this community, it may seem strange to have to learn about

Newton’s laws, Maxwell’s equations or Noether’s theorem without consulting the works

written by these authors. In this chapter we present two episodes that illustrate the use of

original sources in the teaching of mechanics and thermodynamics. The purpose of the

episodes is to try to extract general methodological aspects that lead to a productive use of

primary sources in the teaching of physics.

1. History (and philosophy) in physics education: a historical sketch

Historical accounts about the development of science have been written for a long time, even

though History of Science became an autonomous discipline only in the XXth century [1].

Analogously, in the very birth of modern science – in the writings of Galileo, Bacon and

Descartes for instance – we often find not only the production of the scientific knowledge, but

also the explicit defense of the validity of such knowledge and of the methods used to attain it

– a concern typically classified as epistemological.

What are the objects that science speak about? Do they really exist or are they simple

instruments to speak about reality? Why is scientific knowledge trustable? What is the relation

between mathematics and reality? How does scientific knowledge evolve? How has a specific

theory been created and why? These are some of the questions addressed by many physicists

through centuries of scientific development.

In this sense, historical and philosophical issues were not considered by many prominent

scientists something strange to the scientific practice. For many of them, to learn physics meant

also to learn about the history of physics1. Perhaps, one of the most noticeable examples was

Ernst Mach, according to whom:

The history of the development of Mechanics is quite indispensable to a full

comprehension of the science in a present condition. It also affords a simple and

instructive example of the process by which natural science is generally

developed. [3] (p. 1).

In order words, to Mach, we do not study the history of physics only to learn about history,

but also to learn physics itself. Furthermore, from historical examples we access an

epistemological dimension, i.e., how science works – an aspect that has been privileged in

many trends of contemporary science education [4, 5].

When Ernst Mach retired, it was Ludwig Boltzmann, one of the founders of Statistical

Mechanics, who occupied his chair on Natural Philosophy at the University of Vienna.

Boltzmann was also deeply concerned about the philosophy of physics and wrote many essays

on this subject [6]. During the twentieth century, many of the lead protagonists of modern

Chapter 2 | 23

physics also engaged in deep philosophical debates, such as Albert Einstein [7], Werner

Heisenberg [8] and Niels Bohr [9].

Someone could argue that, although history and epistemology of physics may contribute

to better understand advanced topics of physics or to better grasp subtle details, this would not

be the case for the introductory levels. Such approach, indeed, adds complexity to physics

teaching, bringing more elements to the discussion and demanding a wider range of skills.

In this sense, it is legitimate to ask whether it would be better for someone who is starting

to learn physics to learn only “physics” first, as we know it today (without all the complexities

that historical and philosophical questions can bring about). Why should a newcomer to such

a complex discipline be concerned about its historical and philosophical aspects? These

questions (and possible answers), however, are not new.

In 1899, Florian Cajori wrote a paper entitled “The pedagogic value of the history of

physics” [10] defending the importance of introducing the historical aspects of science in the

elementary teaching. Cajori identifies four chief pedagogical contributions of the history of

physics, which we briefly outline:

I) “In the first place, a knowledge of the struggles which original investigators have

undergone leads the teacher to a deeper appreciation of the difficulties which pupils

encounter.” (p. 278). Not rarely, teachers have a hard time figuring out why students do not

understand certain concepts, or how it is possible that they make some “basic” mistakes. This

is what Gastón Bachelard [11] called pedagogical obstacles (the teacher does not understand

why the student does not understand). As Cajori points out, however, when one studies history

of physics, it is possible to appreciate how concepts that today are considered obvious were

also obscure to the scientists themselves. The concepts of mass and weight, or heat and

temperature, which sometimes are wrongly interchanged by students, were also confused along

the history of physics. They may seem obvious for someone with a long training in physics,

but they are anything but obvious for anyone starting to study physics, even if the person is

Isaac Newton!

II) “While to the instructor the history of science teaches patience, to the pupil it shows

the necessity of persistent effort.” (p. 279). When one learns physics concepts from a textbook,

one may have the impression that this concept is obvious or that it was easily grasped by some

genius. This narrative usually creates a distorted picture of science and scientists that make

students feel apart from the scientific endeavor. By studying the history of physics, on the other

hand, one may realize that scientific knowledge is the consequence of a long, collective, and

laborious set of efforts. By being aware of this, one may feel closer to the scientific endeavor

instead of picturing it as a distant and abstract practice.

III) “A third lesson to be drawn from historical studies is the necessity of checking

speculation and correcting our judgment appeal to the facts, as determined by experiment.”

(p. 280). This may be a philosophical or epistemological contribution. Again, as it was pointed

out by Gaston Bachelard, the scientific practices consist of a permanent correction of our

conceptions about nature. In science, we make hypotheses, we propose assumptions, but in the

end, we are always concerned about the confrontation of our theories with empirical data. One

of the sources of confidence in the scientific knowledge is the fact that it is not a product of

human reason only, it also considers the results of many different experimental set ups. Thus,

as pointed out also by Mach, by learning history of physics we also learn how science works.

It highlights its objective character, as opposed to a mere subjective one.

IV) “Another point which I desire to make is that history of science demonstrates the

futility of the pedagogical theory, which the pupils in the laboratory should be made to re-

discover the laws of nature.” (p. 281). During some time, it was a common assumption the idea

that humans could be considered a blank slate and that physical laws could be directly obtained

from empirical data, without any theoretical formulation [12]. If this were the case, one should

24 | Karam R., Lima N.

expect that leading students to the laboratory would be enough for them to learn physics. This

conception, however, was widely contested along the XXth century. The production of physical

laws and the learning of physic is a deeply complex process and it cannot be reduced only to

performing experiments (although experiments are an important step of the process). There are

several episodes in the history of physics where the same set of empirical data led to different

(sometimes controversial) theoretical frameworks and, thus, we cannot expect that students

would learn physics only by performing experiments. History of physics shows us that to learn

physics demands a complex and collective process.

Finally, Cajori highlights that the insertion of history of physics in physics education may

be a source of interest for students, a factor that can greatly contribute to learning:

I have pointed out how the history of physics disproves a certain pedagogical theory,

how it shows the holding speculation in check by experimentation, how it emphasizes

the necessity of patience on part of the teacher and perseverance on part of the

student. I might have spoken of the great liberalizing effect of the view which it

affords of the development of the human intellect. But with the practical teacher all

these considerations dwindle into insignificance as compared with the aid to be

derived from history as a stimulant, of exciting interest. If a teacher creates a living

subject, all other difficulties vanish. (p. 282)

Despite this early recognition of the pedagogic value of the history of physics, during the

XXth century, different pedagogical approaches have been emphasized. Chiefly due to the

tensions created by the cold war, the scientific pedagogy turned out to be more focused on

technical, instrumentalist approaches [13, 14]. Instead of discussing historical and

epistemological aspects of physical theories, as well as their foundations, twentieth century

scientific pedagogy highlighted the domain of mathematical skills and problem-solving

techniques. In this period, historical discussions were neglected or even it was preferred to

present quasi-historical narratives, which emphasized mythological and over-simplified

descriptions of science [15].

In the end of the eighties, however, it was possible to observe a new movement toward the

integration of the history and philosophy of science in science education [16]. One of the

symbols of this new rapprochement was the creation of the journal Science & Education and

the emblematic paper written by Michael Matthews: History, philosophy, and science teaching:

The present rapprochement [17]. In Matthews’s paper, one finds a detailed history of the

development of history of science in science education along the XXth century. Also, in 1989,

the creation of the IHPST group – International group of History and Philosophy in Science

Teaching – may be considered an important mark in the consolidation of history of science as

an important element of contemporary Science Education.

In the last three decades, since the publication of Matthews’s paper and the creation of the

IHPST group, many things have changed and the field of history of physics in physics

education has gathered a wide community, working in different historiographical perspectives,

assuming different epistemological and philosophical commitments [18] and with different

implications for the physics classroom [19].

In this sense, the defense of history of physics in physics education should not be thought

as a homogeneous movement; instead, it should be recognized as a complex and plural

movement that for different reasons and with different methodologies recognize the

pedagogical values. In general lines, we would like to address three chief categories of works

and didactic propositions that can be found nowadays2.

First, we can find research and proposals that adopt the historical aspect as an intrinsic part

of physics and, thus, imply that to teach physics means to teach to some extent history of

Chapter 2 | 25

physics. Some examples are found in [20–22] or in Part I of the International Handbook [18].

These works are more associated with internalist historiographical perspectives and highlight

the construction of scientific concepts as historical processes. There are many epistemological

perspectives that can be associated with these works. It can be emphasized the interplay

between physics and mathematics, the importance of scientific models, the rational evolution

of science, the role of creativity, and so on.

A second group of approaches can be associated to a social historiography of science –

which is often motivated by Thomas Kuhn’s influential work – The Structure of Scientific

Revolutions [23]. These works emphasize science as a social practice and discuss how it affects

and is affected by society in general. In this case, usually the aspects of science that are

emphasized encompass the social, axiological, political, cultural aspects that connect science

with society. Many approaches in this sense can be used in what is called STS perspective

(Science, Technology and Society), taking from historical episodes insights about how science

works to better understand contemporary socio-scientific issues [24]. In this perspective, we

find many different studies that discuss the “Nature of Science” in a broader sense. An overview

of the field of research on Nature of Science can be found in [25].

Finally, a third possible group can be associated to a cultural historiography of science

[26]. As the second category, these works emphasize the social dimension of science, but they

focus on a non-structuralist perspective, highlighting the role of material instruments,

communities, forgotten characters, practices and cultural arrangements in the development of

science. Some examples may be found in [27].

These different approaches are committed to different pedagogical objectives,

epistemological perspectives, and historiographic methods. In this sense, we understand that

depending on the context and objectives of each educational program, these different

perspectives may contribute to promote a better understanding of physics and of science in

general.

Our focus in this work will be on the first approach, namely the one in which historical

episodes are used to promote a better and deeper understanding of physics. In the next section,

we present two case studies with the purpose of extracting some pedagogical lessons from

selected excerpts of original sources. We decided to choose rather well-known topics that are

widely taught – i) Newton’s original proof of Kepler’s first two laws of planetary motion and

ii) Clausius’s original proposal of the concept of entropy – to make the argument more

appealing to a broad audience.

2. Case studies

2.1. Newton’s proofs of Kepler’s first two laws of planetary motion

One of Newton’s greatest scientific achievements was to show that Kepler’s laws of planetary

motion follow from the assumption of an inverse-square central force. Despite its importance,

this connection is rarely taught in physics courses at introductory level due to the mathematical

complexities involved in the proofs. Can some of Newton’s original writings help us

circumvent this didactical challenge?

We believe so, mainly because of the geometric nature of Newton’s reasoning. To illustrate

our point, we will focus on two theorems he proved in a manuscript presumably titled De motu

corporum in gyrum (“On the motion of bodies in an orbit”) [28]. This manuscript was sent to

Edmond Halley in November 1684 after Halley visited Newton and asked him what would be

the shape of a planet’s orbit, if the force of attraction towards the Sun were reciprocal to the

square of the distance between the planet and the Sun. De motu contains the first formal

deduction of this connection.

26 | Karam R., Lima N.

2.1.1. Theorem 1: Deriving Kepler’s area law from a central force

Let us start with Theorem 1 of De Motu, where Newton shows that if one assumes a central

force, then the line segment connecting the sun and the planet sweeps out equal areas in equal

times. The proof is based on Figure 1 [28].

Consider that the sun is located at point S and the planet is initially at point A. In the

absence of a force acting on the planet, it follows a straight trajectory with a uniform velocity,

going from A to B. If it were to follow this inertial path, it would continue to move in a straight

line from B towards c (lower case c). Given that the lines AB and Bc have the same length

(equal time intervals), and that the triangles ∆SAB and ∆SBc have the same height (the distance

between the line that contains AB and point S), these triangles have the same area (see Fig. 2).

Thus, the first part of Newton’s proof in Theorem 1 shows that the area law would follow if no

force acted on the planet.

However, in order to take the interaction between the sun and the planet into account,

Newton assumes that the planet receives an “instantaneous kick” when it reaches B, which

deviates its trajectory, making it reach C (upper case C) instead of c. The crucial assumption is

that this “kick” is central, i.e., it points in the direction of BS. Therefore, the line cC is parallel

to the line BS. In the second part of the proof, Newton shows that the triangles ∆SBC and ∆SBc

have the same area. This is indeed the case because these triangles have a common base (SB)

and equal altitudes (distance between the two parallel lines that contain SB and Cc,

respectively) (see Fig. 3).

2

A . G eom et r ical D er ivat ion

This derivat ion is based on Newton’s original argu-ments and has the advantage of not relying on any cal-culus prerequisite.

FIG. 1: Newton’s original diagram

In Figure 1 the sun is at S, the planet is init ially atpoint A. In this part of the argument the sun is notsupposed to exert any force on the planet , which, hence,is supposed to follow a straight t rajectory with a uni-form velocity. The planet ’s t rajectory can be divided inequal space distances corresponding to equal t ime inter-vals. In Newton’s words, the planet moves from A toB in a st raight line due to its “innate force”3 and, if noforce acted on the planet , it would cont inue to move ina straight line from B towards c (lower case c). Sincethe lines AB and B c have the same length (equal t imeintervals), and the triangles ∆ SAB and ∆ SB c have thesame height , these t riangles have the same area (Fig. 2)[15]. Thus, the first part of the proof shows that the arealaw would follow if no force acted on the planet .

FIG. 2: ∆ SAB and ∆ SB c have the same area

3 T he term “innate force” may appear misleading to the modern

reader, but it was actually used by Newton. Nowadays we would

probably say instead: “Due to it s inert ia...”.

In order to take the interact ion between the sun andthe planet into account , Newton assumes that the planetreceives an “instantaneous kick” when it reaches B , whichdeviates its t rajectory, making it reach C (upper case C)instead of c (Fig. 1). The crucial assumpt ion is that this

“kick” is central, i.e., it points in the direct ion of−!B S.

This implies that the change in velocity4 (−!cC) is paral lel

to−!B S.

When traveling from B to C the line connect ing thesun to the planet will sweep out the area of ∆ SB C. Sincethe line cC is parallel to the line B S, the ∆ SB C has thesame area as the ∆ SB c (Fig. 3)[15], and therefore alsoas the∆ SAB . Assuming cent ral kicks at the end of eachsame-t ime segment , the argument is applied further sothat the area of the ∆ SCD is equal to ∆ SB C and soforth (Fig. 1), proving that , if one assumes a cent ralforce, the line segment sweeps out equal areas in equalt imes. It is important to st ress that there is no forceact ing on the planet between these kicks, thus the mot ionfrom one kick to the next is uniform. Furthermore, thisconst ruct ion of the orbit is only approximate, convergingto the correct one when we let t ime intervals betweenindividual kicks get shorter.

FIG. 3: ∆ SBc equal with ∆ SBC

This geometrical argument is a masterpiece of the his-tory of physics, but it is quite challenging to grasp inthe original. Furthermore, there is a certain dynamicaspect in the proof that is hard to visualize in a stat icfigure. Therefore, we decided to give to the students amore didact ic presentat ion of the proof made by GaryRubinstein in his YouTube channel.5

B . A naly t ical D er ivat ion

The second derivat ion relies on arguments from vec-tor calculus and is adapted from Feynman [10]. Letus assume that the planet ’s posit ion is represented by

4 In the original, Newton talks about change in motion, which

makes it confusing for a modern reader.5 https://www.youtube.com/watch?v=m00Ep14uTPM

Figure 1. Newton’s original diagram

2

A . G eom et r ical D er ivat ion

This derivat ion is based on Newton’s original argu-ments and has the advantage of not relying on any cal-culus prerequisite.

FIG. 1: Newton’s original diagram

In Figure 1 the sun is at S, the planet is init ially atpoint A. In this part of the argument the sun is notsupposed to exert any force on the planet , which, hence,is supposed to follow a straight t rajectory with a uni-form velocity. The planet ’s t rajectory can be divided inequal space distances corresponding to equal t ime inter-vals. In Newton’s words, the planet moves from A toB in a st raight line due to its “innate force”3 and, if noforce acted on the planet , it would cont inue to move ina straight line from B towards c (lower case c). Sincethe lines AB and B c have the same length (equal t imeintervals), and the triangles ∆ SAB and ∆ SB c have thesame height , these t riangles have the same area (Fig. 2)[15]. Thus, the first part of the proof shows that the arealaw would follow if no force acted on the planet .

FIG. 2: ∆ SAB and ∆ SB c have the same area

3 T he term “innate force” may appear misleading to the modern

reader, but it was actually used by Newton. Nowadays we would

probably say instead: “Due to it s inert ia...”.

In order to take the interact ion between the sun andthe planet into account , Newton assumes that the planetreceives an “instantaneous kick” when it reaches B , whichdeviates its t rajectory, making it reach C (upper case C)instead of c (Fig. 1). The crucial assumpt ion is that this

“kick” is central, i.e., it points in the direct ion of−!B S.

This implies that the change in velocity4 (−!cC) is paral lel

to−!B S.When traveling from B to C the line connect ing the

sun to the planet will sweep out thearea of ∆ SB C. Sincethe line cC is parallel to the line B S, the ∆ SB C has thesame area as the ∆ SB c (Fig. 3)[15], and therefore alsoas the ∆ SAB . Assuming cent ral kicks at the end of eachsame-t ime segment , the argument is applied further sothat the area of the ∆ SCD is equal to ∆ SB C and soforth (Fig. 1), proving that , if one assumes a cent ralforce, the line segment sweeps out equal areas in equalt imes. It is important to st ress that there is no forceact ing on the planet between these kicks, thus the mot ionfrom one kick to the next is uniform. Furthermore, thisconst ruct ion of the orbit is only approximate, convergingto the correct one when we let t ime intervals betweenindividual kicks get shorter.

FIG. 3: ∆ SBc equal with ∆ SBC

This geometrical argument is a masterpiece of the his-tory of physics, but it is quite challenging to grasp inthe original. Furthermore, there is a certain dynamicaspect in the proof that is hard to visualize in a stat icfigure. Therefore, we decided to give to the students amore didact ic presentat ion of the proof made by GaryRubinstein in his YouTube channel.5

B . A naly t ical D er ivat ion

The second derivat ion relies on arguments from vec-tor calculus and is adapted from Feynman [10]. Letus assume that the planet ’s posit ion is represented by

4 In the original, Newton talks about change in motion, which

makes it confusing for a modern reader.5 https://www.youtube.com/watch?v=m00Ep14uTPM

Figure 2. ∆ SAB and ∆ SBc have the same area

Chapter 2 | 27

Since it was already shown that the triangles ∆SBc and ∆SAB have the same area, we

conclude that the areas of ∆SAB and ∆SBC are also equal. Assuming central kicks at the end of

each same-time segment, the argument is applied further, so that the area of ∆SCD is equal to

∆SBC and so forth (Fig. 1), which concludes the proof. It is important to stress that there is no

force acting on the planet between these kicks, thus the motion from one kick to the next is

uniform. Furthermore, this construction of the orbit is only approximate, converging to the

correct one when we let time intervals between individual kicks get shorter. In sum, Theorem

1 shows that, if one assumes a central force, the line segment sweeps out equal areas in equal

times. But it says nothing about the magnitude of this force. This is the goal of Theorem 3.

2.1.2. Theorem 3: Newton’s PQRST formula

In order to obtain an expression to calculate the magnitude of the force, Newton constructs the

diagram presented in Figure 4. Consider the trajectory of a planet described by a general curve

APQ (not necessarily an ellipse!) with the sun located at S (not necessarily the focus!). At a

given instant, the planet is located at P. If the sun were not exerting force at the planet, it would,

by its inertial tendency, keep moving in a rectilinear and uniform motion in the direction of PR.

However, because the sun is constantly exerting a central force on the planet, it will end up at

point Q, i.e., it will be deviated from its inertial trajectory. Newton’s aim with Theorem 3 was

to express the magnitude of this force based on relations between segments of Fig. 4.

Figure 4. Theorem 3, Force proportional to QR/(SP2.QT2)

One difficulty to determine the magnitude of the force is that it might change while the

planet moves. In order to circumvent this problem, Newton considered that point Q is infinitely

close to point P, so that it is reasonable to assume that the force does not vary when the planet

moves from P to Q.

According to Newton’s 2nd law, force is proportional to acceleration, thus, the acceleration

of the planet will be taken as constant when it moves from P to Q. This is equivalent to a local

Der iv ing and apply ing Newton’s PQRST formulawit h pre-service physics t eachers

Yuvita Oktarisa1,2⇤ and Ricardo Karam1

1: Department of Science Education, Universi ty of Copenhagen, Denmark and2: Department of Physics Education, Sultan Ageng T ir tayasa Universi ty, Indonesia

One of Newton’s greatest scient ific achievements was to show that Kepler ’s first law follows fromthe assumpt ion of an inverse-square cent ral force. Despite it s importance, this connect ion is rarely

taught in physics courses at int roductory level due to the mathemat ical complexit ies involved inthe proof. A possible didact ic solut ion to this problem is to focus on a conceptual understanding

of Proposit ion VI of Newton’s Principia. In this paper, we report a study conducted with the goalof teaching pre-service physics teachers key aspects of Proposit ion VI, as well as its applicat ion

to determine the force law, given the orbit shape and the sun’s posit ion. Our findings consist ofstudents’ interpretat ions and difficult ies when t rying to understand Newton’s original reasoning.

I . I N T R OD U CT I ON

In December 2016, Isaac Newton’s Principia Mathe-matica made the news by becoming the most expensivescience book ever sold.1 It is hard to overest imate theimportance of this work for the development of modernscience, although it is also fair to say that this book ismore revered than read [1].

One episode that mot ivated the writ ing of the Prin-cipia is a visit paid by Edward Halley to Isaac Newton inAugust 1684. Together with other members of the royalsociety, including Robert Hooke and Christopher Wren,Halley was seeking for an explanat ion for planetary mo-t ion. More specifically, Halley asked Newton which curvewould be described by the planets supposing the force ofat t ract ion towards the sun to be reciprocal to the squareof their distance from it [2].

Newton’s prompt answer was “an ellipse” and a proofwas sent to Halley months later in a manuscript t it ledDe motu corporum in gyrum (On the mot ion of bodiesin an orbit ). In Theorem 3 of this manuscript2 Newtonexpressed the cent ripetal force as a general geomet ricalrelat ion between segments, and later applied this theoremto derive different force laws, i.e., F = F (r ), for dif ferentt rajectories.

De Motu’s Theorem 3 (aka. the PQRST formula3) isan absolute gem of the history of science and illust ratesessent ial aspects of Newton’s original reasoning. We areconfident that there are numerous reasons to teach it ,even at high school level. This mot ivated us to design anintervent ion to teach the PQRST formula to pre-servicephysics teachers, and invest igate how they try to makesense of it .

⇤ yuvit a.oktarisa@ind.ku.dk1 ht tps:/ / www.theguardian.com/ science/ 2016/ dec/ 05/ principia-

sir-isaac-newton-first -edit ion-auct ion-christ ies-new-york.2 De Motu ’s T heorem 3 is Proposit ion VI in the Pr incipia.3 T his term was coined in a T PT paper by Prent is et al. t it led

El lipt ical Orbi t = = > 1/ r 2 Force [3], which is t ruly a pedagogical

masterpiece and was a major inspirat ion for this work.

I I . D ER I V I N G N EW T ON ’S PQRST FOR M U L A

Newton’s PQRST formula expresses the magnitude ofthe centripetal force exerted by the sun on an orbit ingplanet . In Fig. 1, consider the t rajectory of a planetdescribed by a general curve APQ (not necessarily anellipse!) with the sun located at S (not necessarily thefocus!). At a given instant , the planet is located at P . Ifthe sun were not exert ing force at the planet , it would,by its inert ial tendency, keep moving in a rect ilinear anduniform mot ion in thedirect ion of PR. However, becausethe sun is exert ing a cent ral force on the planet , it willend up at point Q, i.e., it will bedeviated from its inert ialt rajectory. Newton’s aim with Theorem 3 was to expressthe magnitude of this force based on relat ions betweensegments of Fig. 1.

FIG. 1: Theorem 3, Force proport ional to QRSP 2 ⇥QT 2

One difficulty to determine the magnitude of the forceis that it might change while the planet moves. In or-der to circumvent this problem, Newton considered thatpoint Q is infinitely close to point P , so that it is rea-sonable to assume that the force does not vary when theplanet moves from P to Q.

According to Newton’s 2nd law, force is proport ionalto accelerat ion, so that the accelerat ion of the planet willbe taken as constant as it moves from P to Q. This isequivalent to a local parabolic approximat ion, i.e., themot ion from P to Q can be treated as the composit ion of

2

A . G eom et r ical D er ivat ion

This derivat ion is based on Newton’s original argu-ments and has the advantage of not relying on any cal-culus prerequisite.

FIG. 1: Newton’s original diagram

In Figure 1 the sun is at S, the planet is init ially atpoint A. In this part of the argument the sun is notsupposed to exert any force on the planet , which, hence,is supposed to follow a straight t rajectory with a uni-form velocity. The planet ’s t rajectory can be divided inequal space distances corresponding to equal t ime inter-vals. In Newton’s words, the planet moves from A toB in a st raight line due to its “innate force”3 and, if noforce acted on the planet , it would cont inue to move ina st raight line from B towards c (lower case c). Sincethe lines AB and B c have the same length (equal t imeintervals), and the triangles ∆ SAB and ∆ SB c have thesame height , these triangles have the same area (Fig. 2)[15]. Thus, the first part of the proof shows that the arealaw would follow if no force acted on the planet .

FIG. 2: ∆ SAB and ∆ SB c have the same area

3 T he term “innate force” may appear misleading to the modern

reader, but it was actually used by Newton. Nowadays we would

probably say instead: “Due to it s inert ia...”.

In order to take the interact ion between the sun andthe planet into account , Newton assumes that the planetreceives an “instantaneous kick” when it reaches B , whichdeviates its t rajectory, making it reach C (upper case C)instead of c (Fig. 1). The crucial assumpt ion is that this

“kick” is central, i.e., it points in the direct ion of−!B S.

This implies that the change in velocity4 (−!cC) is paral lel

to−!B S.When traveling from B to C the line connect ing the

sun to the planet will sweep out the area of ∆ SB C. Sincethe line cC is parallel to the line B S, the ∆ SB C has thesame area as the ∆ SB c (Fig. 3)[15], and therefore alsoas the ∆ SAB . Assuming cent ral kicks at the end of eachsame-t ime segment , the argument is applied further sothat the area of the ∆ SCD is equal to ∆ SB C and soforth (Fig. 1), proving that , if one assumes a cent ralforce, the line segment sweeps out equal areas in equalt imes. It is important to st ress that there is no forceact ing on the planet between these kicks, thus the mot ionfrom one kick to the next is uniform. Furthermore, thisconst ruct ion of the orbit is only approximate, convergingto the correct one when we let t ime intervals betweenindividual kicks get shorter.

FIG. 3: ∆ SBc equal with ∆ SBC

This geometrical argument is a masterpiece of the his-tory of physics, but it is quite challenging to grasp inthe original. Furthermore, there is a certain dynamicaspect in the proof that is hard to visualize in a stat icfigure. Therefore, we decided to give to the students amore didact ic presentat ion of the proof made by GaryRubinstein in his YouTube channel.5

B . A naly t ical D er ivat ion

The second derivat ion relies on arguments from vec-tor calculus and is adapted from Feynman [10]. Letus assume that the planet ’s posit ion is represented by

4 In the original, Newton talks about change in motion, which

makes it confusing for a modern reader.5 https://www.youtube.com/watch?v=m00Ep14uTPM

Figure 3. ∆ SBc equal with ∆ SBC

28 | Karam R., Lima N.

parabolic approximation, i.e., the motion from P to Q can be treated as the composition of a

uniform motion PR and a uniformly accelerated motion (“free fall”) RQ.

Motion with constant acceleration was studied extensively by Galileo. In modern

terminology, the relation between distance and time for such motion can be expressed by 𝑑 =1

2𝑎𝑡2. Thus, the magnitude of the acceleration is proportional to distance, and inversely

proportional to the square of the time (𝑎 ∝𝑑

𝑡2). Since force is proportional to acceleration, 𝐹 ∝𝑑

𝑡2.

In Fig. 4, the distance travelled in the direction of the force is QR. In order to determine

the time, Newton uses the relation proved in Theorem 1, which states that the line segment

connecting the sun and the planet sweeps out equal areas in equal times. Another way to

formulate this theorem is to say that the time elapsed is proportional to the area swept-out by

this line segment, which is approximately equal to the area of the triangle SPQ, since Q is

infinitely close to P. This leads to the following expression

𝐹 ∝𝑄𝑅

𝑆𝑃2. 𝑄𝑇2

(1)

, which is the essence of Theorem 3. This expression, which we will call Newton’s PQRST

formula [32], expresses the magnitude of the centripetal force in terms of three segments from

Fig. 4. It provides the key to finding the force law, given the orbit shape and the location of the

sun.

But applying the PQRST formula is far from being trivial. The reason is that as Q

approaches P, both QR and QT tend to zero, which leads to the challenges of calculating with

infinitesimals. The solution involves realizing that although both QR and QT tend to zero when

Q approaches P, the ratio QR/QT2 does not. The trick is then to use geometrical properties of

the given orbit shape to express this (ultimate) ratio as a function of SP, and thus obtain 𝐹 =𝐹(𝑟), i.e., a force law.

In his De Motu, Newton applied Theorem 3 to solve three problems, i.e., to obtain three

different force laws given three different configurations. In Problem 1, the planet’s trajectory

is circular with the sun located at the circumference, and the force law obtained is 𝐹 ∝1

𝑟5. In

Problem 2, the trajectory is an ellipse with the sun is at the center, and the solution is 𝐹 ∝ 𝑟.

Finally, in Problem 3, the trajectory is an ellipse with the sun in one focus, leading to 𝐹 ∝1

𝑟2.

Thus, Halley’s question was answered, and the connection between 𝐹 ∝1

𝑟2 and the elliptical

trajectory with the sun at the focus was demonstrated. Figure 5 summarizes the three problems.

Figure 5. Three problems solved in Newton’s De Motu

The solution to these problems involve applying highly complicated geometrical

properties, especially in the elliptical case, which make them rather inaccessible for the

2

a uniform mot ion PR and a uniformly accelerated mot ion(“free fall”) RQ.

Mot ion with constant accelerat ion was studied exten-sively by Galileo. In modern terminology, the relat ion be-tween distanceand t ime for such mot ion can beexpressedby d = 1

2at2. Thus, the magnitude of the accelerat ion is

proport ional to distance, and inversely proport ional tothe square of the t ime (a / d

t 2 ). Since F / a, we have

F /d

t2(1)

In Fig. 1, the distance t ravelled in the direct ion of theforce is QR. In order to determine the t ime, Newton usesa relat ion proved in De Motu’s Theorem 1, which statesthat the line segment connect ing the sun and the planetsweeps out equal areas in equal t imes (Kepler’s 2nd law).Another way to formulate this theorem is to say that thet ime elapsed is proport ional to the area swept-out by thisline segment , which is approximately equal to the area ofthe the triangle SPQ, since Q is infinitely close to P .Subst itut ing these considerat ions in Eq. (1),

F /QR

SP 2 ⇥ QT2. (2)

Voilà! This is Newton’s PQRST formula. It expressesthe magnitude of the centripetal force in terms of threesegments from Fig. 1. This formula provides the keyto finding the force law, given the orbit shape and thelocat ion of thesun. Itsderivat ion wasgiven to pre-servicephysics teachers in a similar way as presented here. Inthe first part of this study, we were mainly interested inthe part icipants’ reasoning and struggles to make senseof this derivat ion.

I I I . A PP LY I N G N EW T ON ’S PQRST FOR M U L A

Although the PQRST formula provides the key tofinding the force law, applying Eq. 2 is far from beingt rivial. The reason is that as Q approaches P , both QRand QT tend to zero, which leads us to the challenges ofcalculat ing with infinitesimals. The solut ion involves re-alizing that although both QR and QT tend to zero whenQ approaches P , the ratio QR/ QT2 does not . The t rickis to use geometrical propert ies of the given orbit shapeto express this (ult imate) rat io as a funct ion of SP , andthus obtain F = F (r ).

After having derived the PQRST formula in the DeMotu, Newton applies it to solve of three problems, i.e.,to obtain three different force laws given three differentconfigurat ions. In Problem 1, the planet ’s trajectory iscircular with the sun located at the circumference, andthe force law obtained is F / 1

r 5 . In Problem 2, thet rajectory is an ellipse with the sun is at the center, andthe solut ion is F / r . Finally, in Problem 3 the trajec-tory is an ellipse with the sun in one focus, leading toa F / 1

r 2 . Thus, Halley’s quest ion was answered, and

the connect ion between F / 1r 2 and the ellipt ical t rajec-

tory with the sun at the focus was demonst rated. Fig. 2summarizes the three problems solved at the De Motu.

FIG. 2: Three problems solved in Newton’s De Motu

The solut ion to these problems involve applying highlycomplicated geomet rical propert ies, especially in the el-lipt ical case [1], which make them inaccessible for thepart icipants of our study. In order to circumvent thisobstacle, and st ill provide an idea of how the PQRSTformula can be used to find the force law, we decided touse an act ivity proposed by Prent is et al. [3]. The act iv-ity consists in asking students to draw an orbit (Fig. 3),measure the values of the segments QR, QT and SP atdifferent points of the orbit , and use the PQRST formulato est imate the force law, i.e., the dependence of force onthe distance between the planet and the sun (F = F (r )).

The process is called “Newton’s recipe”, and is de-scribed by the authors in the following six steps ([3], p.23):

Given only two ingredients — the shape ofthe orbit and the center of the force— “New-ton’s recipe” allows one to calculate the rel-at ive force at any orbital point . The recipeconsists of the following steps:

1. The inertial path: Draw the tangent lineto the orbit curve at the point P where theforce is to be calculated.

2. The future point : Locate any future pointQ on the orbit that is close to the init ial pointP .

3. The deviation line: Draw the line segmentfrom Q to R, where R is a point on the tan-gent , such that QR (line of deviat ion) is par-allel to SP (line of force).

4. The time line: Draw the line segment fromQ to T , where T is a point on the radial lineSP , such that QT (height of “t ime triangle”)is perpendicular to SP (base of t riangle).

5. The force measure: Measure the shapeparameters QR, SP , and QT , and calculatethe force measure QR/ (SPX QT )2.

Chapter 2 | 29

majority of students taking physics courses at all levels. In order to circumvent this obstacle,

and still provide an idea of how the PQRST formula can be used to find the force law, we

strongly recommend a teaching sequence developed by [32]. The sequence involves asking

students to draw an orbit, measure the values of the segments QR, QT and SP at different points

of the orbit, and use the PQRST formula to estimate the force law, i.e., the dependence of force

on the distance between the planet and the sun (𝐹 = 𝐹(𝑟)). We refer the interested reader to

this reference for further details about the teaching activities.

2.1.3. Some pedagogical lessons extracted from case study 1

Now that we had a glimpse into Newton’s original derivation of Kepler’s first two laws, let us

reflect on the educational potential of this case study:

• Kepler’s laws are usually taught and learned as kinematical truths, without being

presented as results that can be derived from the assumption of an inverse-square central

force. Thus, this episode highlights the deductive structure of physics theories. Even

though Kepler’s laws were known to Newton and the community at the time, there was

a need to derive them from first principles, and this is among Newton’s most important

scientific achievements. One thing is to know how the planets move, but another one is

to know why they move the way they do. The latter is a major goal of physics. Perhaps

this epistemological aspect should be more emphasized in physics lessons.

• A deep understanding of how Newton derived Kepler’s first two laws from the

assumption of an inverse-square central force involves identifying which aspects of this

force account for each law. Theorem 1 shows that if one assumes a central force, then

the line segment connecting the planet to the center of force sweeps out equal areas in

equal times (area law), regardless of how the force depends on the distance, so Kepler’s

2nd law is valid for any central force. But in order to obtain Kepler’s 1st law, i.e., the

elliptical orbit with the sun in one focus, we need the 1

𝑟2 dependence.

• The PQRST formula is a statement of proportionality, not equality. This will likely

create conceptual difficulties for students trying to understand some of Newton’s

original proofs. Thus, a careful explanation of proportionality would be needed if one

wanted to convey an authentic picture of Newton’s reasoning.

• The PQRST formula is valid only in the (theoretical) limit 𝑄 → 𝑃. This is a crucial

point and exemplifies the genesis of Newton’s geometrical calculus, i.e., his concept of

ultimate ratio. Here we have a good opportunity to discuss the important difference

between approximations made with paper and pencil in drawings, and approximations

made with the mind.

• Newton is famous for having said that he does not make hypotheses (Hypothesis non

figo). Although this issue is up for heated debates among historians and philosophers,

the PQRST formula does illustrate Newton’s position. Contrary to Kepler and Hooke,

who had physical reasons/models to justify their force laws, Newton does not have to

make any physical assumption about the nature of gravitation and is able to deduce the

inverse square force law from pure logical reasoning.

• Comparing the force laws of having the sun at the center and at the focus of an ellipse

can be extremely instructional. Considering that the eccentricities of the orbits in our

solar system are rather small, it is quite counter-intuitive that changing the position of

the sun from the focus to the center should produce such a drastic difference.

Furthermore, when the sun is at the center, we have 𝐹 ∝ 𝑟, which implies a gravitational

30 | Karam R., Lima N.

force that increases with distance, like a Hooke’s law type of force, contradicting our

most basic intuitions about gravity.

2.2. The genesis of entropy with Clausius

Teaching the concept of entropy is challenging due to many reasons and several studies have

already shown student difficulties and misconceptions with the topic [33, 34]. Entropy is a

difficult concept not only because of its intrinsic mathematical nature, but also due to the lack

of direct references to everyday life phenomena. Perhaps a closer look into the original

formulation of this concept could shed some light into this challenge and provide some

pedagogical insights. This is what we aim to explore in the second case study.

The original idea of entropy, although not with this name, was first presented by Rudolf

Clausius in 1854 in a paper titled On a modified form of the second fundamental theorem in the

mechanical theory of heat [35]. The term second fundamental theorem refers to the nowadays

well-known Carnot theorem, which specifies limits on the maximum efficiency any heat engine

can obtain. According to Carnot, all heat engines between two heat reservoirs are less efficient

than a Carnot heat engine operating between the same reservoirs. As we will see, it is the need

to formulate Carnot’s theorem more precisely, that originated the concept of entropy.

Clausius’s conceptual framework focuses broadly on the transformations that occur in heat

engines, dividing them into two groups: transmissions and conversions. A transmission is, as

the name implies, the flow of heat from a hot source to cold source, or vice versa. Conversions

then, describe the conversion of heat into work, or vice versa [36].

A crucial distinction between these processes is that they can be categorized as natural and

unnatural. As the name implies, natural processes occur without the need of external agents.

For transmissions, the natural is for heat to flow from hot to cold, whereas the opposite (heat

flowing from cold to hot) is unnatural and would demand external agents to occur. Similarly,

although less intuitively, Clausius classifies the conversion of work into heat as natural (think

of a bicycle pump heating up or simply the production of heat by friction), whereas the

conversion of heat into work is unnatural (we need a heat engine to make this possible).

The central assumption in Clausius’s theory is that unnatural processes must be driven by

natural ones. Thus, for any construction that converts heat into work (unnatural), there must be

a natural flow of heat from hot to cold. Similarly, for any construction that transmits heat from

a cold source to a hot source (unnatural), there must be a natural conversion of work into heat.

This idea is at the heart of Clausius’s reasoning and provides the key to understanding the

original concept of entropy. Fig. 6 summarizes this conceptual framework.

Figure 6. Clausius’s classification of transformations into transmission and

conversion, where each one can be natural or unnatural. The key assumption is

that these transformations occur in pairs, as if the natural would “drive” the

unnatural. In heat engines, heat flows from hot to cold (natural) so that heat can

The origins of ent ropy PUK Peter Hent rich-Spoon

natural or unnatural. Heat naturally flows from hot to cold, even though it can be unnaturally forced

to flow from cold to hot . Work naturally creates heat , even though heat can unnaturally be forced to

create work. The point Clausius is making, is that any unnatural process must be driven by a natural

process in order to happen. So for any const ruct ion that converts heat into work, there must be a natural

flow of heat from hot to cold. Similarly, for any const ruct ion that t ransmits heat from a cold source

to a hot source, there must be a natural conversion of work into heat . This idea is really at the heart

of everything Clausius later goes on to show mathemat ically, and it provides the key to understanding

ent ropy as Clausius understood it , as will be seen later on:

With this conceptual framework in mind, Clausius states that since the unnatural is always paired with

the natural, there must be some way to mathemat ically formalize this relat ion. Nature does not allow

any unnatural t ransformat ion to occur alone, so the quest ion then is, in what way is some unnatural

t ransformat ion compensated for by some natural t ransformat ion? How does Nature determine what nat -

ural t ransformat ion must happen in order for some unnatural t ransformat ion to be allowed? Or, to use

terminology closer to how Clausius formulated it originally in German, what is the equivalence-value of an

unnatural t ransformat ion to a natural t ransformat ion? This is the quest ion Clausius sought to answer.

The first step Clausius takes toward answering this quest ion, is formulat ing a specific case he can work on.

With this in mind, he const ructs the Clausius cycle, as seen below:

The Clausius cycle is reversible, and constructed so that it has some unique propert ies that make it

especially easy to work with, in the context of formalizing t ransformat ions of heat . Specifically, the unique

property of this cycle is that the heat that goes into the gas at step 3 (the heat Q2 from a heat source K 2

2

Chapter 2 | 31

be converted into work (unnatural). In refrigerators, work is converted into heat

(natural) so that heat can flow from cold to hot (unnatural).

Following Carnot’s tradition, Clausius begins by focusing on cyclic and reversible

processes. For these, he will claim that the transformations of transmission and conversion

must be somehow equivalent. In fact, he wishes to create a mathematical quantity that

expresses this equivalence, and this is the precursor of entropy, which was first called

equivalence-value (Äquivalenzwert). In order to separate the natural and unnatural processes

clearly, Clausius comes up with an ingenious cycle of six steps, which we will call Clausius’s

cycle (see Fig. 7).

Figure 7. Clausius’s cycle, a slightly modified version of Carnot’s cycle.

(Source [36])

As we can see, Clausius’s cycle is similar to the more famous Carnot cycle, the only

difference being that two expansions (one adiabatic and one isothermal) are added. The goal of

this addition is to separate the transformations of transmission and conversion. More

specifically, the assumption is that the amount of heat that goes into the gas at step 3 (heat Q2

comes from a heat source K2 at a temperature t2) is equal to the heat that is removed from the

gas at step 5 (heat Q2 goes to a heat sink K1 at a temperature t1). This allowed Clausius to

conclude that all the heat Q absorbed by the gas at step 1 was converted into work during one

cycle. This system is schematically represented in Fig. 8.

Figure 8. Schematic representation of the two transformations occurring in a

Clausius cycle. The natural transmission of Q2 is equivalent to the unnatural

conversion of Q into work.

SYSTEM

Q from

K at t

Q2 from

K2 at t2

Q2 to

K1 at t1

Work = Q

32 | Karam R., Lima N.

As previously mentioned, Clausius seeks a mathematical quantity to express the

equivalence between these transformations, which is called equivalence-value. He assumes that

this quantity should be proportional to the amount of heat (transmitted or converted) and the

temperatures involved (one for conversions and two for transmissions). For the conversion

transformation, this equivalence value is expressed by

−𝑓(𝑡)𝑄,

(2)

denoting that a quantity of heat Q, initially extracted from a reservoir at temperature t, was

converted into work in one cycle. The negative sign is because the conversion is unnatural. The

other transformation is a transmission of Q2 from a reservoir at t2 to another at t1, and its

equivalence value is

𝐹(𝑡1, 𝑡2)𝑄2,

(3)

which is a function of two temperatures and is positive because it is natural (from hot to cold).

The equivalence between the transformations is expressed by the following equation:

𝐹(𝑡2, 𝑡1)𝑄2 − 𝑓(𝑡)𝑄 = 0.

(4)

Next, Clausius tries to find a way to get rid of the function of two temperatures 𝐹(𝑡2, 𝑡1)

related to transmission by expressing it in terms of functions of conversion. To do that, Clausius

first considers another one of his cycles with the only difference that another quantity Q’ is

extracted from K at a temperature t’ and converted into work. This leads to a new equation

representing the equivalence

𝐹(𝑡2, 𝑡1)𝑄2 − 𝑓(𝑡′)𝑄′ = 0.

(5)

Substituting this new equation in (4), he obtains

𝑓(𝑡)𝑄 = 𝑓(𝑡′)𝑄′, (6)

which means that the function of temperature f(t) is inversely proportional to the amount of

heat converted. Then, Clausius considers a Carnot cycle in which Q’ is extracted from a hot

source K’ at t’ and Q is rejected to a cold source at t, meaning that Q’ – Q was converted into

work. The equivalence relation in this case is represented by

𝐹(𝑡′, 𝑡)𝑄 − 𝑓(𝑡′)(𝑄′ − 𝑄) = 0.

(7)

Substituting (6) in (7), one obtains the following equation

𝐹(𝑡′, 𝑡) = 𝑓(𝑡) − 𝑓(𝑡′),

(8)

Chapter 2 | 33

which enables one to get rid of the function of temperatures (transmission) and express them

in terms of functions of conversion.

Figure 9. Schematic representation of Carnot cycle. The natural transmission of

Q is equivalent to the unnatural conversion of Q’ – Q into work.

Applying (8) to (4), we have

𝑓(𝑡2)𝑄2 − 𝑓(𝑡1)𝑄2 + 𝑓(𝑡)𝑄 = 0,

(9)

whereas for the Carnot cycle (7) we have

𝑓(𝑡′)𝑄′ − 𝑓(𝑡)𝑄 = 0.

(10)

Thus, a pattern appears to emerge and it seems possible to generalize these equivalence

relations by

∑𝑓(𝑡)𝑄 = 0.

(11)

But what is the form of this function of temperature? One hint comes from results

previously derived by Carnot and Kelvin, expressing relationships between the heats

extracted/rejected from/to the hot/cold sources and their temperatures. Calling the indices H

for hot, and C for cold, we have the familiar relationship for Carnot cycles

𝑄𝐻

𝑇𝐻

−𝑄𝐶

𝑇𝐶

= 0,

(12)

which suggests that this function of temperature is just the reciprocal of the absolute

temperature. Although Clausius does not justify this choice explicitly in 1854, it is related to

the very definition of absolute temperature by William Thompson (Lord Kelvin). Digging into

the original formulation of this concept would be another interesting and pedagogically

relevant episode to explore.

In any case, assuming that 𝑓(𝑡) =1

𝑇, the general equivalence relationship becomes

SYSTEM

Q’ from

K’ at t’

Q to K

at t

Work = Q’ – Q

34 | Karam R., Lima N.

∑𝑄

𝑇= 0

(13)

If we consider infinitesimal and reversible transfers, this sum becomes an integral

∮𝛿𝑄𝑟𝑒𝑣

𝑇= 0

(14)

Note that the quantity 𝛿𝑄𝑟𝑒𝑣

𝑇 is a state variable since its closed line integral is path

independent. This motivates Clausius to propose a new state function 𝑆, expressed by

𝑑𝑆 =𝛿𝑄𝑟𝑒𝑣

𝑇, which later became known as entropy. As we have seen, for cyclic and reversible

processes ∮ 𝑑𝑆 = 0, because the natural transformations are equivalent to the unnatural. What

about non-reversible processes? In these cases, Clausius argues, what happens is that some

transformations are uncompensated, i.e., natural transformations do not have their counterpart.

Among the examples provided are i) the transmission of heat by mere conduction, when two

bodies of different temperatures are brought into immediate contact, and ii) the production of

heat by friction.

This leads to a more general theorem formulated by Clausius: “The algebraic sum of all

transformations occurring in a cyclical process can only be positive”. The reversible process

becomes the limiting case and, in general, one has:

∮𝛿𝑄

𝑇≥ 0

(15)

Here, we begin to see what later became the famous: The entropy of the universe tends to

a maximum. However, this was only stated by Clausius ten years later (ninth memoir in [35]),

and during these years Clausius’s work testifies how complex and erratic the formation of the

entropy concept was. In fact, historical accounts of the conceptual development of entropy

illustrate a vast diversity of formulations and interpretations [37–39]. Even today it is fair to

say that there is no clear consensus in the physics community about the meaning of entropy

[40], which can explain some of the challenges involved in its teaching.

2.2.1. Some pedagogical lessons extracted from case study 2

Now that we have an idea of the original formulation of the concept of entropy by Clausius in

1854, as well as its original motivation, let us try to extract some pedagogical lessons from this

case study:

• The conceptual framework proposed by Clausius, i.e., the classification of

transformations in transmissions and conversions (natural and unnatural) is rather

plausible and powerful, although not very well known by the physics community.

Perhaps this scheme could be used more often in teaching to convey a deeper

understanding of some important conceptual struggles in the birth of thermodynamics.

• One of the main challenges when teaching entropy is how to motivate the need for this

concept/quantity. Clausius (1854) offers a clear answer. Entropy is a mathematical

quantity created to express the relationship/equivalence between the transmission of

heat due to temperature difference and the conversion of heat into work (and vice

versa). It was actually first called equivalence value.

Chapter 2 | 35

• The Clausius cycle is likewise not very well known by the physics community and has

potential to be used as a didactical tool to illustrate core elements of Clausius’s

conceptual framework, since it has been cleverly designed to separate the processes of

transmission and conversion. By carefully analyzing the heat and work involved in each

step, one can conclude that all the work done by the gas in the first isothermal expansion

is equal the total net amount of work produced in one cycle. To the best of our

knowledge, there is no didactical presentation of the Clausius cycle. The following is a

as an attempt3 to do that.

Figure 10. A closer look at each step of the Clausius cycle.

The integral of each step of the Clausius cycle represents either work being done by the

gas or work being done on the gas, which is why PV-diagrams are useful in the first

place (see Fig. 10). Note that the green area under the curve at step 3, must be equal to

the red area under the curve at step 5, by design (in isothermal processes, the work

done/received is equal to heat received/rejected). Since these areas cancel, we know

that only the heat Q supplied at step 1 can be responsible for the work we get out of this

cycle (the other processes are adiabatic). This work can be represented by the black area

beneath the curve at step 1. This also means that the blue area must cancel out with the

two yellow areas, in other words, the work we put into the gas during the adiabatic

compression must exactly cancel the work that the gas does during each adiabatic

expansion. We can thus conclude that the black area must also be equal to the area of

the Clausius-cycle itself, which means that whenever we look at a Clausius cycle, we

only need to focus on the curve at step 1 to determine what comes out of this cycle,

since the heat and work involved in every other step cancel out.

• A brief look into the historical development of the concept of entropy shows a complex

and erratic process. This episode provides a good opportunity to discuss the subjective

character of physics, i.e., how concepts are also creations of the human mind, which

are useful for certain purposes but not for others. If we teach entropy in a dogmatic way,

and make it appear a natural – even trivial – concept, we lose a valuable opportunity to

bring this aspect to the attention of our students. This is probably valid for all concepts

we teach in physics, but is particularly flagrant with entropy.

3. Conclusion

Textbooks are the main sources we use to teach and learn physics. This is the result of a well-

established tradition and has many advantages. However, it also makes physics teaching more

The origins of ent ropy PUK Peter Hent rich-Spoon

at a temperature t2), is exact ly equal to the heat that is removed from the gas at step 5 (the heat Q2 goes

into the heat sink K 1, which is at a temperature t2). Since the cycle is constructed in such a way, we can

easily see that the heat which is converted to work, must be the heat Q from the source K at temperature

t at step 1. Another way to look at it is the following:

The integral of each step of the Clausius-cycle represents either work being done by the gas or work being

done on the gas, which is why PV-diagrams are useful in the first place. Note that the green area under

the curve at step 3, must be equal to the red area under the curve at step 5, by design. Since these areas

cancel, we know that only the heat Q supplied at step 1 can be responsible for the work we get out of this

cycle. This work can be represented by the black area beneath the curve at step 1. This also means that

the blue area must cancel with the two yellow areas, in other words the work we put into the gas during

the adiabat ic compression must exact ly cancel the work that the gas does during each adiabat ic expansion.

We can thus conclude that the black area must also be equal to the area of the Clausius-cycle itself, which

means that whenever we look at the Clausius cycle, we only need to focus on the curve at step 1 when we

talk about what comes out of this cycle, since the heat and work involved at every other step cancels.

Now that Clausius has const ructed a cycle that has these propert ies which makes it easy to work with,

the next step in his process is looking at the available research. Clausius knows that the heat Q, which

is responsible for the work-output of this cycle, is a funct ion of temperature t , at which this heat was

supplied. Looking at the Clausius-cycle with the colored integrals, this point is easy to see. Raising the

temperature at step 1 (for the same volume), raises the pressure, which means that the curve represent ing

step 1 is moved further up in the PV-diagram, which again means that the black area beneath the curve

becomes larger, and so the work-output must also be greater for the same amount of heat Q. Clausius

also knows that the heat flow of Q2 from the source K 2 to K 1, is only dependent on the temperatures t2

at K 2 and t1 at K 1, a fact that Clausius knows from Carnot ’s analysis, which was ment ioned earlier in

this essay.

3

36 | Karam R., Lima N.

distant from the original ideas of the discipline and tends to obscure their historical genesis.

What if we went back to the origins and read primary sources?

This idea may sound romantic until one opens a random original source (e.g., Newton’s

Principia) and is overwhelmed by its complexity. Unfamiliar concepts, notation, mathematical

formalism, etc. often make primary sources simply unintelligible. Does this mean that we

should just return to textbooks and conclude that original sources have no pedagogical use?

Well, but history of physics does have numerous pedagogical benefits, as Cajori stressed

more than a century ago. Just to name a few, by getting a glimpse at the original formulation

of concepts and theories one can i) Find new (usually less abstract) ways to explain them; ii)

Appreciate the original problems that motivated their genesis; iii) Reflect critically about the

way we teach them; iv) Appreciate how they take time and effort to be developed.

Thus, perhaps it is worth trying to reach a compromise. The two case studies presented

here aimed at illustrating this possibility. In sum, the proposal is to select small, but key,

excerpts from original sources and focus on the pedagogical lessons that can be extracted from

them. In the way presented here, the target audience consists of pre- or in-service teachers, who

already have a solid knowledge about the consolidated tradition of teaching these topics.

For the challenge of implementing this in the classroom, it is essential to develop specific

activities within teaching-learning sequences that allow students to work on key concepts and

consequently learn them. A research work is needed that, to use an established term from the

French tradition, carries out the “didactic transposition” of the key concepts to the teaching

materials for the classroom.

Finally, another important role that history and philosophy of physics can play in physics

education is to inform curriculum choice. Quite often, learning objectives and teaching

activities are based on school tradition or the idiosyncrasies of the teacher. A careful

epistemological analysis, as illustrated in the two case studies, provides the teacher with the

ability to choose a learning path well-founded in theoretical arguments from physics.

Notes

1. Helge Kragh [2] defended a similar standpoint for the case of quantum physics education.

2. We do not aim to provide a complete or strict definition of pedagogic or historiographic

movements. Instead, we aim to provide just a rough sketch of possible roles that the history

and epistemology of science can assume in the physics classroom.

3. We are thankful to Peter Hentrich-Spoon for coming up with this explanation and allowing

us to include it in this chapter.

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Part II

Contemporary Physics topics in the curriculum

40

Chapter 3

Quantum Mechanics in Teaching and Learning physics:

Research-based educational paths for secondary school

Marisa MICHELINI, Alberto STEFANEL Research Unit in Physics Education University of Udine, Udine, Italy

Abstract: Quantum mechanics has now entered the school curricula of most nations on all

continents, due to its founding role in how contemporary physics looks at phenomena and

builds new knowledge, due to its significant weight in many technological applications, due

to the cultural value of the debate that accompanied its birth and which still surrounds the

research into its theoretical foundations. Interest in quantum technologies, such as quantum

computing, quantum cryptography, teleportation (also promoted at institutional level) has

recently contributed to a shift towards didactic approaches developed by Physics Education

Research that deal with basic conceptual knots of the theory, rather than the stages of the origin

of the so-called old quantum theory, which has acquired a certain tradition in schools and

textbooks.

Although in an extremely varied scenario, research into physics education has identified the

conceptual issues to be addressed and the obstacles to overcome to provide secondary students

with a sufficiently coherent framework for quantum theory, which might constitute an

effective basis for further study and development. In the light of Model of Educational

Reconstruction, the different educational strategies developed and validated by research to

address quantum mechanics in secondary school are discussed here by outlining the approach,

the phenomenological study contexts and the contents covered. These proposals are organized

here according to the following three main disciplinary choices: critical reconstruction of the

historical path that led first to the theory of quanta and then to quantum mechanics;

introduction of quantum formalism based on analogies and analysis of its physical meaning;

discussion of the founding nuclei of quantum mechanics starting from the meaning and role

of the superposition principle and the consequences deriving from it. Some of the main

research-based educational proposals that exemplify these different approaches are also

discussed and compared, highlighting their strengths and main criticalities. A specific section

is dedicated to the bridge role of computers for learning quantum concepts and anchoring them

to specific phenomena, proposed with videos, simulations, games.

1. Introduction

In the last thirty years, quantum mechanics has been added to the school curricula of an ever-

growing number of nations on all continents [1–6]. Physics Education Research [7–18], the

academic world more generally [19–23] and policy institutions [24–25] paid increasing

attention to understanding important aspects of quantum physics for new generations to know

and master both on a cultural and technological application level. Quantum mechanics

(henceforth QM) actually constitute the theoretical paradigm of reference for the physical

description of the world [3, 26–34]. Its peculiar linear character unifies the greater part of

modern physics and constitutes a guideline to develop new physics [26, 35–44]. It constitutes

one of the 1900s’ most innovative contributions to scientific knowledge, with cultural value

beyond the disciplinary context of physics [26, 40, 43]. It has made it possible to broaden

research fields into nature and create new technologies, many of which make a great impact on

our daily life [45–50]. Areas such as quantum computing, quantum cryptography, teleportation

and the technologies connected to them will pervade everyday life in the near future and new

professions will be required, in which the competence on quantum concepts will be

fundamental [3–4, 21–22, 30, 51]. Several studies highlight its relevance at both disciplinary

Chapter 3 | 41

and didactic level, also in border sectors between different disciplines, such as chemistry [52–

53], materials science [54], nanotechnology [55], nanobiology [56] and also neuroscience [57].

Experience of the “quantum way of thinking” [36], of the methodological and epistemic

characteristics peculiar to QM, how it builds knowledge about the world, interprets phenomena

and directs modeling of systems is a relevant objective to prepare new generations with an

adequate vision of the NOS [2, 26, 30–35, 58], to develop the theoretical thinking of an average

citizen [11, 17–18, 31–32, 59], and give the conceptual instruments with which today’s students

will be able to tackle future challenges in our society and in the workplace [16, 41, 51 , 60–

63]. It can also provide the conceptual tools, on the one hand to address specific examples in

quantum terms, such as the description of the atom, or the operating principle of technological

instruments in our everyday life such as lasers [16, 47–50]; on the one hand, to analyze the

problematic contexts in which QM developed and the profound debate that led to it [26–27, 30,

35, 44, 64–65] and more generally concerning the meaning of quantum theory [37–45, 66–69];

on the other hand, to develop technological skills based on the principles of QM that will

become increasingly relevant in the near future [1–2, 7, 17–16, 22, 46–51].

The aforementioned growing interest in quantum technologies, also emerging at

institutional level [24–25], such as quantum computing, quantum cryptography, teleportation,

has recently helped shift attention towards didactic approaches, dealing with the basic

conceptual knots of the theory, rather than the stages of the origin of the so-called old quantum

theory [51, 62–63]. In schools, the historical approach to the old “theory of quanta” has defined

a certain tradition in schools, in textbooks and in exams [1–4, 70–72]. If, on the one hand, a

historical approach to quantum concepts might have undoubted value for forming the NOS,

underlying an important cultural contribution and helping to support student motivations [73–

76], on the other hand it shows its limits in favoring the construction of models (such as the

planetary model of the atom), which, according to various studies, constitute a serious obstacle

to constructing an adequate quantum-mechanical vision of phenomena [7, 77–80] (the

generality of this conclusion has been criticized, at least in the case of university students [81]).

On the other hand, the analysis of the high school students' learning paths activated by

didactic strategies attempting to address the founding concepts of QM conducted in pilot

classes, showed that it is possible to address the basic concepts of the theory and most of the

"strangeness” of the quantum world, with positive student learning outcomes and motivation

[74, 82–83].

The unavoidable formal and conceptual difficulties needed to account for a coherent

interpretation of quantum phenomena and how they change, with respect to the framework of

classical physics, have led to abandoning completeness [15, 18, 30, 52–53], rather preferring

to focus on selected aspects that characterize QM, nevertheless chosen on the basis of non-

shared criteria of importance and novelty that they introduce [3–4, 17–20].

The research literature on QM didactics, at all levels of education, had limited or even little

relevance until the last few years of the second millennium [84–85], although it has seen a

notable expansion in the last twenty years [1–4, 18]. For this review, more than 400 articles on

the subject have been analyzed and while limiting itself to considering only the didactic

proposals developed and validated with research for upper secondary school, the picture that

emerges is extremely broad and varied in terms of approach choices, and didactic strategy,

ways of proceeding, in the analysis plans adopted and in the topics considered, in the

phenomenological contexts explored [3–4, 17–20, 86–89].

As discussed in the next section, a key to reading the variegated panorama mentioned, we

let ourselves be guided by the perspective of the Model of Educational Reconstruction [90] for

which we organized the didactic proposals on the basis of the different didactic reconstructions

of the contents. According to this perspective, we recognize the following three main ways of

organizing contents for an introduction to quantum mechanics [18]:

42 | Michelini M., Stefanel A.

1- QM is constructed as a result of successive extensions of classical mechanics or classical

physics more generally, considering the phenomenological contexts, which have historically

constituted an interpretation problem in the classical framework;

2- The quantum mechanical formalism is constructed using formal analogies with classical

physics and the physical interpretation of that formalism is discussed a posteriori or in general

or by analyzing specific phenomenologies.

3- The concepts underlying QM are discussed in defined phenomenological contexts,

subsequently bringing out the conceptual role of the formalism that describes them.

The core of this paper will be the discussion of these three ways to approach QM, referred

to below as the “historical” approach; "formal analog" approach; “conceptual” approach.

Examples will be given of how these three approaches have been implemented in didactic

projects tested in high schools and documented in literature. In a preliminary section, these

proposals are compared, concerning topics treated, context addressed, demonstrating the open

research problems concerning the educational proposals on QM for high school students. The

review is completed by an overview on the contribution of the multimedia in teaching/learning.

The paper concludes with a summary of the main points and some final remarks.

2. The methodological choices of this review

In the following, we will explain the basic choices made regarding the literature and how the

presentation of educational proposals on teaching and learning QM was organized.

We have chosen to discuss only the didactic proposals that were discussed in the literature

and validated by research experiments with high school students. A systematic search was

carried out for publications concerning teaching of quantum mechanics in high school, in a

journal or in a book, starting from the following physics and science education research

journals in English: American Journal of Physics, Physics Education, Eur. J. Phys, Physical

Review Physics Education Research, International Journal of Science Education, Europa &

Eurasia Journal of Mathematics, Science and Technology. We also considered the proceedings

of congresses such as Girep and Esera and we used both public domain search engines (such

as Google Scholar) and search engines belonging to the International Federation of Library

Associations and Institutions. Non-systematic references to literature in Spanish, German and

Italian as well as to literature on proposals for the undergraduate university level were also

made when useful to complete the outlined panorama.

As mentioned, over 400 articles were considered for this review, many of which are listed

in the extensive bibliography. The vast and variegated panorama that emerged could be

organized in different ways: by content, by phenomenological contexts explored, by

methodological / didactic choices, and by lines chosen for the treatment [9, 11, 13, 18, 20]. The

different formulations of quantum mechanics such as wave mechanics, matrix mechanics,

rather than those of Dirac [92] or the many paths of Feynman [93], although equivalent on the

formal level, have given rise to different ways of looking at quantum phenomena and as many

different didactic paths [3, 16, 18, 19–20, 86–87]. Some examples will be discussed below.

Even the role given to formalism in a didactic proposal can profoundly affect its nature and

development [30, 48, 58, 80]. For example, an approach that is more oriented towards acquiring

problem-solving skills, which at university level is often translated into “Shut up and

calculate!” [40], will typically be more oriented towards building skills on the formal

techniques to solve exercises and problems. An approach that is more oriented towards building

conceptual understanding will be finalized to grasp the conceptual meaning of the formalism

[31, 58, 94].

Chapter 3 | 43

The different interpretations of the theory also entail very different didactic perspectives

[87–88]. For example, from Dirac's perspective to QM, it makes sense to consider a single

quantum event in a didactic proposal such as the interaction of a single electron or a single

photon with an apparatus. According to a statistical interpretation [95], a coherent interpretation

of QM’s formal entities requires that they represent sets of identical quantum objects, and

therefore in a didactic proposal only one set of identical quantum particles will have to be

considered. From an orthodox perspective (regardless of what is meant by orthodox), it makes

no sense to talk about the trajectory of a quantum particle, and it becomes an important didactic

objective for students to acquire the idea that it is impossible to attribute a trajectory to a

quantum particle. An approach based on the Feynman path integral leads to a similar conclusion

(a photon / electron "does not follow a single path!"), although starting from the idea that it

"explores each alternative path" [96]. In an approach to non-local hidden variable theory, the

concept of trajectory is recovered, even if it is not accessible and depends deeply on the context

[97], aspects that should become the relevant objective of a didactic approach following this

interpretative line of QM.

The weight given to the different conceptual aspects brings about notable differentiations.

In the didactic and popularizing tradition, quantization of energy and Heisenberg's uncertainty

principle are very important [1, 70]. We are fully aware that quantum theory is based on the

concept of state and the principle of superposition, from which quantization of energy and

Heisenberg relations derive respectively as an accidental aspect, related only to bound systems,

and as a formal transposition of incompatibility [36]. Should a didactic approach necessarily

focus on the superposition principle? Or could it be coherently developed by focusing on partial

concepts such as those mentioned above? The elementarization process stated by the Model of

Educational Reconstruction [90] should lead to an approach centered on general and

fundamental concepts, but significant approaches in the literature attribute centrality to the

uncertainty principle and not to the superposition principle (often marginal or not even

mentioned) [see for instance 77, 80] and some approaches focused on quantum behavior,

without stressing the concept of state and without explicitly introducing the superposition

principle [see for instance 49, 82, 98]. Is it like asking whether we can think of a didactic

proposal on classical mechanics without talking about the second principle of dynamics?

Very different didactic perspectives can be derived from looking at fundamental or

philosophical / epistemological aspects of the theory, rather than at the consequences that

derive from it, for example, its application to describing the physics of the atom, rather than to

scattering phenomena, or aspects of great technological impact such as q-bit and quantum

computing, quantum cryptography, teleportation. In the first case, much weight will be given

to the conceptual aspects, such as the concepts of measurement, of state and its differentiation

from that of properties, preparation, superposition, incompatibility [33, 38, 58, 99]. Anyone

intending to talk about the atom will need to introduce the Schrödinger equation [79]. Finally,

anyone focused on quantum technologies will probably not be able to avoid talking about

entanglement and non-locality [51, 61–62]. It is important to point out here that a didactic

proposal for the university level can combine the different perspectives in a single proposal,

but it is obvious that for the high school level, it is necessary to make drastic choices both to

limit the time spent on QM with respect to the rest of the physics topics, and to adequately

measure the contents to be proposed to the students [1, 52].

These different choices are also intertwined with the geographic contexts in which they

have been developed, especially as regards the different national curricula and school

organizations [1, 70]. For example, in Germany, at least three main proposals have been

developed with relevant treatment of the quantum atom because it is a topic included in

different Gymnasium curricula [77, 79–80]. The Italian didactic research groups have explored

different ways of tackling the main learning nodes of QM in the school, in the context of

44 | Michelini M., Stefanel A.

research projects coordinated at national level from 1983 to date [18, 100–101], developing

four different proposals validated with students with a prevailing focus on the scientific-

cultural and conceptual foundation, compared to the applicative one, for which the quantum

atom is not treated or is in any case a marginal topic, as one example. The added value of the

Italian experience was the sharing of the proposals in a second-level Master’s degree for

professional teacher development at a national level in which discussions on the comparison

between the different proposals and the results that emerged with the students were an

important part of the training activities [101].

3. A preliminary comparative view of different didactic proposals

In this paper, we have chosen to organize the didactic proposals according to the different ways

in which the topics have been organized on a disciplinary level. The three main approaches

(historical; formal analog; conceptual) will be discussed by outlining the general characteristics

that even quite different paths share, some of which will be exemplified by summarizing the

logical development of the key contents. In discussing the various proposals, taking into

account the MER [90] and the literature on student learning processes, some critical issues

were taken into account, selected from those addressed in the teaching proposals [7, 15, 46,

77–80] summarized in the table of appendix A, designed by twelve research groups and

documented in the literature both concerning the didactic path, and regarding their validation

in research experiments with high school students. The critical issues identified are listed

below:

1. How is the passage from the macroscopic to the microscopic proposed

2. How is the transition from a classical to a quantum vision discussed? What

role is played by semi-classical models?

3. How is the issue of the ontology of quantum systems (e.g.: ontological

status of photons and electrons) discussed?

4. How the following issues are introduced and the role they play in the

educational proposal:

4.1. Wave-particle dualism

4.2. Heisenberg Uncertainty relations/principle

4.3. Complementarity/incompatibility observables

4.4. Concept of quantum state

4.5. Superposition principle

4.6. Distinction between state and property (or values of an observable)

4.7. (Unitary) time evolution of the quantum state (time dep. Schrödinger

eq.)

4.8. Measurement in QM and probabilistic nature of QM

4.9. Intrinsic or non-epistemic indeterminism of the measurement process

in QM

4.10. Entanglement and non-locality

4.11. Statistical vision of QM

4.12. Trajectory and quantum system

4.13. Superposition vs statistical mixture

5. Phenomenological context analyzed:

5.1. Interference/diffraction

5.2. Two-state systems (e.g. light polarization, spin, double well, Mach-

Zehnder interference…)

5.3. Infinite or finite single potential well/box

Chapter 3 | 45

5.4. Quantum atom

5.5. Tunnel effect

5.6. Technological applications

6. Basic formalism of QM

Table A in the appendix summarizes the comparison of the cited proposals designed by

twelve research groups, regarding the issues listed above. According to what we found in the

cited papers, a score from 1 to 3 was assigned for each issue, depending on the role played in

each proposal, based on the works consulted and cited: 1- issue addressed in a marginal way;

2 - issue addressed in depth; 3 - issue plays a central role in the proposal. The empty boxes

indicate that it was not possible to identify the corresponding issue in the articles consulted and

cited in the literature. Table A of the appendix also provides a useful reference and

schematization for the discussion in the following sections.

Here it may be useful to discuss some general aspects emerging from Table A. An overview

allows us to immediately highlight the differences between the different ways of proposing

quantum content at high school level and the overall problematic framework regarding choices

of content and areas to be addressed, which has already been mentioned. The last row of the

table provides a crude indicator of these differences. It shows the sum of the scores attributed

to each of the 23 issues selected for each of the twelve didactic projects. The various projects

receive a score ranging from a minimum of 19/69 to a maximum of 43/69, with a number of

issues included in the teaching proposals ranging from a minimum of 35% to a maximum of

80%. No educational project covers all the issues indicated. More specific differentiations

could be highlighted by considering the different sections of the table separately, but without

going into these details, that we will leave to the interested reader, it seems more interesting to

consider the last column of Table A. It shows the mean values of the scores assigned for each

issue. It can be immediately seen that no issue achieved a maximum score. The quantum

measurement process is the only issue addressed in all educational projects, but with very

different weight. Another relevant aspect in the various educational projects is the concept of

state: central in 4 roposals; relevant in 3 proposals; marginal in 5 proposals. We can stress two

aspects. The first aspect is that the only prevision that we can make on a single quantum

measure is the probability of obtaining one of the possible results (but this is common to every

measurement process strictly speaking). The second aspect focuses on the most characterizing

node of the general intrinsic / non-epistemic stochasticity of the QM measurement results (more

precisely a measurement on a quantum system in a superposition of states or that is not in

eigenstates of the measured observable).

Obviously the two aspects are connected, but the first does not necessarily include the

second.

In fact, some proposals [14, 33, 77, 79] characterize the quantum measurement in a more

generic way as a probabilistic process. Other proposals [27, 49, 58, 80, 102–105] focus on the

intrinsic and specific role of the use of probability in quantum physics.

It is generally exemplified by referring to the specific phenomenologies addressed (the

atom as in the case of Niedderer's project [79], rather than two-state systems, as in various

proposals [58, 80, 102]), although often illustrating the general characteristics. The

superposition principle is stressed in 7 projects, despite its role as the cardinal principle of

quantum mechanics. Obviously, it can be questioned here that it is implicit, for example, in the

path integral, rather than in the structure of the Schrödinger equation, but it is strange that it is

not even mentioned in some proposals. It would be like saying that we omit to mention the

second law of dynamics in a classical mechanics course.

One further aspect widely included in the different didactic proposals concerns the

measurement process, on which we can stress two aspects. The first aspect is that the only

46 | Michelini M., Stefanel A.

prevision that we can make on a single quantum measure is the probability of obtaining one of

the possible results (but this is common to every measurement process strictly speaking), The

second aspect focuses on the most characterizing node of the general intrinsic / non-epistemic

stochasticity of the QM measurement results (more precisely a measurement on a quantum

system in a superposition of states or that is not in eigenstates of the measured observable).

The two further aspects very frequently addressed in the twelve proposals were the crux

of the passage from the macro-world to the micro-world and the different ontological status of

quantum systems with respect to classical systems. As an example, the first aspect concerns the

need to reinterpret the laws of high intensity phenomenology as laws that characterize the

probability with which single microscopic processes can occur. The second aspect, on the other

hand, concerns the most crucial issue of the different nature of quantum physical systems,

compared to the classical ones. Although these points are shared, they are dealt with very

differently. The difference is even better understood if we consider issue 2 of the comparison

between classical view and quantum view and whether or not we consider the crux of the

trajectory (issue 4.12). Furthermore, the choice of including elements of formalism or limiting

oneself to qualitative / conceptual aspects significantly differentiates the proposals. In the

analysis proposed here, this point was not explored or explained in further detail, but it would

again reveal a rather varied and differentiated scenario both in terms of the type of formalism

used and the role that is given to it in the proposal.

Further aspects demonstrating great differences concern the absence or the presence and

the way of dealing with Heisenberg relations, complementarity and wave-particle dualism.

One last aspect that appears in only two didactic paths is the difference between state and

property, crucial in characterizing the quantum state and quantum behavior, but evidently not

considered as fundamental as a node to be proposed in education. With regard to this aspect,

obviously, the choice of QM interpretative reference for the different proposals plays a crucial

role.

Finally, with regard to the contexts considered in the different paths, the most frequently

considered are the two-state systems, in which the Mach-Zehnder interferometer prevails (more

than the more traditional Young interferometer) and then the phenomenologies of polarization

and spin.

4. Layouts of the historical approaches

In the approach that we have called "historical", a process of gradual re-construction of the

quantum concepts that gave rise to the so-called physics of quanta is followed. The reference

to the conceptual development line of the treatment is given by the historical path, which is

followed with varying degrees of rigor depending on the case. Two main lines of development

can be recognized. The first line follows a rational reconstruction of those phenomenological

contexts dealt with in the first thirty years of the twentieth century both on a theoretical and

experimental level, which constituted an interpretative problem for classical physics, which

was answered with the first quantum hypotheses [27–30, 64, 74, 106–109]. The second line

provides a path in which students explore in an experimental and / or simulated laboratory

some of the experiments that we can call crucial, that is, which have gradually led to recognition

of the need for a profound revision of classical mechanics (usually the photoelectric effect, the

Compton scattering, the Franck-Hertz experiment) [110–115]. While not explicitly referring to

a historical re-construction of the contents, this approach evidently draws on history and has

many points in common with the reconstruction.

Several university texts have one or more introductory chapters, which retrace the

problems that historically led to the formulation of quantum mechanics, and which constitute

Chapter 3 | 47

the reasonably integrated premise of the rigorous treatment of quantum theory [116–117]. To

better characterize this approach, we can look at how Born organized the contents of quantum

physics in his book “Atomic physics” [116]. The quantization or discreteness of the energy

exchanges between radiation and matter is introduced by discussing the photoelectric effect

and the Bohr model. The Compton effect constitutes experimental proof of the corpuscular

nature of light. The dual nature of matter emerges from De Broglie's hypothesis, according to

a particle of energy E and momentum p is associated with a frequency and a wavelength

by means of the equations: E = h and p = h / ,where h is the Planck constant. The dualistic

vision is recomposed by the complementarity, the explicit expression of which is the

Heisenberg principle of uncertainty. It expresses the fact that “h represents an absolute limit to

the simultaneous measurement of coordinate and moment” [116, p. 99]. The Bohr quantization

conditions for adiabatic invariants are then generalized. The conceptual limits of this approach

open the way to the Heisenberg's matrix mechanics and the wave mechanics, developed by

Schrödinger, who not only gave this formulation of the new mechanics, but also demonstrated

the formal equivalence of the two formulations. The physical meaning of the wave function

is that 2dv provides "the probability that an electron is found exactly in the volume element

dv" [116, p. 147]. This allows the atom to be visualized in terms of probability distribution or

electronic cloud.

The distinctive character of the Born proposal is that the sequence of interpretative

difficulties, which arise from time to time, is progressively overcome with new hypotheses,

which gradually find reconciliation with the framework up to that point outlined at a higher

level of interpretation. Concepts that were apparently contradictory at the previous level find a

coherent collocation at the next level. The innovative nature QM emerges only for those aspects

that can be somehow understood with descriptive categories of classical physics. Quantum

mechanics emerges as the evolution and completion of quantum physics, of which it also

incorporates and re-obtains the results, with no emphasis on the profound differences in the

underlying assumptions. On the contrary, the effort is to bring out a unified framework for both

classical physics and quantum physics.

The historical approach to introducing QM was the first to be followed in various scientific

disseminations texts [see for instance 118], in texts outlined by the national curricula [1, 4, 9,

13, 15, 18, 71–72, 106–107], in most school texts [18, 70–71, 119], in the first experiments test

carried out in schools [74, 120]. Furthermore, part of the academic world believes that the

contents it proposes should be included in the concepts addressed by students at school level

[3]. Several recent proposals also adopt this perspective for the undoubted cultural value,

particularly in terms of reflection on the nature of science and physics, and its interdisciplinary

value [3, 27–30, 34, 71, 105–111].

The undoubted cultural value of such an approach, appreciated when devoting a

sufficiently long time to the subject and adequate formal tools, has made a significant cultural

contribution to teachers’ professional development [101, 121–122]. The learning outcomes

with high school and college students were not as positive with teachers. Research with

students has shown, in fact, that historical approaches to quantum physics led to forming

concepts that are antithetical to QM theory concepts and that hinder subsequent learning [7,

15, 77–80, 123].

This presumably can be linked to two problematic aspects. The first concerns the often

qualitative-discursive approach with which the birth of quantum ideas is proposed in schools,

both due to the students’ poor mathematical literacy, and for the limited time that can be devoted

to the topic at school. The result is a simplified (trivialized) treatment of the problems faced

and the solutions proposed, in which the cultural value of serious historical and critical analysis

does not emerge, a significant appropriation of contents is not made and an effective idea of

the quantum theory is not provided. The second, perhaps more problematic and fundamental,

48 | Michelini M., Stefanel A.

aspect concerns the use of semi-classical models and ad-hoc hypotheses, which inevitably must

be introduced in a historical approach to QM, and which are intrinsically contradictory and do

not help to understand the conceptual meaning and the cultural value of quantum theory. On

the contrary, there is a strong risk of providing a framework of ideas and solutions that solve

specific problems and that do not substantially affect the vision that classical physics has on

the world.

One research problem that remains open is how to recover the rich cultural debate in

teaching, which led to the birth of QM theory and still inspires the research on its foundations

[31, 37–45, 66, 68–69, 96]. In fact, there is widespread agreement about the importance of

showing how physics is evolving knowledge, about reflecting on its birth to also gain

awareness on the nature of physics [2, 4]. However, there is no consensus on whether it is more

productive to implement a historical approach, or if it is preferable to revisit it later after having

introduced the founding concepts of QM [18]. Some school texts in Italy have tried to enhance

the historical debate by integrating it into a discussion on the concepts of the theory [124] or

an analysis of conceptual and applicative aspects [125–126].

The Weizman Institute research group has answered this question with a proposal that

integrates the Israeli historical approach with a treatment of the founding nuclei of the theory

and its basic formalism, as illustrated in Table 1 [33, 127]. The documented outcomes show

positive student learning paths. The number of hours required (30 hours) seems to be a major

obstacle to exporting this proposal to other contexts, such as Italy, where a maximum of 10–15

hours is available to deal with aspects of quantum physics. One critical aspect of this proposal

may be the difficulty in maintaining the coherence of the treatment of the different sections

listed in Table 1.

Table 1. The structure and components of the developed curriculum of Quantum

Theory at high school level [from Ref. 33].

Conceptual nucleus Body Periphery

- Particle-wave duality

- Light duality

- Matter duality (de Broglie)

- Quantum particle –

Quanton

- Einstein interpretation of

photoelectric effect

- Thomson Jr. Electron

diffraction

- Double slit experiment with

light

- Double slit experiment with

electrons

- Compton scattering

- Classical waves of light and

matter

- Light interference in double

slit experiment (Young)

- Electrons passing through

double-slit screen

- Physical state – basis states

and compound states

- Principle of superposition

of states

- Wave function, probability

and measurement

- Uncertainty

(indeterminacy) principle

- Schrödinger

- Measurement in Dirac

notation

- Classical state (x, p),

motion, trajectory

- Classical determinism and

uncertainty (Heisenberg

initial interpretation of

uncertainty)

- Schrödinger matter waves

- Momentum and energy

conservation

- Bohr model

- Operators of physical

observables and equation of

state (Schrödinger

equation)

- Transition between states

- Schrödinger equation

(symbolic form – Dirac

notations)

- Tunneling (Radioactivity)

- Physical quantities and the

equation of motion

- Potential well, State

stability

- Fermions and bosons

- Pauli principle

- Atomic structure and the

Periodic Table of Elements

- Photons and Laser

- Matter particles,

- single type of mass

Chapter 3 | 49

Conceptual nucleus Body Periphery

- Nonlocality

- Quantum entanglement

- EPR thought experiment

and Bohm modification for

photons

- Bell inequality and Aspect

experiment

- Locality principle

- Hidden variables theory

5. Layout of formal approaches based on analogies (Formal-analogic)

Several researchers focused their educational proposals on the structural role of formalism in

QM, proposing a direct approach to theory, to its principles and its mathematical formulation.

Common features are the centrality of formalism from the outset and the use of analogies to

introduce it, which motivate the formal-analogic name we give to them. The mathematics on

which QM is based are built in specific classical contexts, such as oscillating systems (strings

and membranes) [79, 128], or abstract systems of n coupled oscillators [129], or the

interference of classical waves or waves in a box [130–132]. The formalism is then interpreted

in probabilistic-statistical terms, applying it to the analysis of microscopic systems, such as the

atom, and processes such as interference made with low-intensity photon or electron beams.

These approaches are based mainly on analogies, which lead to the description of the

quantum state with the formalism of the wave function. At university level, wave formulation

is developed in texts which, although dated, still constitute a significant reference [115–117,

133]. This was also the first formulation to be used to introduce formal aspects in secondary

education. Typical examples are those proposed by Ebison [131] and Haber-Shaim [132],

whose lines of development are outlined below.

It is proposed to determine the particle nature of light, for example by analyzing the

photoelectric effect, the radiation pressure or the Compton effect to establish the E = hc / λ and

p = h / λ relations. The analysis of diffraction and interference patterns, first carried out in the

laboratory in the case of high intensity and then re-proposed with films in the case of a low

number of photons [131], leads to recognition that the points of the single photon impacts are

stochastically distributed and therefore they are only probabilistically predictable. To describe

the process, it is assumed that the mathematical formalism to be used is similar to the

interference of classical waves. An amplitude Ψ, or wave function, is then associated with each

of the classically possible alternatives. The superposition of these wave functions makes it

possible to correctly predict the minimum intensity position in the interference figure.

Statistical significance is attributed to the association thus constructed. The analogy of the

interferential figures obtained with electrons and neutrons and those obtained with photons

suggests adopting a similar formal description for material particles as well. The wave packet

concept is introduced as a superposition of plane waves of different frequencies, to try to

describe a particle. Finally, the case of a confined particle is considered and described with

standing waves and consequently discrete levels of energy [132]. The quantitative analysis of

the Gaussian wave packet analytically brings out the uncertainty relations, making it possible

to discuss the measurement process. It follows that it is impossible to describe the trajectory of

a particle and the only acceptable assertion is that the particle at any instant can be "located in

a finite region of space" (not in a point). The formal tools introduced make it possible to build

semi-quantitative models to estimate the atomic size and energy of the fundamental state of the

hydrogen atom; recognize the inconsistency of the Bohr model; account for the existence of

the meson, the nuclear forces, the Lorentzian broadening of the spectral lines, and the

impossibility of confining an electron in a nucleus [132].

In this type of treatment, the aim is to build the necessary tools to recognize the

interpretative potential of the new mechanics, particularly in relation to the atomic structure

50 | Michelini M., Stefanel A.

and the phenomena connected to it. In proportion, less attention is paid to the recognition of

peculiar elements of quantum physics, such as indeterminism, the incompatibility of some

quantities. The formalism used has the advantage that, at least in the basic aspects (the use of

a function R→R), it is also familiar to secondary school students. However, any attempt to

overcome a first qualitative or semi-qualitative level, even for the simplest aspects, collides

with formal complexities that are difficult for high school students to overcome. This is

essentially the reason why there was no real use in schools for proposals with a formal-analogic

approach, until the advent of the PC, which, as will be illustrated in a subsequent paragraph,

has opened up new opportunities and educational perspectives [82]. In the following

subsections, we will analyze didactic proposals that illustrate different lines of development of

formal-analog approaches to QM.

5.1. Approaches based on uncertainty relations and/or De Broglie relations

The first line of development concerns approaches that use Heisenberg's uncertainty relations

as a formal construct to investigate relevant consequences. Two approaches are used to

introduce these relations: whoever introduced the concept of wave function can formally derive

the uncertainty relations from analyzing position and momentum dispersions in a Gaussian

wave packet; whoever opts for a phenomenological approach can derive analogous relations

by constructing the product of the position and momentum dispersions in a single slit

diffraction phenomenon or by resorting to the Heisenberg microscope [27, 108]. The diffraction

context seems more appropriate to bring out the intrinsically stochastic nature of the

measurement process in QM. Heisenberg's microscope has received numerous criticisms:

firstly that inducing the idea that the uncertainty in the quantum measurements results is due to

the inevitable disturbance created by the measuring apparatus on microscopic objects [40]. The

first method is organically integrated with the QM approach through the wave function

described above [131–132]. The use of Heisenberg's ideal experiments, also typical of

historical approaches, is relevant here with reference to the proposals that extend the

uncertainty relations, explore their meaning and applying said relations to analyzing various

aspects such as the stability of an atom and determining the fundamental state of the hydrogen

atom or estimating the average life of the meson [120, 134].

Recently, the Heisenberg relations in teaching have found new impetus. For example, after

introducing the uncertainty relations in the context of single-slit diffraction, Johansson and

Milstead [135] discuss the impossibility of simultaneously measuring the position and

momentum of a particle with arbitrary precision. They then introduce the uncertainty

relationship between energy and time and use it to analyze the forces of interaction between

elementary particles, the tunnel effect and radioactive decay. As the authors also state, the

approaches being described introduce students to quantum phenomena and ideas, rather than

constitute organic proposals for theory. Tests with students showed that they were able to derive

the relevant formula without using complex mathematical formalism, they were able to explain

the physical meaning of the uncertainty relations, and realize its main consequences in the

microcosm. The same authors comment on the results saying that they are partial results and a

true approach to QM would require a complete change in the curricula [18, 106, 129].

Other approaches recover formal constructs of the old quantum theory, such as the de

Broglie-Einstein relations also valid in QM, to quantitatively describe quantum phenomena,

such as the stability of the atom and the emission / absorption processes [136]. Still others have

reconsidered the use of the Bohr model as a tool to introduce the structure at energy levels of

the atom and as a bridge to the quantum view of the atom based on the Schrödinger equation

[81].

Chapter 3 | 51

5.2. Oscillating systems as a bridge to the QM

The second formal-analogic approach considered here is proposed by the Niedderer group. It

has two main objectives: a) achieve a good understanding of the basic conceptual and formal

aspects of QM; b) develop a clear spatial view of the quantum atom [79, 128]. The formalism

is introduced by analogy with those of the standing waves in one, two, three dimensions and

using software modeling tools ("STELLA" simulation environment), which use a symbolic

representation of variables and formal operators, avoiding the difficulties associated with the

use of differential equations. These sw tools are used to model the Schrödinger equation for

atoms, molecules, real solids and in parallel to build a view of the atom as a charge density (or

cloud), thereby supporting the construction of the physical interpretation of the square module

of Ψ [128]. In this way, students are allowed to try their hand at “more interesting” systems,

such as atoms with more electrons, than any which can be accessed with a typical student’s

mathematical knowledge, which can be analyzed both qualitatively and quantitatively [128].

In a later development, the "electronium" atomic model [137–138] is integrated into the

proposal, used as a conceptual bridge between students' classical knowledge and quantum

concepts [139–140]. The study carried out on learning shows that students tend to preserve the

concept of trajectory in their description of quantum systems, while managing to adequately

use concepts such as state to describe aspects such as the emission and absorption of light, and

develop an adequate view of the quantum atom. To answer this specific need to approach the

quantum world while holding deep-rooted classical ideas, studies have been carried out that

have highlighted the importance of constructs or models that act as a bridge between classical

deterministic ideas and those based on the intrinsic uncertainty that governs the quantum world

[139].

The research group of the University of Rome uses a similar context to that used by

Niedderer to introduce and discuss the main quantum concepts. The linear formalism used to

describe the dynamics of n coupled oscillators is transposed in the quantum field and re-

interpreted in probabilistic terms. The basic concepts, such as state and superposition, are

discussed within this formal structure built by analogy with the classical many-body system.

This didactic approach takes its premise from a complete revision of the concepts, such as that

of state, which are usually taken for granted when teaching physics, and it makes formalism

indispensable because it is founded in quantum theory. This experiment has had positive results

as a proposal for pre-service teachers, while the learning results obtained with the students in

experiments carried out by teachers trained with this approach are of little significance [101].

5.3. Feynman's approach to many paths

The new opportunities offered by computers have made it possible to overcome the

considerable formal difficulties of a didactic approach to QM based on the Feynman-like

method of sum over paths [92, 141], while at the same time enhancing the more intuitive

aspects for the educational level, as proposed by Taylor [96, 142]. Different groups developed

research based educational proposals following and/or elaborating Taylor’s suggestions [14,

97, 104, 119, 144–148].

This approach introduces the following rules, which subsequently account for the behavior

of quantum particles: a) if a particle at time ta is in position xa (event A), to evaluate the

probability that at a later time tb, the particle is located in xb (event B), one must consider the

rotation of a hand of an imaginary “quantum stopwatch” that starts when the particle is emitted

in A and stops when it is detected in B; b) the particle explores all possible paths between the

two events A and B and for each path, the hand will stop in a direction that identifies it; c) the

probability sought is given by the square modulus of the vector, which is obtained as the

52 | Michelini M., Stefanel A.

resultant vector of all the vectors that identify the directions that characterize each path [96,

see 144 for this exposition of rules]. The simplicity with which it is possible to evaluate the

temporal evolution of the wave function from these rules makes it possible to reconstruct the

classical phenomenology [145] or deal with typical propagation phenomena such as those of

the interference from thin sheet and diffraction [142, 144–142], or Mach-Zehnder

interferometry [146–147].

Some nodes have not found an answer in the research that has used this approach: A) how

to account for the method’s rules, for example by basing them on analysis of the diffraction

phenomenology; B) how to extend the method to more complex cases; C) how to overcome

the problem of the impossibility of associating a trajectory to quantum systems after having

founded the approach on exploration of the different trajectories. In correlation with this last

node, clarification is still required on what kind of ideas students develop regarding quantum

systems and trajectories; the possibility of passing from classical and quantum systems simply

by continuity by decreasing, for example, mass and dimensions.

The relatively recent didactic proposal from the Pavia group is quite culturally rich, giving

weight to the analysis of both the conceptual and applicative aspects, and it is careful in trying

to overcome some of the highlighted criticism [104, 119, 148–149]. It introduces the method

of the sum over the paths, by means of the interpretation according to the Huygens principle of

the interference of classical waves. The discontinuity with quantum behavior emerges when

the photon concept is introduced through discussing three experiments: the photoelectric effect,

to highlight the discreteness of the energy exchanges in the light-matter interaction; the

experiment by Grangier and colleagues "on photon indivisibility"; the single photon double slit

experiment, with video, to introduce probabilistic interpretation. Grangier's experiment shows

that the photon does not split into two parts at a beam splitter. The double slit experiment

highlights that the photon "has the property of being distributed in space”. The idea of “the

photon following all the possible paths” can be a logically consistent answer to account for the

three phenomenologies. Each path is associated with an amplitude and a phase, in analogy with

the classic case introduced initially, and the amplitude of each path at the detection point is

added to obtain the resulting amplitude. Unlike the classical case, the square of said amplitude

is reinterpreted as a quantity proportional to the probability of detection of the photon.

The analysis of three further single photon experiments allows students to focus on

quantum conceptual processing: the Mach-Zehnder interferometer, to demonstrate the

impossibility of attributing a single trajectory to the photon; single-slit diffraction, to discuss

the uncertainty principle; Zhou's experiment to discuss the role of measurement and which-

way information. The proposal is then completed with a discussion on the limit of geometric

optics and the correspondence principle, the extension of the path method to the case of material

particles and the analysis of tunneling and of a confined system (potential well and atom of

Bohr simplified).

The whole path is supported with simulations made in Geogebra that allow the student to

actually implement the Feynman method without the burden of analytical calculations [104].

The studies carried out on student learning show that "the sum over paths approach may

be effective in overcoming some of the educational difficulties when teaching basic concepts

of quantum physics" [149]. In particular, it is an interesting result that a student expressed the

idea that the photon follows the path of one of the two arms of an interferometer in only one

case, while 70% of the students proved to have appropriated the idea of many paths and of the

associated probability [149]. The studies conducted by Otero and colleagues have shown

different outcomes on this point and in particular, that "It was an obstacle to the students to

understand the path concept established in this didactic sequence" [14].

5.4. Quantum field physics

Chapter 3 | 53

Educational approaches based on the quantum field theory constitute the last list we included

in the formal-analogic approaches. This type of approach is based on the inspiring idea that the

most coherent way of proposing quantum ideas is to consider quantum fields as basic

ingredients of the universe and particles as quanta of energy and momentum of fields. Hobson

was the first to formulate a didactic proposal on the founding principles of quantum mechanics,

based on this idea [150]. His path has been resumed and operationally translated in Italy by the

Milan unit, which also followed some pilot experiments based on this type of approach [151],

while other authors have deepened the quantum field concept from a didactic perspective [152].

These proposals construct a unified vision of radiation and matter in terms of photons as

quanta of the electromagnetic field and electrons as quanta of the related field. Photons and

electrons have the same ontological status in this perspective. The interferential phenomena

characterize both the light and the beams of that, usually referred to as matter (electrons,

neutrons, atoms), that are the quanta of the fields that fill the space with continuity [151]. This

type of approach is based on a unifying and, in principle, shared basic idea. Its operational

didactic translations, however, either remain at a descriptive qualitative level, in the

implementations in schools, or they need mathematical support, accessible to teachers, but

difficult to reconcile with the mathematical skills of high school students. It was therefore

usefully proposed in teacher training activities, in particular for the analysis, comparison and

discussion of different teaching approaches to QM [153]. The transpositions experimented in

the classes with the students gave rise to modest learning outcomes, despite a good motivational

impact [101, 151].

6. Layout of the conceptual approaches to QM and the two-state systems

The approach that has been called conceptual here overturns the previous perspective, placing

and giving main weight to the introduction and discussion of the basic elements of the theory,

with respect to introducing its formalism.

It starts by analyzing phenomenological contexts to explore how phenomenology is

connected to concepts. Dirac [91], in his introduction to quantum mechanics, discusses the

phenomenologies of double-slit interference and polarization in this perspective to introduce

the concepts of indeterminism and the superposition principle. Sakurai [36] proposes that the

reader tunes into the "quantum-mechanical way of thinking" with "shock therapy" based on the

initial analysis of the phenomenology of spin as an "example that illustrates, in a fundamental

way, perhaps better than any other example, the inadequacy of classical concepts” [36]. The

approach used in these and other university-level texts to which we can add the illuminating

high-level popularization treatment Sneaking a look at God's Cards [44] in which Ghirardi

discusses the crucial conceptual nodes of quantum mechanics in the context of polarization of

light.

These approaches have been taken up and developed by different didactic research groups

that have developed and tested different projects for teaching / learning quantum mechanics in

secondary school [26, 42, 58, 83, 94, 154–156] and more generally at under-graduate level

[157–160].

Generally, these are approaches based on analyzing specific two-state systems which are

the simplest quantum systems that can be conceived and are the "less classical and more

quantum-mechanical systems" [36], which thereby make it possible to highlight, both on a

conceptual and formal level, practically all the conceptual and peculiar novelties of quantum

theory with the minimum possible use of formalism. The contexts considered are the more

traditional double-slit interference [77, 80, 123, 161], Mach-Zehnder interferometry [80, 105,

160, 162, 164], polarization of light [80, 99, 154–155], electron spin [156–160, 163], and the

54 | Michelini M., Stefanel A.

double potential well [102, 166, 160]. Approaches that are more immersed in everyday school

life consider the phenomenologies offered by physical optics, relatively easy to explore in the

laboratory. In particular, the analysis of polarization and spin lead more directly to constructing

the concept of state and quantum measurement. The interference phenomenon is a privileged

didactic context for introducing the concept of quantum inference and the crucial role that

phase plays in it.

In these proposals, the specific context chosen becomes the reference phenomenological

context in which the basic concepts of the theory are discussed, such as the concept of state,

the principle of superposition, and the concept of incompatibility. It also provides an

opportunity to address concepts such as entanglement, non-locality or the problematic nodes

of macro-systems and measurement. Until a few decades ago, these aspects were topics

considered on the border between physics and philosophy, but which thanks to the famous

experiment by Aspect and colleagues and the experiments by Zeilinger and colleagues have

become very interesting not only because they allowed us to experimentally verify the

correctness of the quantum theory predictions, but they also provide the basis for technologies

of great interest and potential social impact, such as quantum computing and cryptography.

The crucial point of the didactic proposals with a conceptual approach is the construction

of a coherent theoretical framework centered on the concept of the state of a quantum system

as an expression and codification of the maximum knowledge on the probability of all possible

outcomes of any measurement that an observer can make on a system. The state of a physical

system is no longer identified, as happens explicitly or implicitly in classical physics, with the

values of the properties of a system in that state (or simply with the system itself). Therefore

in this type of approach, more than in others, the following are emphasized: the principle of

superposition and the link with non-epistemic indeterminism, which characterizes quantum

processes; the crucial difference between quantum state and properties that can be associated

with said system; the concept of preparing a system; the role and particular nature of

measurement in quantum mechanics [58, 94, 154–156].

In some of the didactic proposals based on this type of approach, the formal translation of

the linear quantum superposition principle in the linear formalism of Hilbert spaces can be

explained by its conceptual content. On the contrary, the analysis of topics such as that of

quantum atom, have more space, for example in the proposals with a formal-analogic approach.

Formalization of the quantum state with a ket vector, an abstract entity free from any

representation, is an aspect that favors overcoming the identification of a quantum system with

the formal entity that represents its state [94].

Perhaps the main criticality of this type of approach is the emergence of general concepts

and laws from particular contexts, which are taken as examples, but which students can confuse

with the entire quantum world. In other words, the construction of a coherent and compact

theoretical construct in a specific context pays off with the risk of providing a restrictive vision

of the cultural and interpretative scope of the theory itself. Another criticality is related to the

differences between the learning objectives of these proposals and those outlined in national

curricula and generally included in school texts, which we know provide an important reference

for teachers [1, 70].

6.1. From two-slit interference to the concepts of quantum mechanics

The reference to the context of double slit interference, for an introduction to the founding

concepts of quantum mechanics, can be well exemplified in the Feynman Lectures on Physics

[167]. He immediately starts the conceptual aspects of the theory, founding the construction of

quantitative ideas starting from the analysis of the interaction processes with a double-slit

screen of a bundle of classic balls, of waves on the water surface, and of a low intensity electron

Chapter 3 | 55

beam. The third process is analyzed in probabilistic terms, in the light of the first experiment.

The mathematics of the second wave experiment suggests associating a complex amplitude

with the probability that each of the outcomes will be achieved.

The Feynman Lectures on Physics constituted the reference for the approaches of two

teaching proposals on QM in high school, one from the University of Berlin [77, 123] and one

from the University of Munich [80, 162].

The proposal by the Fischler group from Berlin considers electron diffraction, a context

considered more appropriate for developing the non-relativistic QM, than optics. The choice

of topics considered, and the sequence line of the path are guided by the potential they offer to

developing concepts and ideas consistent with QM. References to classical physics, the Bohr

model or dualism are therefore avoided, because they constitute learning obstacles. The goal

then is to introduce quantum ideas directly: immediately addressing the phenomenology of

electrons; adopting a statistical interpretation of the phenomena; and introducing Heisenberg's

relations early. [77, 123, 168]

The advantage of this approach is constructing QM by analyzing the phenomenology of

electrons, avoiding the introduction of the photon concept. At the same time, the wave

interpretation of optical diffraction/interference is used as an analogical tool to construct a

quantum interpretation of the electron diffraction. Another critical aspect is founding the

uncertainty principle on a statistical interpretation, then using it to recognize the existence of

the ground state of a (single) atom.

Müller’s proposal [80, 162] firstly analyzes the phenomenology of photons, and then that

of electrons. With a spiral strategy, the concepts introduced in the first area are re-examined

and formalized when considering the material particles. After measuring ħ and introducing the

idea of a photon with the standard analysis of the photoelectric effect, in the context of photon

interaction with Polaroids, the concept of preparation is introduced as a “systematic production

of a dynamic property of a system”. The Mach-Zehnder interferometer, explored in a simulated

experiment, leads to the recognition that neither the wave nor the particle model can describe

the phenomenon of interference for weak beams. It then addresses the construction of a model

in which to incorporate both descriptions. It is concluded that the photon is a non-localized

entity and that it does not have a trajectory in any case. Since the interferential phenomena

emerge only by repeating the same experiment many times, we arrive at the idea that QM make

statistical predictions on repeated measurement results on a set of identically prepared quantum

objects. In the case of electrons, the path proceeds in a similar way, introducing the wave

function and the superposition principle. In a new version, the wave function is considered only

qualitatively “as an abstract entity” [162].

The critical points of the proposal are a) to base the interpretation on the concept of

dualism, which, as observed by some authors, is not consistent on a disciplinary level [68] and

can produce obstacles to student learning [77]; b) it does not explain why the formalism is only

constructed in the case of electrons, and not photons.

Both the Fischler and the Müller approaches are still important references concerning

student learning and are particularly effective at giving students a significant quantum vision

of physical phenomena.

6.2. From the phenomenology of polarization to the founding concepts of QM

The proposal developed by the Research Unit of the University of Udine on teaching / learning

QM in secondary school [58, 83, 94, 169–171] constitutes a coherent educational proposal,

based on the Dirac approach. This proposal implements a conceptual approach, following the

stimuli of IBL tutorials [172] to explore the phenomenology of the photon polarization [173],

studied in the laboratory first, and then analyzed in a set of ideal single photon experiments

56 | Michelini M., Stefanel A.

[174]. Malus’ law is constructed as a phenomenological law in the lab, without giving a

preliminary classical description [83, 171, 175]. The validity of Malus’ law for single photon

experiments leads to reinterpreting it in probabilistic terms and recognizing that polarization is

a property of each photon (it is not a collective property). The filtering of photons from

Polaroids is read from the perspective of preparation or measurement of a dynamic property of

the photons themselves. This property is identified with a symbol (for instance: the symbols

∆,*,▪ respectively for vertical, horizontal, 45° polarization property). This symbolic

representation helps students grasp the difference between state (eigenstate) and property

eigenvalue of a quantum system. Moreover, the iconographic representation of the polarization

property offers the students formal (not mathematical) instruments to construct a personal

hypothesis. The recognition of a state associated with a physical property of light (polarization)

is the prelude to identifying mutually exclusive properties, each of which is incompatible with

any other polarization property.

Quantum indeterminism and the identity of quantum systems emerge as a generalization

from the behavior of linearly polarized photons in the interaction with Polaroids. The

impossibility of associating a trajectory to a quantum system is exemplified in the context of

the interaction of photons with two birefringent crystals aligned, one directly and the other

inversely, as a consequence of the fact that the polarization state in a certain direction cannot

be considered a statistical mixture of two orthogonal polarization states. The same context of

the interaction of birefringent crystals and photons helps us recognize that experimental results

cannot be predicted on the basis of information possessed a priori by quantum systems.

Therefore, the evidence emerges that even according to alternative interpretations to the

standard one, microscopic systems have essentially non-classical behavior. [154–155, 171]

The re-examination of the simple experiment in which a beam of photons interacts with

Polaroids, offers the chance to associate a vector belonging to a two-dimensional abstract

vector space to the state of a linearly polarized photon. This description acquires interpretative

value by recognizing that it is sufficient to characterize the statistical behavior of photons in

the interaction with Polaroids and birefringent crystals. The peculiar character of the

superposition principle can be explained formally in the interferential terms of the transition

probabilities relating to the process in question.

The association of linear operators-physical observables is constructed by calculating the

expectation value of the observable polarization in a defined direction.[94, 155].

The results, rules and concepts obtained and introduced in the case of polarization are then

generalized in different contexts as, the quantum atom or the quantum interpretation of

diffraction [95, 155]. The conceptual tools introduced can be used to discuss entangled systems

and single-slit photon diffraction [176] or to analyze the historical debate on the foundations

of QM [44, 58, 101].

The path proposed by the Udine research unit has been tested in different contexts through

modules lasting 10–12 hours [83, 170–171, 175]. The documentation of the students' learning

highlights that concepts such as state, superposition of states, incompatibility are mastered,

even if limited to the specific context being explored. The didactic strategy adopted has proved

capable of providing tools for the autonomous construction of interpretative hypotheses. It

emerged that students generally orient themselves with sufficient coherence: towards a

quantum-type interpretation, unified by the idea that a measurement process can be analyzed

in terms of transition between states; an interpretation with hidden variables in which epistemic

indeterminism plays a fundamental role [171, 175]. The main limitation of this proposal lies in

the weight given to the analysis of the context of polarization and therefore in the need to

foresee the generalization of concepts and formalism, not always feasible in a few hours of

activity. In some cases, just where it was not possible to adequately carry out this transition

Chapter 3 | 57

from the specific case to the general case, the learning, however good, was not detached from

the explored context of polarization [94].

A similar approach focused on polarization is proposed by Pospiech [26, 41–42, 177]. She

considers simple experiments of light interaction with birefringent crystals, and then reanalyzes

them as single photon processes. The need immediately emerges to abandon a classical

description, to adopt a quantum point of view in which the measurement process is

characterized as an irreversible operation of projection on one of the eigenstates of the

considered observable. The simple context of polarization constitutes the experimental

reference for discussing the uncertainty principle, the complementarity principle, the link

between complementarity and measures, the complex relationship between the macro and

micro world [41].

Compared to the approaches in which an interference phenomenon is analyzed, the context

of light polarization offers the following advantages: the phenomenology of polarization is

easily reproducible, it can be explored both qualitatively and quantitatively even using poor

materials [173]; the direct operation that can be offered to students allows them to acquire

mastery of the experimental context; the simplicity of the situations that are explored favors

starting from the students' conceptions, the construction of interpretative hypotheses and their

comparison with the facts [83, 171, 175]; the particular geometric structure of Polaroids and

birefringent crystals makes it possible to build a direct bridge between phenomenology and

formalism, which does not require an intermediate classical interpretation of the phenomena

[171]. The main limits of introducing QM in the context of photon polarization are the

following: the concepts developed would find a coherent interpretation in the physics of

quantum fields, while in fact they concern non-relativistic quantum mechanics which is known

to only be valid for material particles; Hilbert's two-dimensional space of polarization states

has the same size as that of polarization directions in physical space, creating the risk of

confusing them; the phenomenology of the polarization of light finds adequate interpretation

in classical electromagnetism and the recognition of polarization as a property of individual

photons is an aspect that must be addressed in teaching, with particular care.

6.3. The phenomenology of spin to build the foundations of QM

The phenomenology of spin studied with Stern and Gerlach apparatuses (SG in this section) is

a context used by various authors to develop didactic proposals that explore quantum

phenomena and build the fundamental concepts of QM. Sakurai's text [36] is a reference for

this approach, which with the development of computers has found the possibility of being

supported with simulations such as OSP - SPINS [103, 178–179, 155–159] or similar [160,

164], to carry out similar SG experiments to those previously described with Polaroid. Here we

recall the initial steps of the path developed by McIntyre for the undergraduate level (Chapter

1 and part of Chapter 2 of the ref. [158]), which has been implemented, with few differences,

also in other university contexts [155] and high school [156, 163]. After an initial introduction

to the SG experiment, using the simulator introduces the probabilistic-statistical nature of the

measurement in QM. The key concepts of the theory are introduced (the postulates in

McIntyre’s proposal - 156) by analyzing four simulated experiments. The first experiment with

two SG apparatuses with parallel orientation and therefore certain and reproducible results,

makes it possible to introduce the concept of preparation, the analyzer (or of measurement),

state and its description with a ket. The second experiment takes two SGs arranged

orthogonally, the outcome of which shows a distribution of outcomes. It is only possible to

predict the probabilities of said outcomes. The third experiment requires that a third apparatus

is inserted between two parallel SGs arranged orthogonally to the other two. This case shows

that the projection of the spin along one direction (e.g. along Z) is incompatible with the

58 | Michelini M., Stefanel A.

projection along another direction. The fourth experiment envisages the same apparatus as the

previous one, but one of the beams leaving the second SG is alternately shielded, or the two

beams leaving it are recombined. This highlights the difference between pure states and

statistical mixtures. The reference to the double slit experiment refers to a context perhaps

better known to students, in which the problematic issue of interpretation is nevertheless

similar.

The four experiments are then reanalyzed in the light of the basic QM formalism for which

the state is represented with a ket, any state can be expressed as a linear combination of a ket

base, the probability of transition between the state of preparation and the system’s state after

a measurement is given by the scalar product of the ket representing said state. Through the

projector concept, operators are also introduced to represent the observables of a system. In the

implementation carried out with high school students, the introduction of the formalism was

contextual to the analysis of the simulated experiments. The results showed a positive impact

of the proposal on the concept of state and superposition, but also a certain unease in mastering

phenomenology [101, 156].

The main strengths of introducing QM in the context of the electron spin phenomena are

different: quantum concepts are immediately tackled by referring to material particles, thereby

avoiding the slippery terrain of extending photons to concepts to which strictly speaking they

should not be referred; the space of the spin states is two-dimensional, while the spin is an

observable that has three real components, favoring recognition of the distinction between the

abstract Hilbert space of states and the phenomenon space of properties; spin has no classical

counterpart and therefore phenomenology can only be interpreted in a quantum conceptual

framework. The criticalities of considering such an area can be summarized as follows: the

difficulty of carrying out a real SG experiment in a didactic laboratory, which can only be

partially overcome with simulators, means that students cannot be offered a phenomenological

connection that both polarization and interference experiments offer; the phenomenology of

the spin-magnetic field interaction is not trivial, nor is it trivial to introduce it in a short time,

albeit using the effective synthesis of McIntyre [157], to high school students, because it

concerns atomic beams and not simply free electron beams, and in fact it requires consideration

of the net force acting between a magnetic dipole and a magnetic field, commonly not dealt

with at high school level. Obviously, it is also possible to introduce an SG apparatus as a

phenomenological game (as Mermin did for example [37]) or as it is done in some approaches

to quantum gamification which will be discussed later [176]), although in this case the risk is

that it might surreptitiously introduce a phenomenology, which students have no way of

approaching and considering as such.

6.4. Single photon (real) experiments at school

A truly innovative proposal in the panorama of QM teaching proposals based on research at

high school level comes from the University of Erlangen [104, 181–182]. The didactic project

is based on the idea of providing modern concepts on QM, as the technological applications of

QM are already influencing students’ social life and will influence it even more in the future.

Quantum physics is formulated as an extension of classical optics, avoiding both references to

mechanics, semiclassical conceptions such as wave-particle dualism and historical issues,

which are the basis of many of students’ conceptual difficulties in QM as highlighted by the

literature [105]. The didactic proposal uses the photon as a quantum object, defined as

elementary excitation of the electromagnetic field [181]. It integrates the discussion of basic

conceptual aspects of quantum theory with experiments from quantum optics labs, displayed

on an interactive screen, which emphasize the quantum nature of light and cannot be interpreted

with semi-classical models.

Chapter 3 | 59

The study of quantum physics is introduced by showing a video that illustrates, for

example, quantum computers and quantum cryptography, particularly showing the importance

of computer security, an aspect that is particularly relevant for new generations. The didactic

proposal is then divided into two parts, each consisting of two 90-min lessons: the first part

introduces the "basic aspects" of quantum optics (particularly preparation of single photon

states) and the “technical aspects” of experiments with single photon detectors; the second part

focuses on the interactive videos of the single photon experiments (Anti-correlation and

Interference of the single photon) and the interpretation of the results that emerge from these

experiments. The analysis of single photon experiments is preceded by explanatory videos and

activities in which beam splitters are introduced with real experiments carried out using laser

beams.

Three key ideas form the conceptual foundation of Erlangen's teaching sequence:

- Superposition of the states and statistical interpretation of QM [95]

- The measurement process and the dynamic properties of quantum systems.

- Quantum interference

The analysis of real single-photon experiments with a beam-splitter makes it possible to

introduce the concept of superposition and therefore the probabilistic nature of quantum

physics. When individual photons strike a beam splitter, the state of the photons is equivalent

to a superposition of transmission and reflection states. At the time of the measurement, only

one of the detectors at the output of the beam splitter counts a photon 50% of the time. This

demonstrates the unity or in-divisibility of photons and also that quantum events are stochastic,

they cannot generally be predicted with certainty, but it is possible to give only a statistical

interpretation. The preparation concept replaces the transmitter-receiver. It is not possible to

just transfer classic concepts in QM. For example, the concept of trajectory loses its meaning

and in particular, we can only speak of position in reference to a measurement process. This

statement is true for all the dynamic properties of a quantum system. Experiments on the

interactive screen of anticorrelation and single photon interference highlight the indivisibility

of photons. They also highlight the need to abandon the idea of the photon as a localized

particle.

The assessment of students' learning outcomes shows significant improvements in

declarative knowledge [181].

The strengths of the proposal are that it starts from quantum technologies, focuses on the

key concepts of QM, and proposes real single photon experiments (not just simulations).

Considering quantum physics as an extension of physical optics is also an undoubted strength,

which however cannot completely avoid the conceptual difficulties related to references to

mechanics. The evaluation undoubtedly provided positive feedback, but it should go into

greater depth not only for the declarative knowledge, but also to identify which concepts the

students actually master.

6.5. Q-bit based quantum mechanics educational sequences and games.

The development of quantum technologies has raised the importance in the world of education

on building effective skills in quantum mechanics precisely regarding aspects that most

characterize QM, its "oddities", which are not usually included in the introductory courses [24,

30, 60, 180, 184]. Some researchers are studying the possibility of teaching the quantum

principles inside the context of quantum technology information, overturning the more

traditional approach to teach first quantum physics and then processing quantum information

technologies as an application. This, for instance, is the perspective of the proposals suggested

by Pospiech in Dresden concerning quantum cryptography conducted until now only with

60 | Michelini M., Stefanel A.

trainee teachers [51]. The approach based on quantum technologies is certainly centered on

conceptual aspects, and for this reason we have included it in this section. However, it has

distinctive features that characterize it and that presumably in the near future will lead us to

recognize it as an autonomous approach to QM: contextualized in technologies; focused on

some aspects of the theory and less on others (unitary evolution has a fundamental role, while

the role of measurement is less central; centrality of the concept of state, while it can do without

the concept of property); it must necessarily introduce formalism, both to understand its

conceptual role and to provide minimal operational skills.

The context of quantum information technologies has a further peculiar character, which

is essentially linked to the abstractness of the context to which it refers: it does not matter if the

q-bit is made with applications of photon polarization, rather than with the physics of ½ spin

particles, rather than with SC q-switches [51, 60, 184].

This has led some researchers to “invent” phenomenologies in which they explore and

construct quantum concepts, answering the difficulty of finding really simple

phenomenological contexts that act as a conceptual anchor and a training ground for conceptual

explorations and an anchor to construct concepts. This has been proposed in several cases in

the form of game contexts. Gamification is a notoriously effective strategy to involve learners,

which has been usefully developed in the case of QM to transform classic games, such as tic

tac toe into quantum games, which bring into play the concept of state, superposition and

entanglement [62, 185–193].

It is interesting to observe that quantum games, just like quantum computing for example,

underlie formal structures that are independent of the phenomenologies with which they can

be implemented in practice. The game environment therefore itself becomes a

phenomenological environment that can be explored by trial and error, after having learned

only a few partial basic rules. Developing strategies to win the game thus produces ownership

of the rules of the game and can activate students’ understanding of the rules of quantum

mechanics, in the case of the games we are talking about here [187].

For example, Corcovilos [189] proposed a game based on the Bloch representation of two-

state systems. The rules governing projective quantum measurements of two-level systems

were the basis for the rules of a two-player game. According to the author, the game aims to

activate student intuition and reasoning about quantum measurements, and statistical a-priori

evaluation of "how much information is necessary to identify a quantum state". It can also be

useful for addressing measurement probabilities, the distinction between individual

measurements and expectation values of repeated measurements, and the “special nature of

measurement eigenstates”.

Dür and coworkers [61–62, 190–191] proposed a quantum game based on the concept of

Q-bit and an associated didactic proposal divided into three parts: Part 1. Context of single

particles to focus on Quantum superposition states, Preparation and measurement processes

(different bases are also considered): Part 2. Context of entangled particle pairs to focus on

Entanglement, Preparation and measurement processes of entangled pairs of particles, and the

difference between classical and quantum correlations. Part 3. Contexts with one particle and

pairs of particles to focus on the concept of decoherence, on the different effects of decoherence

on single-particle pure states and respectively mixed states; the effect of decoherence on

entangled states of pairs of particles. The authors supported the effectiveness of the game

reporting in a generic way, that high school students 16 years old engaged in the games

highlighted that it was useful “to understand the new concepts”.

One environment which can be used to access games (as well as various materials on

quantum technologies and quantum concepts) is https://www.qplaylearn.com/ [192], a platform

aimed at students and teachers of all levels, educators and the general public. One of the game

applications on the platform is TiqTaqToe, an extension of the classic Tria game, with rules

Chapter 3 | 61

inspired by Quantum Mechanics. The game offers four quantum levels: none (the classic

game); Minimal (including implementation of superposition states); Moderate (includes

entanglement states of you own and your opponent’s square); High (provides the possibility to

implement both superposition and entangled states and to cause the collapse of the states) [192–

193]. In a recent activity, the game was offered to high school students who had followed a

brief introduction to the founding concepts of the 3-hour QM. From the questionnaire

administered to the students, in addition to the motivational involvement elicited by the game,

the students recognized its value in clarifying the concepts of state, entanglement and

measurement [194].

7. The contribution of the computer

Applets, materials and more generally learning environments, offered on the web and that can

also be used locally, play a very important role in the various proposals on the QM didactic that

we have discussed. The COMPADRE portal provides access to one hundred multimedia

resources available on the web [195], many of them included in the recommendations from the

MPTL international group [196]. The great potential of using computers for learning modern

physics and in particular QM regards:

- the opportunity to create environments in which to visualize phenomenological

contexts and grasp their quantum nature, also proposing real

phenomena/experiments interactively [105, 182], simulating ideal phenomena [7,

16, 80, 82, 87, 104, 119, 128, 138, 96, 146, 164, 166], offering experimental

simulated labs for free exploration of specific phenomenologies [48, 103, 157,

160, 174, 178–179, 197–201], creating completely abstract contexts, governed

by the real quantum world rules [62, 185–173]

- recover intuition in the understanding of quantum facts, providing didactic

supports for the construction of concepts [47–49, 87], creating the chance for

students to bridge the phenomenology and the quantum concepts, a particularly

crucial aspect in the case of learning a theory as abstract and formal as QM, which

designs a world of phenomena that are indescribable to us without using

mathematical language [59, 79–80, 83, 178–179],

- the chance to offer didactic materials for students and teachers (able to promote

active learning, interactivity, deepening…) [47–49, 63, 103, 114–115, 123, 129,

179, 200–204].

The formal difficulties, that constituted an obstacle for introducing QM in secondary

schools, are, nowadays, largely overcome by the opportunities offered by computers, and more

general availability of resources, applets and rich learning environments for teaching/learning

QM, that are user friendly. In fact, software has been designed to represent and display the

wave function, for instance, or more precisely its real and / or complex part and / or its square

module, in stationary situations or simulating its time evolution in the dynamic case [87, 119,

96, 146, 177–179, 196, 198–199]; modeling the energy levels and wave function of an electron

confined in a single, double or multiple potential well [48–49, 166, 168]; modeling atomic

systems with static multi-representations or dynamic representation of atomic transitions [137–

140, 176, 186–188, 205–209]; modeling two state systems [157–162, 166, 171, 174, 178–179,

198–203].

We will not analyze these proposals, given our self-imposed limitation of the high school

environment. Instead, we discuss five examples of applets for which there is documentation of

their use in the high school environment. They also provide references and examples for

62 | Michelini M., Stefanel A.

literature on the subject, which despite being in continuous development, shows very few

elements of actual novelty.

The applets developed within the Kansas University group VQM project led by Zollman

[16, 48–49] were among the first to be created, validated using research experiments with

students and offered as open source on the net. They are particularly flexible as they are

designed to be used as open didactic tools in which a student can explore a phenomenology in

a simulated laboratory without the filter of a specific model.

These characters emerge, for instance, in the Spectroscopy Lab Suite - VQM Emission

[16, 49, 209], which only requires the previous knowledge that an atom can have discrete

energy levels, and a specific atom model does not have to be adopted. It allows students to

build a structure of energy levels by comparing the emission spectrum that would derive from

it with that of spectra actually observed experimentally in the laboratory. It stimulates the

implementation of problem solving on spectra, in which students operationally find answers to

questions on conceptual nodes relating to spectra such as: What connection is there between

the structure of the energy levels of an atom and the structure of its emission spectrum? How

many levels are at least needed to produce an n-line spectrum?

Similarly, VQM's Wave Functions applet allows both high school and college students to

get closer to the phenomenology of photon diffraction / interference (supported in the Zollman

proposal by real experiments in the lab at great intensity), but also to that of other material

particles such as electrons, nucleons, pions. This makes it possible to re-discover the

relationships between energy, mass and momentum and wavelength frequency associated with

these particles.

One common feature of the VQM applets is figuratively simulating real experiments plus

being able to display system parameters and measured quantities in graphs, diagrams, analogue

or digital viewers.

Another example of a simulated experimental laboratory is the JQM applet [114, 174],

created to support the educational project of the Udine research unit QM. It was conceived as

an explorative ground for freely designing experiments on the interaction between polarized

photons and (ideal) Polaroids and birefringent crystals, to explore hypotheses, comparing its

predictions with the experimental results obtained. It differs from the previous ones, apart from

the phenomenological context, due to the stylized graphics chosen to include conceptual

elements in the representation, such as the direction of polarization. JQM makes it possible to

assemble a photon source (projector / laser), with polarizing filters, birefringent crystals,

screens, photon counters. It helps answer crucial questions to understand quantum behavior,

such as: How does the genuinely stochastic nature of the outcomes of quantum measurements

manifest itself? Is it possible to attribute a trajectory to a quantum particle?

The SPINS applet, proposed by Schroeder [178] and subsequently renewed several times

[103, 183], allows an exploration to be carried out with Stern and Gerlach equipment in the

context of electronic spin, quite similar to that described for JQM. The visualization of the

experimental situations in this applet is very schematic and makes no reference to how a real

Stern-Gerlach apparatus can be presented in a laboratory. This type of simulator, designed for

the undergraduate level, has also been used with high school students [156, 163]. Alternatives

to OPS-Spin are the QuVis' Quantum and classical uncertainties applet [160, 200, 204] and the

applet developed at Georgetown University.

The Mach-Zehnder interferometer is another type of apparatus of which there are several

proposals for simulators. For example, a Mach-Zehnder interferometer simulator was

developed in the context of the Müller project with the aim of introducing the probabilistic

nature of quantum phenomena, the concept of state, the impossibility of attributing a photon

trajectory in the interferometer, the non-locality of quantum phenomena [80, 162, 212].

Chapter 3 | 63

Simulators of this interferometer are at the center of several proposals also developed recently

both at high school level [184, 213–214], and undergraduate and university level [215].

Among the various simulations carried out as part of the Colorado University PhET project

[179, 204, 216], we consider the Quantum Bound States simulation here. This simulation

makes it possible to explore the quantum behavior of a particle confined in a potential well, or

in a pair of potential wells or in a succession of n periodic potential wells. The user can vary

both the parameters that define the well (depth, width), and the shape (rectangular well or

Coulomb like), and the possible separation between the wells. The mass of the confined particle

can also vary. The software makes it possible to view the real part and / or the complex part of

the wave function or the probability density of locating the particle in some position when it is

in the ground state. However, similar representations can also be viewed for the states relating

to any energy levels. The simultaneous display of energy levels and the mentioned

representations related to the wave function make the simulation particularly effective as a tool

for connecting formalism and the explored context. It is also particularly effective for

visualizing and accounting for how bands are formed in solids. The possibility of defining the

state of the system, allows you to view what pertains to energy eigenstates, that is stationary

states, and superimpositions of said states, that show a not trivial time evolution and therefore

can be used as a context for discussing that important point.

The applet developed by Faletic at the University of Ljubljana was specifically designed

to study the temporal evolution of the quantum state and the role played by time in successive

measurements on a quantum observable. The simulation of the double well [102, 166] has the

added value of allowing us to tackle this node in the situation of a two-state system, in addition

to addressing other significantly important nodes such as: the concept of state, indeterminism

and probability, superposition and statistical mixtures. In fact, it proposes the approximation of

a two-state system by considering a confined particle in a double well with a potential barrier

suitably made so that the first two energy states are almost degenerate. The superposition of

these states allows states to be created in which the probability of locating the particle either

the left or the right well is practically unitary. The software can be used to analyze the evolution

of the system when it is prepared in a state with a defined localization, rather than a defined

energy, highlighting the incompatibility between the observables’ energy and position of the

particle confined in the double well and the consequences that arise.

Although aimed at undergraduate and graduate students, it seems important here to recall

the package of simulators developed in the context of an innovative project on quantum

teaching by the University of St Andrews-UK Ante Kohle group [197–200]. This package

includes, among others, a Mach-Zehnder interferometer simulator and an experiment simulator

with Stern-Gerlach apparatus. It can be used to perform an experiment with entangled spin ½

particles explicitly aimed at exploring the difference with a hidden variable approach.

In conclusion, we can recall the documented and positive outcomes for student learning

produced by the use of applets, such as those discussed here but not only them. In particular,

they play an important role as a bridge between phenomenology and theory, to familiarize

students with quantum aspects, phenomena and behaviors, to overcome some conceptual

nodes, such as the existence of incompatible observables and the impossibility of attributing a

trajectory, avoiding various difficulties related to formalism. [18, 175].

Some research issues remain open: What relationship do students see between simulation

and experiment? To what extent is the simulation perceived by students as a replica of an actual

phenomenology? Which model elements necessarily introduced in any simulation are

perceived as such and not as phenomenological elements? What is the ontological status

attributed by the students to the represented entities? What learning problems are activated or

reinforced by the use of a specific simulation?

64 | Michelini M., Stefanel A.

A partial answer to these questions comes from using a real experiment conducted in the

lab at high intensity as an introduction to the use of the applet implementing single particle

experiments, such as in different proposals [16, 33, 48–49, 83, 105].The van den Berg proposal

is interesting for this concern, because it combines optical experiments and Phet applets on

tunneling [217] to create a unique vision and then a unitary interpretation of the two

phenomenologies.

8. Conclusion

Recognition of the paradigmatic role that QM plays in the study and description of the world

has led to many countries renewing their curricula, including elements of quantum physics in

secondary school. Since the last decade of the 20th century, research has been conducted on

studying strategies for teaching QM at high school and on student learning processes in this

area. They are tests of the feasibility of meaningful teaching of QM in schools. They

highlighted the main learning problems and some ways to overcome them, although the choices

of didactic approach and content are extremely diversified and made on the basis of unshared

criteria. One aspect that emerges from the analysis performed for this review shows that not all

proposals explicitly address the crucial role of the superposition principle in quantum theory

and deal with the other crucial node of the measurement process in a very different way.

The most widespread choice, which was followed for drafting the didactic texts and

initially adopted at school, involves introducing the quantization of the main descriptive

quantities of microscopic systems, through analysis of classically stable unresolved problems,

experiments or non-interpreted aspects, such as the black body spectrum, the photoelectric

effect, the Compton effect, the Franck and Hertz experiment. This choice has been briefly

referred to here as a "historical approach" as it often translates into the rational reconstruction

of ideas, which led to quantum physics. It is based on assumptions which, especially in the

didactic field, are not always adequately motivated and emerge as ad hoc hypotheses. They

give rise to obstacles to learning concepts consistent with quantum theory that are difficult to

remove, as has been highlighted by a large part of the research.

Due both to these difficulties and to the great time and non-trivial formalism required for

an adequate historical approach, several researchers have studied approaches to the wave

formalism of QM using classical analogies. In an axiomatic way or using weak analogies, the

wave function is introduced to represent the quantum state. It constitutes the instrument used

to reach the main objective of this approach indicated herein as formal analogical, which is to

have some peculiar elements of the QM recognized on the one hand, such as indeterminism,

incompatibility of some quantities, on the other hand the explanatory potential of the QM, in

particular in relation to the atomic structure. However, going beyond a qualitative or semi-

qualitative treatment requires, even for the simplest aspects, the use of formal tools, which are

difficult for high school students to manage. Only recently have computers made it possible to

largely overcome the formal difficulties in the operational management of the wave function,

although leaving open the conceptual issue of how to account for why it describes the state of

a quantum system. For US college level, strategies have been proposed aimed at recovering

intuition in the understanding of quantum facts, through the use of applets with which the wave

function of the systems and the quantities associated with it are represented.

The new opportunities offered by computers have also made it possible to overcome the

considerable formal difficulties of a didactic approach to QM based on the Feynman sum over

paths, while at the same time enhancing more intuitive aspects. One of the strengths of this

approach lies in the possibility of determining the temporal evolution of the wave function in

a simple way, even if only in situations involving free systems. The approach to the "rules" of

Chapter 3 | 65

the method, however, is also axiomatic in this case, with an a-posteriori link between concepts

and phenomena reality. A second methodological problem concerns constructing the concept

of wave function and therefore the impossibility of attributing a trajectory to a quantum system

starting precisely from exploring all possible classical trajectories.

To overcome the axiomatic approach to formalism or an approach based on weak analogies

with classical physics, some researchers have chosen to develop didactic paths in which the

concepts of quantum-mechanical state and linear superposition are gradually constructed,

considered fundamental and therefore indispensable. These paths adopt the approach called

conceptual here, which refers to Dirac's formulation of QM. The aim is to provide the basic

methodological and conceptual contents of quantum theory, showing its potential to unify the

vision of microscopic phenomena. Formalism is introduced as a conceptual tool to codify the

constructed concepts. The symbolic representation of this formalism allows the link between

concepts and their mathematical representation to emerge relatively simply. The contexts being

analyzed are those offered by physical optics, which can be easily analyzed in educational

laboratories, described with minimal mathematical equipment, accessible to high school

students, and used to account for the novelties and peculiar aspects of QM.

The didactic strategies based on an operational approach to the analysis of the considered

phenomenologies and to the construction of theoretical thinking, implemented in the didactic

transpositions of the different types of layouts, have been shown to help overcome

identification between system, state and its representation, found in research on learning QM.

While analyzing specific phenomenologies in depth, if on the one hand it allows us to recognize

the conceptual consequences of QM principles, on the other it offers a very limited insight into

the potential of the theory. It is therefore fundamental to generalize the results, also recovering

the cultural contribution of the historical debate that led to the birth of QM, bringing out the

role of QM in developing new technologies.

The research on teaching / learning QM has achieved some shared results regarding the

sustainability of teaching QM at high school, the importance of linking phenomenology and

theory through active use of the real and simulated didactic laboratory. It highlighted the serious

obstacles to the construction of quantomechanical concepts created by using semiclassical

models from the quantum world. These are generalized results that make it difficult to be a

historical approach in school. The difficulties that students highlight following other

approaches, for example regarding the concept of state or the impossibility of attributing a

trajectory to quantum systems, indicate that the research is far from over. Much work must also

be done to identify which aspects to prioritize when teaching QM in high school. In particular,

the potential and limits of content choices must be studied: more oriented towards the peculiar

aspects of QM and breaking with classical concepts, as has happened mainly in continental

Europe; more careful to consider the aspects of continuity between classical physics and

quantum theory, also through the potential offered by the use of computers, as seen in the

Anglo-Saxon world.

66 | Michelini M., Stefanel A.

Appendix

Table A. Comparison of 12 educational proposals on QM discussed in the literature and tested

in high school, regarding the extension and role (blank: absence; 1: marginal; 2: extensive; 3:

central) of the issues selected from papers presenting the different approaches.

Chapter 3 | 67

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76

Chapter 4

Introducing Einsteinian Physics in High School and

College

Irene ARRIASSECQ National Council for Scientific and Technical Research (CONICET).

ECienTec, Facultad de Ciencias Exactas,

Universidad Nacional del Centro de la Provincia de Buenos Aires, Argentina.

Ileana M. GRECA Department of Specific Didactics, Universidad de Burgos, Spain

Abstract: This chapter reviews various proposals for teaching Einstein’s special and general

theory of relativity in high school and college introductory courses and proposes two teaching-

learning sequences for the last years of high school. They have been designed following a

contextualized approach, within a theoretical framework that considers epistemological,

psychological, and didactic aspects. It presents the teaching materials produced and some

results from implementation in real classroom settings.

1. Introduction

Research has shown that although students are motivated and interested in relevant ideas from

the special theory of relativity (STR) and the general theory relativity (GTR), they have great

difficulty in understanding the core concepts of these theories [1, 2]. Moreover, limited training

of high school teachers in this subject leads them to use the same textbooks they recommend

to their students [3, 4] as their main resource. This aspect is important because, if teachers have

not had the opportunity to analyze STR concepts in depth during their training, they will find

it difficult to learn them from the textbooks they usually consult which deal with these theories

very superficially and sometimes wrongly. At university level, although teachers are well

qualified to teach this subject, there is no variety of didactic material, as most textbooks are

based on just two proposals [5], as we will discuss below.

In addition, the area of research in physics concerning STR and GTR teaching—dealing

with either students´ and teachers´ conceptions and difficulties, or with new approaches and

teaching materials—is scarce compared, for example, with another subject as old,

revolutionary, complex, novel in its time, and relevant, as quantum mechanics. A simple search

in any database shows that, in terms of published articles, research in STR or GTR didactics

barely totals a third of quantum mechanics didactics.

Therefore, two teaching-learning sequences (TLS)1 were designed from a contextualized

perspective in terms of epistemological, psychological, and didactic aspects [6–8], with which

we have been working for more than a decade. These materials present a discussion of the

relevant conceptual aspects of the STR and the GTR. They have been designed to help students

to understand the profound changes that these theories have made in physics itself and beyond

this science.

In this chapter, we first review the main strategies for approaching the STR and the GTR

that have been published internationally and then present the TLSs, describing their structure

and analyzing some of their activities. It should be noted that although these TLS have been

developed to be implemented in high school, they can be used to introduce the STR and the

GTR at undergraduate level.

Chapter 4 | 77

2. Different strategies for teaching the special and the general theory of relativity

The visions that have shaped teaching on relativity derive from the opposing proposals for

teaching the special theory of relativity (STR) in college introductory courses that appeared in

Resnick's [9] and Taylor and Wheeler's [10] books [5]. As previously mentioned, given the

scarcity of textbooks specially written for high school, these two books also guide the

presentations in high school textbooks [5, 11]. Resnick presents the STR following a historical

approach, which emphasizes the physical significance of the relativistic effects and their

empirical corroboration. Taylor and Wheler, on the other hand, move beyond the historical

aspect and present a formal development of the STR that emphasizes the geometrical

formulation using Minkowski diagrams. It should be noted that neither of them—nor the

didactic texts inspired by them—consider the difficulties faced by students when first

confronted with the STR and the GTR [11].

Therefore, as for other topics in Physics, a range of strategies have been proposed in an

attempt to improve the STR and/or the GTR teaching-learning process. We are presenting,

below, a brief selection of strategies that have been published since 1990 in journals included

in the Web of Science database, organized according to their aim of improving class

explanations, any possible demonstrations, and/or the types of representations [12]. Although

what we present is not an exhaustive compendium, we consider that the selection is

representative of the types of strategies designed to introduce the STR or the GTR at high

school and university.

Proposals to improve how relativity is explained in introductory courses can be divided

into four strategy types: using one or more concepts as the central axis for presentation, using

examples of paradigmatic "objects", presenting the content in a way that students do not feel is

"strange", and finally, introducing the relativity content from a perspective that considers

historical and/or philosophical aspects. Thus, for example, Sandin [13] argues that the concept

of relativistic mass should be used as the central aspect of teaching the STR because it brings

consistency to introductory courses. Karam, Cruz & Coimbra [14], starting from common

misconceptions, put into practice a strategy to improve students’ concept profile of time to

incorporate the notion of relativistic time.

Concerning the use of paradigmatic models, linked to teaching the GTR, two proposals

stand out: Ehrlich’s [15] strategy on the discussion of tachyons, given their speculative and

controversial nature, and Muller’s [16] focus on wormholes.

To reduce the "distortions of perception" students experience when faced with the STR,

Dimitriadi and Halkia [17] propose a non-mathematical introduction, which avoids presenting

the phenomena as odd and strange and terms considered difficult to understand or confusing,

and which is based on simple examples that can be justified using the two axioms of the STR.

There are many wide-ranging proposals using elements of the history and/or philosophy

of science (HPS) and, in most cases, their use is relevant not only for conceptual understanding

but also for contextualizing and understanding the production of scientific knowledge. Levrini

[18, 19] proposes presenting the idea of relativity through the different ways in which the

concept of space can be viewed. She stresses that although the geometrodynamic interpretation

of the GTR is widely accepted by physicists nowadays, since the assumption of a real space

introduces a strong criterion for interpreting the basic principles of the GTR, the STR is still

usually taught as the theory which overthrew Newton's absolute concepts, including the idea

of a substantival space. She argues that it would be interesting to present the original view of

the STR proposed by Minkowski, which could be considered a substantivalist interpretation of

the STR and, consequently, the key to building a consistent substantivalist line running from

Newtonian mechanics to the GTR. Guerra, Braga, and Reis [20] suggest discussing the

relationship between science and other cultural productions to help students reach a more

78 | Arriassecq I., Greca I.

meaningful understanding of how knowledge is built and therefore, a better grasp of the

questions and solutions presented by Albert Einstein in his works. One last example of this

kind of teaching comes from Provost and Bracco [21], who suggest using the explanation of

the perihelion shift of Mercury, an interpretation which was a major success for Einstein in

1915 and which allows a critical discussion of ideas about physics that have contributed to the

genesis of the GTR.

With respect to demonstrations, due to the very nature of the possibilities of performing

relativity experiments, stand-out proposals include thought experiments (TEs) and laboratory-

assisted ICT tools. Valentzas and Halkia [22] used Einstein's elevator and Einstein's train TEs

as tools for teaching basic concepts of the STR to upper secondary school students. Wegener,

McIntyre et al [23] developed and evaluated game-like virtual reality software, Real-Time

Relativity, which simulates a world obeying special relativistic physics and is used as a virtual

laboratory.

Finally, several researchers have worked on developing and evaluating different types of

representation that might be useful for enhancing students' understanding. These include

geometric tools, conceptual schemes, analogies, metaphors, and ICT-based tools. As an

example of geometric tools, Zahn & Kraus [24] propose the use of sector models, which allow

curved space to be described similarly to approximating a curved surface by plane triangles.

They developed several sector models for high school and undergraduate students, for example,

to introduce the notion of curved space using sector models of black holes. Kneubil [25] uses

conceptual schemes, which emphasize visual patterns of knowledge organization, to discuss

transformations in the meaning of the concept of mass between classical and relativistic

theories.

Regarding the use of analogies, Prado, Area et al [26] explore some analogies between the

STR and geometrical tools developed by the ancient Greeks. As an example, they solve the

kinematics of one-dimensional elastic collisions with ruler and compass constructions on conic

sections. Exploring the role of metaphors for teaching the GTR, Kersting & Steier [27] studied

how conceptual metaphors found in the literature led students to conceptions of gravity that

differ from what is accepted scientifically. Thus, they developed a teaching sequence that states

the strengths and weaknesses of the rubber sheet analogy and addresses students' conceptual

difficulties, aiding teaching of the GTR.

Finally, in recent years, there has been a notable increase in the development of ICT-based

tools—simulations, games, and virtual reality films—to help students think about the true

observational consequences of, for example, length contraction and time dilation, which can

help to sharpen the understanding of these effects. Kraus [28] outlines the use of interactive

simulations that adopt the first-person point of view, allowing observation and experimentation

with relativistic scenes. Sherin, Tan & Kortemeyer [29] present an open-source toolkit for

simulating the effects of the STR within the popular Unity game engine. In their game, the

player only operates in the first-person view and therefore the scene cannot be viewed from

any other frame of reference. The authors stress that their toolkit considers that what would be

measured is not what would be seen: due to the finite time that it takes light to go from the

source to the observer, length contraction does not necessarily make objects appear shorter, as

Lampa [30] discovered and many textbooks wrongly state or implicitly discuss. Finally, Van

Acoleyen and Van Doorsselaere [31] developed a virtual reality film that takes students on a

boat trip in a world with a slow speed of light, in the spirit of George Gamow's The adventures

of Mr. Tompkins [32]. They show different relativistic effects (length contraction, time dilation,

Doppler shift, light aberration) that come up during the boat trip. The immersive 360°

experience allows students to specifically discuss the directional dependence of the effects.

In the next sections we present our teaching proposals for STR and GTR, that combine

some of the strategies described here: conceptual emphasis; the use of the history and

Chapter 4 | 79

philosophy of science; selected concepts as the central axis for teaching; examples of

paradigmatic "objects"; thought experiments; and geometric and ICT tools.

3. Teaching Learning Sequence for the STR

3.1. Theoretical framework

Our proposal assumes that elements from history and philosophy of science, psychology, and

didactics must be considered to develop a TLS. A contextualized approach makes it possible to

determine the epistemological obstacles used to select relevant teaching content. This kind of

approach can also be used to discuss production of scientific knowledge, the role of the socio-

cultural context in which the knowledge is produced, and its repercussions inside and outside

the scientific sphere, to generate students' interest in science [33, 34]. It should also include a

strong conceptual emphasis on the topics addressed, which is essential for the historical-

epistemological discussions to make sense. This perspective favors the achievement of

curricular proposals which focus on training scientifically literate citizens who should construct

knowledge of and about science during schooling.

The epistemological axis aids selection of the fundamental scientific ideas that students

should meaningfully learn about the scientific topic in question. Because of its emphasis on the

epistemological obstacles that must be overcome to understand a scientific theory, we focused

on elements of Bachelard's [35] epistemology. Epistemological analysis of the STR content

based on this framework [36] allowed us to delimit the concepts to be learned by the students:

space, time, frame of reference and its associated notions of observer, simultaneity, and

measurement, which are indispensable for the relativistic understanding of space-time.

According to Bachelard's notion of obstacle, if students are to meaningfully learn the concept

of time, then they must review the notion of time in classical physics, from which the relativistic

notion is developed.

The psychological axis considers the principles used by students to conceptualize and learn

content in a classroom situation, as well as the role of the teacher in this process. To this end,

we synthesized several perspectives, Vergnaud [37], Ausubel et al. [38], and Vygotsky [39], to

be used as complementary theoretical frameworks. Our main hypotheses were as follows:

- Conceptualization is at the core of cognition. Cognitive processes and students’ responses

depend on the situations they meet. As they progressively master the situations, they shape their

knowledge. Such knowledge is relevant for conceptual analysis of the situations used by

students to develop their schemata.

- To achieve meaningful learning, students must be willing to learn and have the

appropriate subsumers for the situations being presented.

- In the school environment, the teacher is the main mediator for the acquisition of accepted

meanings in science, by mastering different instruments, signs, and sign systems from those of

the learner. Teaching takes place when students and teachers can share meanings. Thus, the

teacher has the essential role of mediator, facilitator, and regulator of situations that allow the

student to internalize instruments, systems, and signs that belong to the social language of

school science.

- The meaningful learning that can be achieved in class is highly conditioned by the type

of interactions fostered between students and teachers and among the students themselves,

stimulating the exchange of accepted meanings within the students' zone of proximal

development.

In the didactic axis, we included the choices about the specific sequencing of TLS, such

as determining objectives and activities to achieve them. Regarding the objectives, we used

Martinand's [40] conception of objective-obstacle. He argues that the objectives of science

80 | Arriassecq I., Greca I.

education cannot be defined a priori and independently of the students' representations but must

be based on the intellectual transformations that occur when overcoming a given obstacle.

Therefore, it is necessary to analyze, among all the existing or possible obstacles for a given

object of study, those that seem most surmountable for a given level and context, according to

the students' representations.

3.2. Design and description of the proposal

To develop the TLS on the STR, we carried out a series of preliminary studies, such as a

historical and epistemological analysis of the STR and the textbooks, and studies related to

teachers' difficulties and students' representations.

The proposed TLS consists of five stages. The first stage is a historical-epistemological

analysis of issues related to the notion of science, characteristics of scientific work, the

evolution of ideas in science, influences of the social, historical, and cultural context on the

emergence of scientific theories, and the validation of these theories. The second stage

thoroughly reviews the concepts of classical mechanics that are necessary to interpret the STR,

as well as any substantially modified by the STR and that constitute the epistemological

obstacles for acquisition of new concepts. The third stage deals with the concepts of

electromagnetism that conflict with classical mechanics and were taken up by Einstein. The

fourth stage discusses the fundamental aspects of the STR, starting from the original 1905

article and using various situations to help students develop new mental schemata, because

they face situations that require reformulation of classical concepts. The fifth part aims to

introduce students to some aspects of Albert Einstein's life as a man, transcending the "myth"

[41].

Based on the hypotheses of the theoretical framework, we designed, sequenced, and

evaluated activities to complement the conceptual explanation. These activities include

qualitative and/or quantitative problem-solving and the famous paradoxes, sequenced in

increasing order of difficulty. The key concepts of the STR are incorporated at different stages

of the TLS, using several representations (linguistic, algebraic, and graphical). Other activities

proposed are reading articles and creating stories, comics, and concept maps. Regarding the

reading, this comprises original texts for students to work on in class with the help of the

teacher, and texts by specialists on the history of physics, dealing with conceptual issues that

have had repercussions in non-scientific fields, such as art. This TLS takes the form of written

material to be used by teachers. It has the structure of a textbook, with five chapters following

the sequence described above.

To set out the expected outcomes clearly so that teachers could easily evaluate them, we

considered the perspective of teaching for understanding [42]. According to this perspective,

understanding is the ability to use what one knows when acting in the world, extending,

synthesizing, and applying that knowledge in creative and novel ways. Thus, analyzing

students’ understanding requires ongoing diagnostic assessment of their performance, through

tasks such as explaining, interpreting, analyzing, relating, comparing, and making analogies,

which differ from other common classroom activities.

Activities are therefore only considered comprehension performances if they are

elaborated on and demonstrate that students have reached important comprehension goals.

These expected performances, based on what teachers can observe, will be indicative of

achieving the goals. Table 1 presents the comprehension goals for learning the STR and those

that the learner should have previously achieved, plus the proposed comprehension

performances.

Chapter 4 | 81

Table 1. Comprehension goals and performances

Comprehension goals

Comprehension performances

• Discriminate between the concepts of

distance travelled and position.

- Decide on the concepts necessary to

describe the motion of an object.

• Establish meaningful relationships

between the concepts of observer,

reference system, measurement process,

and instruments.

- Construct a concept map with a personal

synthesis of fundamental concepts for

understanding and solving problems in

classical mechanics, such as the following:

invariance and independence of space and

time, the impossibility of defining an

absolute frame of reference, and the notion

of simultaneity.

• Analyze the conceptualizations of space

and time they have constructed and

compare them against the major

approaches to these concepts throughout

the history of science.

- Draw a concept map interpreting the

phenomena linked to electromagnetism,

those explained by the theories of the time

and those that raised problems.

• When analyzing motion, recognize the

need to consider the frame of reference

with respect to which something is said to

be moving.

- Interpret a drawing representing motion

from the perspective of two different

observers.

• Recognize the need to use transformation

equations when solving a problem that

requires information from different frames

of reference.

- Analyze the invariance of concepts such as

"space" and "time" in different frames of

reference at relative rest.

- Distinguish phenomena that require a

relativistic interpretation from those that

are explained by classical theories.

- Choose appropriate frames of reference to

solve problematic situations related to the

STR.

• Identify concepts relevant to making

measurements, primarily of space and

time, from different frames of reference.

- Critically read the introduction to the

article published by Einstein in 1905 in the

prestigious German journal Annalen der

Physik under the title: On the

electrodynamics of moving bodies.

• Discuss notions such as "synchronization"

and "simultaneity" and link them to the

need for observers to have the appropriate

means of communication.

- Explain in different ways how they

interpret, based on their readings and

discussions with their peers and the

teacher, the two postulates of the STR and

compare them with other concepts

analyzed in Newtonian mechanics, for

example, frame of reference or unresolved

questions at that time, such as the "ether

problem".

3.3. Implementation and review of the proposal

The TLS was implemented twice, with students in the last year of high school in Argentina. In

the first implementation, we worked with a group of twenty-seven students, in two one-hour

classes per week. During the classes, the students carried out the various activities included in

the didactic proposal, such as readings and text analysis, debates, comics, concept maps,

exercises, and problems. In the evaluation, it was observed that the central ideas, the objectives,

and most activities were adequate. However, the students showed difficulties in understanding

the space-time concept, which involves the concepts of simultaneity, proper and improper time,

and proper and improper length. Although we presented several situations that required

82 | Arriassecq I., Greca I.

analysis and/or construction of Minkowski diagrams to explore these latter concepts, working

with these pencil and paper diagrams was quite complicated and time-consuming. Therefore,

in the second implementation, students worked with interactive Minkowski diagrams using

applets, which facilitate conceptualization by making qualitative and quantitative estimations

(Fig. 1 and Fig. 2).

Figure 1. Opening of train doors observed from a frame of reference

located in the middle of the train

.

Figure 2. Opening of the train doors observed from a frame of reference

outside the train

Below, we provide examples of how students worked on the following activities:

Activity 4: A passenger on a train, with constant speed relative to an inertial frame of reference

located at the midpoint of the carriage, switches on a lamp and the beam of light travels towards

the walls where two doors, P1 and P2, are located. The train has a mechanism that ensures that

a door opens when the light hits a wall. The train is travelling at a speed of 0.5 c.

Chapter 4 | 83

a) Using algebraic operations, establish the possible simultaneity of the door openings for

observers located inside the carriage (O') and another (O) on the train platform, for the case

where the train speed is 0.5 c.

b) Using space-time diagrams, establish the simultaneity of the events.

Solution for (b)

84 | Arriassecq I., Greca I.

Activity 5: Represent the history of a quasar using a space-time diagram for events occurring

in two spatial dimensions plus the time dimension. Describe the absolute past, present, and

future of the event.

3.4. Some results

The results obtained in the first implementation show that most students managed to achieve

the objectives related to classical mechanics, such as interpreting time and space and analyzing

these concepts from a philosophical and scientific perspective, considering the need to establish

a frame of reference to solve problems that involve the concept of motion, and analyzing the

close relationship between observer and measurement process. As far as the STR-related

concepts are concerned, the students were able to recognize the concept of length contraction

although they were unable to solve the problem. They also achieved the objectives related to

historical and epistemological aspects. In particular, they were able to see that the STR is a

theory with sufficient experimental verification, and were able to explain its technological

applications, such as the Global Positioning System (GPS).

Chapter 4 | 85

The results from the second implementation [43] show that most of the comprehension goals

were achieved, in particular those related to classical mechanics (differentiation of the concepts

of trajectory, distance traveled and position, analysis of the concepts of space and time,

simultaneity of events, use of transformation equations in inertial frames of reference, and

interpretation of the incompatibility of classical mechanics with aspects of electromagnetism)

and others related to the STR (determination of time dilation and length contraction occurring in

proper and improper systems, application of the Lorentz transformation equations to the

calculation of velocity in different frames of reference, and calculations to determine the

simultaneity of events). On the other hand, using the applets allowed students to understand and

make meaningful use of Minkowski diagrams to represent space-time events.

In terms of comprehension performance, most students performed well or very well in

most of the proposed activities. Particularly noteworthy was their understanding of inertial

frames of reference and their interpretation of events from the perspective of different

observers, their interpretation of the Michelson-Morley experiment, the resolution of activities

that involved interpreting and relating the postulates of the STR, the use of Minkowski

diagrams to establish the simultaneity of events in different inertial reference systems, and their

understanding of the different experimental verifications, applications, and repercussions of

the STR. On the other hand, the most difficult comprehension tasks were related to the selection

of appropriate coordinate systems, use of transformation equations to represent motion from

different frames of reference, problem-solving using transformation equations between frames

of reference or using the Lorentz transform to calculate velocities of objects in different frames

of reference, and algebraic problem-solving that involves establishing the simultaneity of

events in different inertial frames of reference.

4. TLS for teaching the GTR

Understanding new scientific knowledge in cosmology and astrophysics over the last decade,

constantly reported in the mass media, requires a deep understanding of GTR concepts—for

example, the expansion of the universe, dark matter, black holes, and the measurement of

gravitational waves. The latter topic, which constitutes a new empirical verification of the GTR,

received wide media coverage in several countries, where time and effort was devoted to

spreading the news of the first measurements. Astrophysicists tried to explain this finding to

the public, why it so shocked the community of physicists and astronomers, what it implied for

science and beyond science, not least for the perspective of the nature of science, and why it

took a hundred years to detect these waves from the time they were predicted by Einstein. The

news reached schools, and students from all around the world showed interest in the subject

[44]. Many of them were also interested in films such as "Interstellar" and consulted their

teachers about physics concepts mentioned in the film. Some recent Korean high school

textbooks mentioned the film [44].

If it is considered relevant to teach the GTR in high school, the next question is how to do

it. Historically, the GTR has not been taught, not even at university level, because it has been

considered extremely difficult. The GTR is based on concepts of differential geometry, often

expressed in the language of tensor calculus. In other words, it requires the use of a more

complex level of mathematics than most undergraduate students can handle.

However, Christensen and Moore [45] argue that almost all undergraduate GTR texts

published in the 21st century move away from the mathematical approach and focus on

conceptual physics. This type of text follows the trend called the physics-first approach. This

approach was proposed by Hartle [46], and his text Gravity is the most representative of its

kind. It addresses the main concepts of the GTR at a mathematical level that does not go beyond

86 | Arriassecq I., Greca I.

the first and second year of undergraduate courses. Two aspects of the book stand out: many

examples of astronomical and cosmological phenomena and the emphasis on physical

concepts, without the need to use mathematics in an initial approach.

Although the physics-first approach has only become widespread at university level in

several countries, we believe that it can be implemented in high school classes if it is

approached within an adequate theoretical framework. Based on assumptions like those

described above for the design of the TLS on the STR, we have developed a similar project for

teaching the GTR in high school.

4.1. Design and description of the proposal

To identify the most relevant GTR concepts to be dealt with in high school, we analyzed the

current curricular designs in several countries, as well as the books Gravity and the popular

text 100 years of relativity [47], written by astrophysicists interested in disseminating the GTR

beyond the scientific sphere.

We also considered the results obtained in a survey answered by students in their last year

at a state high school in Argentina, after having dealt with the subject of gravitation and having

seen the film "Interstellar".1 This survey aimed to identify, among other aspects, which GTR

concepts addressed in the film interest students most, and determine which concepts of classical

mechanics students require to meaningfully understand GTR concepts.

The topics this analysis identified as relevant were: the principle of equivalence, curved

space-time, the relationship between gravity and time, the relationship between matter and

space-time, GTR empirical contrasts, black holes, gravitational waves, cosmological models,

and technological applications. The proposed comprehension goals for the GTR are presented

in Table 2.

Table 2. Comprehension goals for the GTR

1.– Interpret the principle of equivalence.

2.– Analyze basic aspects of non-Euclidean geometries.

3.– Characterize curved space-time

4.– Determine the relationship between gravity and time

5.– Determine the relationship between gravity and space

6.– Identify the relationship between matter and space-time

7.– Interpret the meaning of black hole.

8.– Recognize the variation of time in the vicinity of a black hole.

9.– Interpret the concept of gravitational waves.

10.– Analyze the different GTR empirical contrasts.

11.– Interpret different current cosmological models.

12.– Reflect on the different technological applications of GTR

13.– Interpret journalistic information linked to the GTR

14.– Debate on the GTR empirical testing process

15.– Investigate the role of female scientists in the GTR empirical verification process.

1 The film "Interstellar", released in 2014, addresses several physics issues (black holes, wormholes, time

dilation, gravitation, tides, etc.). It engages students, with special effects that led the film to win an Oscar. It was inspired by the work of Kip Thorne, one of the most renowned experts on the applications of the GTR to astrophysics, and the scientific consultant for the film. He wrote the book "The science of Interstellar", in which he uses scientific rigor to develop all the calculations necessary to simulate the visual effects of the physical phenomena involved in the story. In October 2017, he received the Nobel Prize alongside Weiss and Barish for their work on the LIGO Project to detect gravitational waves.

Chapter 4 | 87

Regarding how to promote understanding, we propose the use of popular documentaries,

newspaper articles with information on relevant scientific advances that directly or indirectly

involve aspects related to the GTR, computer simulations, science fiction books, and films that

deal with the subject, among other resources that are generally interesting for most students.

To exemplify our proposal, we selected the topic of gravitational waves. Table 3 shows the

goals and comprehension performances identified for this specific topic.

Table 3. Comprehension goals and performances related to gravitational waves.

Comprehension goal

Comprehension performance

• Interpret the concept of gravitational

waves.

- Differentiate the concept of gravitational

waves from the other types of waves

discussed in the workshop.

• Analyze the value of gravitational wave

measurements as a GTR empirical

contrast.

- Identify the experiments that made it

possible to test the GTR.

• Interpret journalistic information related to

gravitational waves.

- Solve the tasks proposed in the didactic

sequence.

• Discuss the process of gravitational wave

detection.

- Formulate specific questions for

interviewing scientists specialized in the

detection of gravitational waves.

• Investigate the role of female scientists in

the process of measuring gravitational

waves.

- Interview women in science (preferably

linked to the subject of gravitational

waves) and identify the main difficulties in

their work, or for their female colleagues,

just because they are women.

• Analyze the reasons why three scientists,

out of the more than a thousand

participating in the LIGO project, were

awarded the Nobel Prize for detecting

gravitational waves in 2017.

- Solve the tasks proposed in the didactic

sequence.

As previously mentioned, high school physics textbooks that incorporate topics related to

the theory of relativity are few and far between. It is even rarer to find teaching material for the

specific topic of gravitational waves. For example, Hewitt's text Conceptual Physics [48]

devotes half a page to this topic. In contrast, there are abundant academic and popular

publications about gravitational waves, especially since their first detection announcement in

February 2016. On the internet, we can find lectures by experts at various universities,

interviews by specialized and non-specialized journalists with scientists working on the

subject, material produced by popularizers, digital material produced by members of the LIGO

Project itself, and popular videos.

For this reason, we have made special use of this material in our design. As there is so

much material, we used the following selection criteria: the source (mass-circulation

newspapers and periodicals, science channels of ministries of education or educational bodies);

the communicators (interviewees should be either scientists who are experts in the subject or

renowned popularizers); the style of communication (attractive and not too lengthy format,

such as a TED talk or interviews with scientists with a layman’s approach); and supplementary

materials (descriptions of the experiment to detect gravitational waves, modelling and

simulations of concepts linked to gravitational waves, space-time, and black holes).

Five activities were run to fit the determined goals and performances. Activity 1 consists

of questions that seek to reveal the students’ prior knowledge on the subject (What other

88 | Arriassecq I., Greca I.

scientific concepts are gravitational waves related to? How are they generated? Is it important

for science to detect them? Why? What facts might indicate that it is important for science to

study gravitational waves?), the information sources they usually consult, and their interest in

the subject. This first activity begins by considering aspects of the nature of science, such as

who first proposed the existence of gravitational waves and in what context, how they are

studied, the importance of studying them, the role of women in the study of this phenomenon,

and the importance given to their detection in the media.

Activity 2 reviews the main characteristics of wave phenomena, which they have already

studied, to subsequently distinguish which aspects of gravitational waves also have these

characteristics. Activity 3 is introduced using newspaper headlines and screenshots of various

television programs from the day of the report of the first detection of gravitational waves. In

the same way, participation of an Argentinean scientist in the LIGO project is highlighted;

information is presented about three scientists being awarded the Nobel Prize in Physics one

year later for their work related to detecting the waves, plus headlines about subsequent

detections. After the introduction, short videos are analyzed. Some of them are interviews or

talks: a TED talk by Dr. Gabriela González, Argentinean scientist and spokesperson for the

LIGO project; another TED talk, discussing the implications of the detection of gravitational

waves in depth; two interviews with the same astrophysicist, one on a television news program

by a non-science journalist and the other by a scientist; and an interview with an internationally

recognized science communicator. The remaining videos correspond to an explanation of

physical phenomena related to the gravitational wave: gravity as a space-time warp, black hole,

black hole collision, and light bending in strong gravitational fields. As a complement, a series

of popular articles are provided on the meaning of gravitational waves, the importance of their

detection, the LIGO project, and the implications for astronomy.

In Activity 3, students should use the journalistic material to identify the concepts they

consider most relevant and any they do not know. Then, they must reanalyze the instructions

from Activity 1 and try to answer them. This activity emphasizes aspects linked to the way

knowledge is produced and topics related to epistemology: what it means that gravitational

waves are a "prediction by the general theory of relativity"; what the phrase "Einstein was

right" means, as so often mentioned in the media; why scientists continue to measure

gravitational waves after the first finding. In the final point of the activity, students are asked

to assess the materials used, videos, and articles, in terms of their interest in the topic, or the

lack thereof, and the material’s potential to help them understand the physical phenomena.

Activity 4 focuses on other aspects of the Nature of Science linked to the sociology of

science in general, and gender issues in particular. Students should investigate and discuss,

based on reading three articles and any other sources they may choose to consult, what the

Nobel Prize is and how important they think it is; what other types of prize they would compare

it to, outside the scientific field; which country has won the most Nobel Prizes and what the

reason for this might be; their opinion regarding how few women have won this prize; if they

consider that it is more difficult for women to dedicate themselves to scientific work; and why

the 2017 Nobel Prize in Physics was shared by three physicists and not awarded to only one

person.

Finally, Activity 5 requires students to build a concept map that answers the focus question:

Why is detecting gravitational waves important for science and society? We chose to use this

powerful metacognitive tool because it has proven to be a very powerful instrument for sharing

and exchanging meanings over the decades. In addition, the exchange of meanings displayed

on the concept map is a further instance of learning and evaluation of what has been understood.

The didactic sequence is set out in a written document, which includes the readings and videos.2

4.2. Implementation of the proposal and some results

Chapter 4 | 89

The didactic sequence was implemented in a workshop called "Waves" for students majoring

in natural sciences, who were in their fifth year at a high school run by the university, in the

city of Tandil (Argentina) during 2018. This is a two-hour weekly course, and at the time of the

study it was attended by twenty-three students. The results of this first implementation are

encouraging in terms of student comprehension; they show the students have achieved the

proposed goals for learning the generative topic of gravitational waves, as well as

epistemological and sociological aspects of the nature of science. However, it would be

necessary to extend the allotted course time, to allow for further debate in the classroom. With

regard to the didactic proposal, given the students are meeting concepts such as space-time for

the first time and need more time to grasp their meaning, an instruction was incorporated for

Activity 2: after Activity 3, they have to rework their answers for Activity 2.

5. Conclusion

The STR and the GTR generate public interest and have scientific relevance inside and outside

the field of physics. They have led to numerous applications in daily life, such as GPS or LCD

screens. Therefore, it seems relevant to introduce these theories at high school and college.

Nevertheless, their presence in textbooks and research in physics education is still scarce. Some

promising proposals have been developed, for example, emphasizing conceptual aspects and

reducing mathematical burden, or drawing on the history and philosophy of science. Other

promising approaches are related to the increasing development of ICT-based tools—

simulations, games, and virtual reality films—to help students think about the true

observational consequences of both theories.

In this chapter, we presented two TLSs and their materials, which delve into topics of

physics that, despite their importance, have not been sufficiently investigated in physics

teaching. The materials have proved very useful to teachers with no undergraduate education

or specific training in the subject, who have used them in high school as the main resource in

their first approach to both the STR and the GTR.

We are convinced that it is possible to introduce elements of these theories at high school

and university level using the materials we have developed, despite lack of teacher training and

limited time. This approach seems not only to benefit students in the sense of bringing them

closer to more "current" physics, but also to allow them to review and better understand

classical physics concepts that go unnoticed in traditional teaching, such as the concepts of

time, space, frame of reference, observer, simultaneity, and measurement.

In the twenty-first century, physics has been revolutionized by validation of theories that

are already a century old. The media devote time in some cases, and space in others, to

disseminating this progress. Students are often enthusiastic about these topics, which are often

covered by films or science fiction novels. Although sometimes such material has strong

scientific backing, at other times the emphasis is more on fiction than science, as these are

cultural products for entertainment rather than education. For those who are interested, there

are no bounds to the possibilities of accessing this information. The formats are very varied:

interviews with specialists, short informative videos, longer documentaries with technicalities

that require previous scientific knowledge, as well as popular ones. Notwithstanding this

available material and huge student interest, in high school physics classes we only deal with

a few topics from the beginning of the twentieth century at best.

It is a fact that most of us teachers lack training in this topic and teaching on texts that deal

with contemporary physics is scarce. It is also true that with only the teachers’ will, the students’

enthusiasm, and the randomly chosen popularization materials without adequate didactic

transposition, it is unlikely teachers will be able to convey certain concepts successfully. At

90 | Arriassecq I., Greca I.

best, students will be able to describe the phenomenon in question but will be unable to

understand the concepts involved. In this chapter, we have presented theoretical and

methodological guidelines, used to develop the didactic sequences and the guides for teachers

and students. They were developed within a theoretical framework that considers it relevant to

address the conceptual aspects of the content plus the epistemological, psychological and

didactic aspects, making it possible to implement these sequences at high school and

undergraduate levels.

Notes

1. Both TLSs are available in Spanish.

For STR at https://drive.google.com/file/d/1jT7BUYoLu6GG3EVPSB0M4gbNx9Xf0T3a/view?usp=sharing

And for the GTR at https://drive.google.com/file/d/1F5RnF78igxUeS_hDAliQwWBDm052iL4h/view?usp=sharing

2. All this material is available in Spanish.

The TLS at: https://drive.google.com/file/d/17Qt3lOh1CVx4EOduDfAbmx_lUC40Zmy_/view?usp=sharing;

The readings at: https://drive.google.com/drive/folders/14cEpekIquSs0L7ws01-9L4_1eYYx6AaU?usp=sharing

And the videos at: https://drive.google.com/drive/folders/1MwP7_-DVRNIk9UCijTGJuoA-R3cnCPM2?usp=sharing

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Part III

Students and teachers as learners in Physics

94

Chapter 5

Research-guided physics teaching: foundations,

enactment, and outcomes

Stamatis VOKOS California Polytechnic State University, San Luis Obispo, CA 93407, United States

Lane SEELEY Seattle Pacific University, Seattle WA 98119-1997, United States

Eugenia ETKINA Rutgers University Graduate School of Education, New Brunswick, NJ 08901, United States

Abstract: In this chapter, we discuss research findings and provide recommendations for what

physics teachers need to know and do, so that they may engage their students in learning

physics by practicing it, and may improve their students’ well-being in the process. To

empower students’ epistemic agency, teachers need to create an inclusive classroom in which

every student grows intellectually and emotionally, and develops a robust physics identity.

Research on teacher knowledge and behaviors indicates that the foundation of such teaching

lies in teacher dispositions and strategic enactment of content knowledge for teaching physics.

But these are not enough. Only when teachers develop productive habits, can they enact

faithfully the everyday Tasks of Teaching, which lead to all students being engaged in “doing”

physics and also feeling capable of doing so.

1. Introduction to the chapter

Recent national and international calls for STEM education at the secondary level stress the

need for engaging students in the learning of the subject by experiencing the subject as

professionals do. This means that physics should not be taught as a finished body of

precompiled physics concepts and principles but that students should infer such principles

through experimentation, argumentation, hypothetico-deductive reasoning, modeling and other

practices that are germane to the physics enterprise. These calls hearken back all the way to the

late nineteenth century when prominent physicists advocated for similar approaches [1–6].

In this chapter, we discuss research findings and provide recommendations for what

physics teachers need to know and do, so that they may engage their students in learning

physics by practicing it and may improve their students’ well-being in the process. To empower

students’ epistemic agency, teachers need to create an inclusive classroom in which every

student grows intellectually and emotionally, and develops a robust physics identity. Research

on teacher knowledge and behaviors indicates that the foundation of such teaching lies in

teacher dispositions and strategic enactment of content knowledge for teaching physics. But

these are not enough. Only when teachers develop productive habits, can they enact faithfully

the everyday Tasks of Teaching, which lead to all students being engaged in “doing” physics

and also feeling capable of doing so.

We adopt a backward design approach to supporting effective learning of physics. This

design approach focuses on the student outcomes as shown at the top of the Fig. 1.

Chapter 5 | 95

Figure 1. Backwards design structure to support science learning

The Next Generation Science Standards (NGSS) in the US outline three-dimensional

learning outcomes which include disciplinary core ideas, crosscutting concepts, and science

and engineering practices [7]. In addition to these cognitive outcomes, we also identify

affective student outcomes, which include belonging, empowerment, and self-efficacy as

physics learners. Next, we identify Tasks of Teaching as those discipline-specific tasks in which

physics teachers can engage to support the cognitive and affective student outcomes. In order

to enact these Tasks of Teaching, teachers will need to draw upon disciplinary content

knowledge (CKT-D) and pedagogical content knowledge (CKT-P) [8] along with dispositions

regarding learning and learners [9]. Even when teachers possess the knowledge and

dispositions needed to enact effective, discipline-specific Tasks of Teaching, they must develop

the habits of enacting those tasks.

Discipline-based educational research must inform this structure at all levels. Research on

student learning is essential for identifying high-impact pedagogical strategies and associated

Tasks of Teaching. Research on teacher practice provides insight into how teachers develop

habits to sustain these Tasks of Teaching. Research on teachers’ CKT is needed to identify

critical CKT and reveal how teachers develop that knowledge. Finally, research on teachers’

dispositions is needed to identify which dispositions support the habituation of high-impact

Tasks of Teaching. In this chapter, we elaborate details of the structure shown in Fig. 1, describe

recent research, and identify areas where more research is needed.

2. Goals of physics education

Physics education research has a decades-long history of documenting the landscape of

conceptual and problem-solving aspects of the learning process in physics. An explicit focus

on equitable instruction and student agency, however, is much more recent. This new focus is

of paramount importance, especially in view of PER-based approaches that have a manifest

96 | Vokos S., Seeley L., Etkina E.

positive impact on conceptual understanding of a broader population of students, but little to

no impact (and, in some cases, negative impact) on students’ epistemological sophistication or

student affect [10, 11]. Investigating approaches that can simultaneously deepen conceptual

understanding, strengthen scientific abilities, and center student voice is of great import to the

community of physics teacher educators [12–15]. We stress that commitments by the teacher

education community to culturally responsive teaching and social justice writ large are perhaps

necessary but not sufficient guiding principles to inform a repertoire of tangible actions that

physics teachers can enact in the moment, in the fog of complex classroom interactions.

First, we need to examine the discipline-specific tasks that teachers are expected to be

carrying out in the classroom (and to prepare to carry out in the classroom), and then infer

design principles for physics teacher education that helps novice teachers of physics on day 1

(and day 2, etc.). These Tasks of Teaching (TOTs) are the centerpiece of our theoretical

framework, and we describe them below.

3. Tasks of Teaching

Educational policy documents all over the world call for a different vision of science education

in the precollege classroom. For example, in Europe an example of such a document is the

Rocard Report [16], while in the US, such documents are the Framework for K-12 Science

Education and the NGSS [7, 17]. These documents envision students who engage in

worthwhile science investigations and engineering design projects but do not prescribe how

teacher education needs to be shaped to produce graduates with the requisite cognitive and

affective orientations to enact this vision. Physics suffers from additional challenges. For

instance, physics is imbued with the genius myth, whose prevalence tends to anti-correlate with

participation from girls and other members of underrepresented groups in physics, at least in

many international settings [18–20]. Furthermore, physics is often taught in ways that make it

seem intellectually unattainable, exclusionary, and irrelevant to one’s daily life or aspirations.

We argue that learning outcomes also include culturally-relevant physics (and scientific)

understanding and inclusive empowerment and self-efficacy as scientific thinkers. All these

learning outcomes are contingent upon a self-evident causal relationship. Teachers can only

influence the learning outcomes of their students by what they actually do.

For a long time, teacher education was focused on pre-service teachers’ knowledge and

dispositions. Ball and colleagues proposed that to improve classroom practice “the core of the

curriculum of teacher education requires a shift from a focus on what teachers know and believe

to a greater focus on what teachers do” [21] (p. 503).

They put forth an argument that teacher preparation should focus on “detailed professional

training”, i.e., the practice of teaching. Using the concept of the “Tasks of Teaching” coined by

Feiman-Nemser and Remillard [22], they argued that “In practice-focused teacher education,

similarly and by design, teachers would learn to do particular tasks such as creating a respectful

learning environment, assessing students’ math skills, or reviewing homework. They would

learn to do these specific tasks, but they would also develop more general and adaptable skills

of practice through their engagement in these tasks [21].

The work of Ball and colleagues is in the field of mathematics education. To apply the idea

of the Tasks of Teaching to physics, we operationalize them as a wide array of discipline-

specific tasks that exemplary physics teachers actually perform in service of learning outcomes

for their students. Etkina and colleagues [8] conceptualized Tasks of Teaching as activities that

permeate every aspect of a physics teacher’s professional life related to student learning:

planning, classroom instruction, assessment, etc. A full list of the tasks of teaching is published

in [8]; here we list only the coarse-grained categories:

Chapter 5 | 97

1. Anticipating student thinking around science ideas;

2. Designing, selecting, and sequencing learning experiences and activities;

3. Monitoring, interpreting, and acting on student thinking;

4. Scaffolding meaningful engagement in a science learning community;

5. Explaining and using examples, models, representations, and arguments to support

students’ scientific understanding;

6. Using experiments to construct, test, and apply concepts

7. While the above tasks are common to all topics of a physics course, Etkina and

colleagues [8] provided a list of specific actions for each of the tasks that relate to the

teaching of energy. For example, two such actions related to tasks VI are:

8. VI. a) Provide opportunities for students to analyze quantitative and qualitative

experimental data to identify patterns and construct concepts

9. VI. b) Provide opportunities for students to design and analyze experiments using

particular frameworks such as energy, forces, momentum, field, etc.

The above examples show that while the idea of using experiments is rather general for

the learning of physics, the issue of finding suitable experiments that can be analyzed using

different theoretical frameworks such as energy, momentum, and forces is specific to the topic

(say, energy) and requires sophisticated understanding of the physics content and

experimentation to be able to envision and execute such experiments.

Tasks of Teaching should always be in service of discipline-specific learning outcomes but

our understanding of this relationship is continually expanding through discipline-based

educational research. For example, physics education research reveals that learners bring a

wide array of intellectual resources that can serve as a foundation for greater self-efficacy in

physics reasoning (see for example, [23, 24]). These research findings illuminate a number of

Tasks of Teaching by which teachers can build on these resources to help learners leverage

them constructively and rigorously. Some Tasks of Teaching, such as anticipating student

thinking around science ideas and monitoring, interpreting, and acting on student thinking [8]

would look very different or even be irrelevant if we focus primarily on student

“misconceptions,” which the students need to get rid of, or conceptualize students as “blank

slates.”

4. Habits

Even if a teacher knows about productive Tasks of Teaching in which they need to engage

while preparing physics lessons and during classroom instruction, the reality of teaching is that

productive decisions or moves while writing a lesson plan or in the moment during a lesson are

much more likely to be implemented if a teacher makes them habitually [25]. Think for

example of the Tasks of Teaching described above – anticipating student thinking around

science ideas, and monitoring, interpreting, and acting on student thinking. In order to

anticipate student ideas in a particular content area, the teacher needs to habitually read papers

and to engage with the physics community. In order to monitor student thinking, the teacher

needs to habitually focus on what students are saying during the lesson and interpret their

answers [26], not on the basis of the “correct answer” but on the productivity of the ideas

inherent in the responses. Developing and maintaining such habits is an important goal of

teacher education.

Etkina, Gregorcic and Vokos [25], using an Oxford dictionary definition of habits as “a

settled or regular tendency or practice, especially one that is hard to give up”[40], identified

three groups of habits that are necessary for physics teachers to develop and grow

98 | Vokos S., Seeley L., Etkina E.

professionally. These are habits of mind (of a physicist and of a physics teacher), practice, and

maintenance and improvement. The definitions of these three categories and examples of those

are in Table 1.

Table 1. Habits of mind, practice and maintenance and improvement

Habit Description Example Why it is important

Thinking like a

physicist

Spontaneous noticing

and/or thinking about the

relevance and application

of physics concepts in the

world around and in the

context of other

disciplines, such as

chemistry, biology, or

mathematics;

Engaging in reductionist

thinking, categorizing

effects on the basis of

their size, estimating

order-of-magnitude of

effects, etc.

Habitually thinking of

physics as a particular

process instead of a set of

prescribed rules;

Habitually asking a

question: How do we

know this?

Given the ease and safety

of physics experiments

and the quick turnaround

time for obtaining a result,

habitually thinking of

experimental testing of

any idea

Developing this habit

helps with the growth of

scientific (and physics, in

particular) epistemology.

Epistemic knowledge or

the knowledge of how a

discipline develops

knowledge is one of the

most important aspects of

knowledge in the 21st

century [27], especially

because physics teachers

must prepare students to

deal with questions that

we have not even

identified yet.

Thinking like a

physics teacher

Spontaneously paying

attention, questioning and

acting upon student

physics-related comments,

questions, and reasoning

and spontaneously

thinking about the

affordances of every-day

situations for student

learning of physics

Encouraging students to

test their ideas

experimentally instead of

waiting for validation

from authority

Focusing on interpreting

student answers without

focusing on the “correct”

use of language when

students are just starting to

learn a new concept

Developing this habit

helps students engage in

authentic scientific

practices and this develops

their own epistemic

knowledge

Developing this habit

helps thinking about

student ideas as

productive resources on

which to build instead of

“misconceptions” that

should be hammered out

[24].

Chapter 5 | 99

Habit Description Example Why it is important

Habits of practice Taking spontaneous

decisions while lesson-

planning and during the

instructional process that

lead to student learning

and improve student well-

being.

These habits are

intertwined with the habits

of mind and cannot be

clearly separated.

Starting every unit and

lesson with an exciting

“need to know”

connecting student

learning to everyday life.

Setting up the classroom

so that students are seated

in groups, not

individually, and have

small whiteboards to work

together.

Setting up the assessment

procedures so that the

students have an

opportunity to improve

their work without

punishment.

Being strict with student

language once the new

idea has been established.

Developing this habit

helps students become and

stay motivated, and

connect physics to

everyday life [28]

Doing science and

learning science is a

collaborative experience,

and addresses the

destructive myth of the

physics lone genius.

Developing perseverance

and grit in students – the

best predictors of future

success, while defusing

impostor syndrome and

other social threats

Helping students learn by

practicing good language

[29]

Habits of

maintenance and

improvement

Continuous learning of the

teacher as an individual

and as a part of the

community, making the

maintenance of a

professional community a

priority, and actively

sharing new findings with

other teachers

Becoming and staying a

member of professional

organizations, reading

research and practitioner

publications, engaging in

a learning community

Developing this habit

prevents attrition and

ensures that the teacher is

using methods that are

validated by evidence [30]

Each of these habits connects directly to the goals of physics teacher education outlined

above. For example, the habit of “Encouraging students to test their ideas experimentally

instead of waiting for validation from authority” addresses the goal of engaging students in the

practice of science when learning physics and the habit of “Setting up the assessment

procedures so that the students have an opportunity to improve their work without punishment”

addresses the goal of the development of confidence and growth mindset.

5. Content Knowledge for Teaching

Once we have identified discipline-specific Tasks of Teaching that support specific learning

outcomes and are illuminated by discipline-based education research, and decided that their

faithful enactment by a teacher is contingent on the teacher’s habits, a next step is to articulate

the knowledge and dispositions that teachers draw upon in their efforts to develop the habits

and consequently to enact these Tasks of Teaching. Following the work of Deborah Ball, we

approach this question empirically, rather than theoretically. Ball and colleagues [31]

developed a theoretical framework of Content Knowledge for Teaching (CKT) that combines

and deepens previously separated content knowledge and pedagogical content knowledge (or

PCK [32]). Specifically, they proposed that the teachers need to have the knowledge of the

subject matter for each content area (in physics this can be forces, energy, electric fields, etc.),

which consists of the common knowledge (level of students), specialized content knowledge

100 | Vokos S., Seeley L., Etkina E.

(that is important for teachers), and horizon knowledge (that goes beyond the level of

knowledge that the students need to learn). In addition to these three levels of knowledge of

the content, the teachers should possess a PCK that consists of the knowledge of student ideas

for this content area, knowledge of curriculum and knowledge of teaching this specific content.

In order to clarify the elements of CKT, let’s examine the CKT for teaching energy. Common

content knowledge: Energy is a conserved quantity, always constant in an isolated system but

can change in a non-isolated system; however, we can always find a system in which total

energy is constant.

Horizon content knowledge: The role of friction in rolling – static friction force makes an

object roll; therefore, we cannot disregard it, but it is not the reason that a rolling object slows

down; it is conversion of kinetic energy into internal energy.

Special content knowledge: when it is useful to choose a system in which energy is constant

and when it is useful to choose a system on which the environment does work;

Knowledge of students: for the students it is difficult to choose a system and be consistent

with it (double counting), to decide on initial and final states and realize that mechanical energy

is converted to internal and the latter is imperceptible;

Knowledge of content and teaching: there are ways of experimentally detecting and

measuring conversion of mechanical energy to internal; energy bar charts are an effective tool

to help students write mathematical models of energy conservation;

Knowledge of content and curriculum: system is a crosscutting concept in the NGSS, a

consistent approach to energy should be used in all physics topics.

In addition to these forms of knowledge, which together make CKT, a teacher needs to

recognize the important role that epistemic framing plays in learning. Epistemic framing helps

students determine "what kind of activity we are involved in at this instant," which in turn

activates or shuts down resources (most notably rich sensemaking resources). We include

epistemic framing in the cognitive aspects of teacher preparation. See, for instance, [33].

A related concept is epistemic agency, the cultivation of which we also categorize in the

cognitive components of teacher education. Epistemic agency is the act associated with taking

responsibility for one's own learning and progress toward deeper understanding. Epistemic

agency undergirds habit formation and supports the refinement of CKT. See, for example, the

work of Emily Miller and colleagues [34].

6. Dispositions

If CKT components form the cognitive toolbox of physics teachers, it is a teacher’s dispositions

that will determine how, if at all, those tools could be deployed. Following Etkina et al. [25],

we define a disposition “as a strong (often subconscious) belief or attitude related to some

aspect of teaching, that in concert with other factors, shape a teacher’s behavior and thought.”

Dispositions motivate habits, while habitual practice reinforce dispositions, both productive

and unproductive. In a study of science teachers in the context of interactive computer-based

simulations and laboratory inquiry-based investigations in physics, Zacharia illustrated that

“beliefs affect attitudes and these attitudes then affect intentions.” [35] Let’s consider the Tasks

of Teaching associated with anticipating and acting on students’ ideas. A physics teacher may

know that students come to the instructional context with prior ideas, they may also know what

the common productive and problematic aspects of student reasoning might be in a particular

context, they might have developed skills in eliciting student ideas, as well as made a habit of

collecting these ideas. What they do with those carefully collected ideas, however, depends on

their disposition toward these ideas. If a teacher views incorrect ideas as misconceptions that

need to be hunted down like weeds that must be uprooted to allow the canonically correct ideas

Chapter 5 | 101

to flourish, will likely enact a different instructional response than a colleague who views

student ideas as the raw material out of which instruction will be built.

Sometimes the best of intentions may lead to the exact opposite of the intended outcome.

In “It's ok — Not everyone can be good at math”: Instructors with an entity theory comfort

(and demotivate) students,” Rattan, Good, and Dweck [36] provide experimental evidence that

even a disposition of caring for the well-being of students, accompanied by an entity (as

opposed to incremental) disposition toward student math intelligence, led to “students

responding to comfort-oriented feedback [who] not only perceived the instructor's entity theory

and low expectations, but also reported lowered motivation and lower expectations for their

own performance.”

Teachers’ dispositions toward student learning will determine whether they consider

student resources important for lesson planning or what curriculum approaches they will use

and how they will approach assessment [26]. We argue that without specific dispositions, it is

not possible for a teacher to develop CKT-P and consequently, productive habits for enacting

it in the classroom. Ultimately, we propose that the development of CKT and habits are

mutually reinforcing the productive dispositions that undergird them. The habitual practices

strengthen knowledge, which, in turn, reinforces positive dispositions, which, in turn cements

habits, in a positive feedback loop.

7. Our Research on Teacher CKT in the Disciplinary Content Area of Energy

Building on the work of Ball and others, we developed a framework for studying the CKT in

physics (in the area of energy) that includes an articulation of the Tasks of Teaching and specific

Student Learning Targets [8]. We used this framework to design and validate 21 multi-part

questions, including multiple choice and constructed-response items, to assess physics teachers'

content knowledge for teaching energy in the first high school mechanics course. We then

divided individual questions on this assessment according to the subcategory of CKT assessed

by that question: Disciplinary Content Knowledge for Teaching (CKT-D) or Pedagogical

Content Knowledge for Teaching (CKT-P). Items categorized as CKT-D require knowledge of

physics that is particularly relevant to teaching contexts but do not require detailed knowledge

of pedagogical strategies or student learning. In contrast, CKT-P questions require an

understanding of content-specific learning trajectories and pedagogical strategies along with

disciplinary knowledge. 362 high-school physics teachers and 311 advanced physics majors

from across the country complete our online CKT assessment. We have presented analysis of

these results in several publications [8, 37, and 38]. Here, we will discuss the implications of

our research findings within the backwards design structure we have presented above.

7.1. Contingency of Productive Instructional Response on CKT-D

In order to support students in 3-dimensional science learning and to empower student

scientific agency, teachers need to recruit, recognize and help students build upon their

productive scientific ideas. But how can teachers prepare for this complex intellectual work?

Our research suggests that teachers can draw upon both foundational disciplinary content

knowledge for teaching (CKT-D) and pedagogical content knowledge for teaching (CKT-P).

We determined composite scores on CKT-D items and CKT-P items for both the teachers and

physics majors who participated in this study. We then set a threshold to categorize a participant

as demonstrating high CKT-D and high CKT-P. Among teachers in our study, 5% demonstrated

high CKT-D and low CKT-P while 51% demonstrated both high CKT-D and high CKT-P. This

shows that teachers who have a relatively high level of disciplinary content knowledge are very

likely to also have a high degree of pedagogical content knowledge. In contrast, among the

102 | Vokos S., Seeley L., Etkina E.

physics majors in our study, 25% demonstrated high CKT-D and low CKT-P and none

demonstrated high CKT-P. This suggests that unlike teachers, physics majors with a relatively

high disciplinary content knowledge are still very unlikely to also have a high degree of

pedagogical content knowledge. In short, CKT-P, as measured by our assessment, is a category

of content knowledge which physics teachers possess to a much greater degree than physics

majors [37].

Figure 2. Trampoline, CKT-D, SR (selected response), percentages for correct

choices are shown in green for teachers and blue for physics majors.

(Adapted from [38])

In order to identify the productive disciplinary seeds that are present in student thinking,

teachers need to locate student ideas within the context of foundational scientific models [39].

Chapter 5 | 103

For example, when students are applying energy conservation ideas, a teacher should be able

to help the students map their ideas onto the foundational, system-dependent, formulation of

the energy conservation principle in physics. This will include helping the student identify the

system that they are implicitly assuming in their analysis and evaluate whether their analysis

is consistent with that choice of system? We found that knowledge of system-dependent energy

reasoning was a weak area of disciplinary content knowledge among both the teachers and

physics majors in our study group. Fig. 2 shows an example of CKT-D question which

challenges a teacher to adopt a systems-based approach to energy reasoning. While physics

teachers outperformed advanced physics majors on this question nearly half (49%) of teachers

scored 0 or 1 out of 5 points. These scores were statistically lower than random guessing.

How significantly does a deficiency in systems-dependent energy reasoning limit a

teacher’s ability to support productive student reasoning? Fig. 3 shows a constructed response

question which was intended to assess the productivity of a teachers’ response to an example

of strong but incomplete student system-dependent energy reasoning.

Figure 3. Atwood’s, CKT-P, CR item

Fig. 4 shows the performance on Atwood’s CKT-P CR questions for various subject groups

including: all teachers, teachers who answered 0 or 1 questions correctly on the Trampoline

question, teachers who answered 4 or 5 questions correctly on the trampoline question, physics

majors who answered 4 or 5 questions correctly on the trampoline question along with teachers

who had relatively high scores on questions not related to systems reasoning. Nearly all (97%)

of teachers who scored 0 or 1 on the Trampoline CKT-D question were unable to respond

productively to any of the three questions posed in the Atwood’s CKT-P CR question. If a

teacher does not themselves possess CKT-D in systems dependent energy reasoning, they will

be severely limited in their ability to respond productively to the disciplinary content of student

reasoning.

104 | Vokos S., Seeley L., Etkina E.

Figure 4. The fraction of subjects who responded productively to student

reasoning in Atwood’s, CKT-P, CR. (Adapted from [37])

These results also show that CKT-D in systems dependent energy reasoning is necessary,

but not sufficient to support a productive instructional response. Of the teachers who scored a

4 or 5 on the trampoline question 84% were able to respond productively to some portion of

the student reasoning in the Atwood’s question but only 29% met all three criteria in our rubric.

We should also note that among a select group of physics majors with similarly high scores (4

or 5) on the trampoline question only 54% of them were able to respond productively to some

portion of the Atwood’s question. Among teachers and physics majors with similar CKT-D, the

teachers were more likely to leverage their CKT-D in order to respond productively to student

reasoning.

It is worth mentioning that these results only reveal a teachers’ capacity for responding

productively to student reasoning. This study did not address whether a teacher would actually

exercise this capacity in a real, classroom context. In addition to a capacity for responding

productively to student reasoning, they must also possess the disposition that the time and effort

required to engage with Taylor’s ideas and question is worthwhile. Finally, they must have

developed the habits of listening for and engaging with the scientific content of student

reasoning.

The Atwood’s example also illustrates an important aspect of student outcomes. Taylor’s

question demonstrates a strong grasp of energy ideas and keen insight. She is articulating one

of the most significant components of scientific reasoning, namely, probing for inconsistencies

in a scientific model. If Ms. Santucci is able to respond productively to Taylor’s reasoning she

will certainly be in a better position to support Taylor’s learning both of disciplinary core ideas

and of scientific practices. In addition, and perhaps even more importantly, by recognizing and

affirming the scientific content of Taylor’s question, she can support Taylor’s empowerment

and self-efficacy as a scientific thinker.

7.2. Flexible knowledge of scientific practices can compensate for incomplete CKT-D

The preceding example suggests that some areas of CKT-D such as knowledge of systems-

based energy reasoning are essential to enable critical Tasks of Teaching which, in turn, support

student learning and empowerment. We also find that teachers can adapt and extend scientific

Chapter 5 | 105

ideas alongside their students. Fig. 5 shows an assessment which consists of a CKT-D question

followed by a CKT-P question. The classroom scenario described in this item is based on a real

classroom experience. The results of our teacher study for this Basketball item were particularly

intriguing because a significantly higher fraction of teachers (70%) selected the correct

response for the pedagogical question compared to the first question which only requires

disciplinary knowledge. One might expect that the pedagogical question would be extremely

difficult for teachers who did not select the correct response on the disciplinary question. Our

findings show otherwise.

Figure 5. Basketball, CKT-D, SR and Basketball, CKT-P, CR questions. The

percentages of teachers answering correctly are shown in green, the percentages

of teachers answering incorrectly are shown in red, and the percentage of

physics majors selecting each answer is shown in blue. (Adapted from [37])

In fact, we found that a teacher's ability to correctly answer the pedagogical question was

essentially independent of their ability to correctly answer the disciplinary question as shown

in Figure 6. We think this result is very encouraging. Even when teachers are not immediately

able to identify the correct answer to a disciplinary question, they may be able to marshal

sophisticated scientific practices in order to support student engagement with the disciplinary

question. We also found that among teachers and physics majors who provided a correct

response to the disciplinary question, the teachers provided significantly more productive

answers to the pedagogical question.

106 | Vokos S., Seeley L., Etkina E.

Figure 6. The fraction of subjects who correctly explained their responses to the

Basketball, CKT-P, SR on the constructed-response question.

(Adapted from [37])

The preceding examples illustrate two different categories of CKT-D which we will call

foundational CKT-D and elaborative CKT-D. Foundational CKT-D, such as knowledge of

systems-based energy reasoning, provides an essential foundation which teachers build upon

when they engage with their student in scientific practices. Elaborative CKT-D, such as the

idea that when two elastic objects interact the object which deforms more also stores more

elastic energy, can be constructed or elaborated through experimental or theoretical

investigation.

Once again it is worth recognizing that a teacher’s capacity to identify a productive

pedagogical strategy does not ensure that they will exercise this capacity in a real, classroom

context. They must also have the habit of listening carefully to their students to identify points

of scientific disagreement and opportunities for further investigation. This habit will be

supported by their disposition to highly value scientific practices particularly when they can be

employed in response to student generated scientific argumentation.

7.3. Flexible application of scientific practices is both sophisticated and elusive

When teachers possess and utilize a flexible knowledge of scientific practices, they can

simultaneously empower their students and extend their own scientific knowledge. This

opportunity depends on the teacher's habit to consistently conceptualize their classroom as an

active space for scientific discovery. But what does a flexible knowledge of scientific practices

entail and how well prepared are teachers to deploy this knowledge? Fig. 7 shows an item from

our assessment, which prompts teachers to carefully attend to student models, predict the

outcome of experiments based on those models and then recognize what is required for an

experiment to support the discrimination of scientific models.

We found that teachers were quite successful in their effort to identify the predicted

outcomes of each experiment based on the models proposed by Jose and Sara. The most

difficult prediction was recognizing that Sara also thinks friction is important and, therefore,

would also predict that the puck would slide significantly less far on the rougher surface. Even

for this challenging case, 67% of teachers identified the correct predicted outcome based on

Sara’s model.

Chapter 5 | 107

Figure 7. Puck launcher item. Percentages show the fractions of teachers and

physics majors who chose a particular correct answer (Adapted from [8]).

The second question on this item proved more challenging for teachers. Only 39% of

teachers were able to both apply and articulate the idea that an experiment must have different

predicted outcomes based on different scientific models in order to discriminate between those

two models. Even fewer physics majors in our study (32%) were able to apply and articulate

this idea. This is a sophisticated ability but it is also an ability that is foundational to

experimental science. In order for teachers to support their students in authentic scientific

inquiry they must themselves possess a deep understanding of scientific practices. We need to

recognize that a flexible knowledge of scientific practices is more sophisticated and nuanced

108 | Vokos S., Seeley L., Etkina E.

than simply memorizing “the scientific method” or even understanding the difference between

an experiment, an explanation, and a prediction.

8. Summary and implications

Teachers of physics at all levels tackle, whether consciously or not, a formidable task. They

enculturate students in the physics enterprise, by which we mean both the products of this

particular scientific community but also a set of its practices, commitments, achievements, and

history--both glory and warts. Teachers are supposed to be tour guides to marvelous vistas

unappreciated by hoi polloi, role models to be emulated, cultural natives to apprentice under,

camp leaders who create immersive experiences. All too often, however, we, teachers, are

instead transmitters of bits and pieces of this culture; pointing to a broken column here and an

old painting there, talking incessantly about strange dishes but only doing at most a show-and-

tell with the odd strange spice, helping our charges to memorize disconnected phrases. And our

students vote with their feet; they feel less empowered, more epistemologically naive, holding

separate the ideas of school physics from how they truly think about and make sense of

phenomena.

To reify the vision of forming empowered participants in the physics enterprise through

enacted Tasks of Teaching, a physics teacher needs to have the appropriate dispositions and the

rich Content Knowledge for Teaching physics so as to engage with the habits of practice, and

the habits of maintenance and improvement, which undergird the habits of mind of a physicist

and a physics teacher.

Three direct implications for teacher preparation and professional development flow from

the framework and the research described here:

1) The framework requires interlinked dispositions of student empowerment, rich and

coherent Content Knowledge for Teaching physics, and productive habits. If one or

more pieces is weak or missing, the whole framework is in danger of collapsing,

predicting therefore a collapse of positive outcomes. Without appropriate dispositions,

for instance, no amount of CKT can forestall student sense of lack of belongingness,

even though the students may exhibit high levels of conceptual understanding.

Similarly, programs that emphasize, cultivate, and produce physics teachers with all the

desired dispositions and strong commitments to social justice, but without adequate,

physics-specific CKT are unlikely to have graduates that bring students along to true

physics participation. Finally, programs or professional development experiences that

do not provide adequate and sustained opportunities for honing productive habits are

unlikely to be effective in moving the needle on either student cognitive or non-

cognitive physics-specific outcomes.

2) Not all CKT is created equal. There is disciplinary CKT, CKT-D, of two kinds:

Teachers who do not have an understanding of foundational knowledge are much less

likely to be able to enact instructional responses that help students develop knowledge

that teachers themselves do not exhibit. On the other hand, if teachers’ elaborative

knowledge of physics is incomplete but their knowledge and comfort with the practices

of the discipline are deep, they can still help their students further their own

understanding. Therefore, physics teacher education programs and professional

development efforts should focus on developing foundational CKT-D (and the

corresponding CKT-P). Advanced courses in physics, as long as they are mainly about

elaborative knowledge, are unlikely to help physics teachers help their students. (This

is not to say that advanced courses cannot be designed to also have other learning goals,

which could help future teachers in their professional tasks.)

Chapter 5 | 109

3) CKT can be developed during teaching, as can be inferred from the comparison of

the performance of physics majors and physics teachers on CKT-P tasks. However, it

seems that foundational CKT is unlikely to be developed during teaching, and the oft-

repeated motto “Teachers can learn alongside their students” seems to be invalid in this

case. It seems that we cannot learn that which we do not know that we do not know

because we do not tend to learn from experience but from reflecting on experience and

we cannot reflect on something that our mind’s eye does not know to focus on.

Furthermore, there are implications for research: we clearly do not know all the habits, nor

do we know how to develop these habits in an efficient manner. Taking on this lens of habit

formation as essential to teacher practice, there is a need to update research results on student

learning and connect them to habit development by teachers. On the policy side, there is a need

to explore the interaction between dispositions and habit formation. And on the cognitive side

of PER, what about a physics concept makes it foundational? Similarly, for a given physics

concept, what are the foundational features associated with learning it deeply enough? These

are some of the important questions raised by the research described in this chapter.

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111

Chapter 6

The educational implications of the relationship between

Physics and Mathematics

Mieke DE COCK

KU Leuven, Department of Physics and Astronomy & LESEC,

Celestijnenlaan 200C, 3001 Heverlee, Belgium

Abstract: Mathematics has been deeply connected to physics, ever since their beginnings.

Not only does mathematics play a technical role, but it also has an important communicative

and structural role in physics. This implies that it is essential to connect both disciplines in

physics learning. At the same time, understanding the different roles of mathematics in physics

is difficult for students. This chapter describes the interplay between mathematics and physics

in physics education both from a more theoretical and an empirical point of view.

1. Introduction

The miracle of the appropriateness of the language of mathematics for the

formulation of the laws of physics is a wonderful gift which we neither

understand nor deserve.

(Eugene Wigner)

This and many other quotes by famous physicists illustrate the deep relationship between

physics and mathematics, ever since their beginnings. The question on the relationship between

both disciplines is as old as philosophy and their mutual influence has played a crucial role in

their development [1, 2]. The way mathematical structures match physical phenomena and can

even be used to make predictions about this physical world appeals to the imagination.

Moreover, mathematics was not only crucial for the development of physics, but also a lot of

mathematical concepts have been derived from the study of nature [3]. Mathematics is deeply

interwoven with physics, and sometimes they are even inseparable.

In an educational context, this mutual relationship is not always articulated. In physics

education, mathematics is often seen as a tool to describe physical phenomena and perform

calculations. In mathematics education, physics is often only seen as a possible context to

illustrate and apply abstract mathematical ideas. Experience shows that this dichotomy creates

difficulties for students. However, if we take scientific literacy–including physics knowledge,

skills, and insight into the nature of physics–as a goal for physics education, we should teach

physics not only by relying on the experiment as an empirical basis but also by showing the

complex and deep interrelation between mathematics and the physical description of the world.

However, research shows this is a difficult and time-consuming task. Many students can solve

quantitative problems using certain techniques but do not deeply understand the underlying

concepts and their relationship with mathematics.

This chapter focusses on the interplay of mathematics and physics, starting from the idea

that these disciplines are deeply connected. This implies that we do not see mathematics as ‘a

tool’ for physics but rather see both in continuous mutual interaction and as such, shaping each

other. This view has implications for how we see the role of mathematics in physics education.

We start by discussing the interplay of mathematics and physics and underlying theoretical

frameworks. We then take a learners’ perspective and report on empirical research into students’

difficulties and views. As (mathematical) representations play a crucial role in the description

112 | De Cock M.

of physical phenomena, we dedicate a separate section to this topic. Finally, we highlight the

role of teachers as they are central to students’ successful learning. To conclude, we formulate

implications for teaching and teacher education.

Given the wealth of interesting research on the mathematics-physics interplay, we had to

be extremely selective. The focus of this chapter is secondary education. However, most studies

deal with university students. So, we include research that deals with the introductory level at

university when instructive for secondary education. We hope that this chapter gives the reader

a starting point to dig deeper into this broad topic. For further reading, we refer to the recent

book by Pospiech, Michelini and Eylon [4] that contains much additional relevant literature.

This book was an invaluable starting point and source of information for this chapter.

2. Describing the role of Mathematics in Physics and Physics Education

In this section, we focus on different perspectives on and descriptions of the interplay between

mathematics and physics in physics (education). Mathematics can play different roles in

physics: it serves as a tool (pragmatic perspective, technical role), it acts as a language

(communicative role), and it provides a structural framework [5].

The interplay between mathematics and physics has been discussed extensively in the

context of history and philosophy of science and by physicists themselves. Many authors

studied and described the development of ideas in physics and the relationship with

mathematics (e.g., [6, 7]). However, although deeply interwoven, there are also differences

between mathematics and physics as disciplines. Their aims, points of view, methods and

cultures are different. Redish and Kuo [8] gave the following take-away message in their paper

on the language of physics and mathematics for higher physics education:

How mathematical formalism is used in the discipline of mathematics is

fundamentally different from how mathematics is used in the discipline of physics—

and this difference is often not obvious to students. For many of our students, it is

important to explicitly help them learn to blend physical meaning with mathematical

formalism. (p. 538)

To unravel this complex interplay and the different roles of mathematics in physics and to

support its teaching and learning process, several models were developed to be able to describe

and highlight selected aspects. Given that there are many aspects in the interplay, it is unlikely

that a single model would be able to capture them all or to serve all research aims. Instead,

several models and descriptions have been proposed, each one taking its own perspective and

attuned to the intended research purpose and/or instructional goal. In what follows, we present

a selection of these models.

A first set of models describes ‘mathematization’, by which we mean transferring or

translating physical processes/phenomena into mathematical elements or structures [9]. This

process of mathematization is essential both in the mathematical description of physical

processes or phenomena and in problem solving. Figure 1 shows a very basic model of

mathematization in physics: it describes how, starting from a physical situation, a mathematical

representation is built before mathematical manipulations are performed. The mathematical

results obtained need to be interpreted within the physical model and should be validated either

according to the physical situation or to the problem statement.

Chapter 6 | 113

Figure 1. Basic Model of Mathematization (Modified according to [10])

Also in mathematics education, the mathematical modelling of a situation of everyday life

plays an important role and models have been proposed to describe this process. The cycle by

Blum and Leiss [11], see Figure 2, indicates the complexity of mathematical modelling. As in

Figure 1, the cycle starts from a real situation that has to be described mathematically, giving

mathematical results that must be interpreted and validated.

Figure 2. Mathematical Modelling Cycle of Blum and Leiss [11]

Uhden et al. [5] transferred the important aspects to a new diagram of the cycle (Figure 3)

which shows connections between three areas: world, physical model and mathematics, and

shows clear similarities with the model in Figure 1.

Although the representations might indicate a cyclical process, empirical evidence shows

that students do not follow the different steps exactly but jump back and forth on very different,

individual paths [12]. Studies on student difficulties when solving physical problems with

mathematical models hint that the step from the simplified situation model and the

mathematical model is the most critical part of problem solving [13, 14] but our traditional

instruction may not put enough emphasis on this step: we tend to focus on the processing steps

(processing/working mathematically).

114 | De Cock M.

Figure 3. Mathematical Modelling Cycle, redesigned by Uhden et al. [5]

Reprinted by permission from Copyright Clearance Center: Springer Nature,

Science & Education, Modelling Mathematical Reasoning in Physics

Education, Olaf Uhden, COPYRIGHT 2011.

Greca and Moreira formulated a different description of the modelling process [15]. They

proposed a model where comprehension of a scientific theory requires the construction of a

mental model. Within this mental model, they distinguish between a physical model and a

mathematical model. The mental model connects all the parts: the physical phenomenon, the

physical and the mathematical model. Although the authors explicitly discriminate the physical

and the mathematical model, they admit that for more advanced fields of physics this

distinction might become problematic.

Uhden and colleagues [5] have two main concerns about these models. Based on the deep

interdependence between physics and mathematics, they argue that it is not adequate to

distinguish between a physical (qualitative) and a mathematical (quantitative) model in physics

education, and that the role of mathematics in physics is much more than mere calculations and

rote manipulations. This structural role is not explicit in the models presented above and needs

more emphasis. Moreover, a more detailed description and distinction between different levels

of understanding and mathematization is needed. The authors therefore proposed a new model

which incorporates the deep interrelationship between mathematics and physics but also makes

it possible to distinguish between technical and structural skills. The model is depicted in

Figure 4.

Figure 4. Physical-Mathematical Model according to Uhden et al .[5]

Reprinted by permission from Copyright Clearance Center: Springer Nature,

Science & Education, Modelling Mathematical Reasoning in Physics

Education, Olaf Uhden, COPYRIGHT 2011.

Chapter 6 | 115

The left part represents the inseparability between mathematics and physics (structural

role) while the right part refers to a purely mathematical aspect (technical role). The arrows (a)

and (b) indicate different degrees of respectively mathematization and interpretation. Arrow (c)

refers to the technical role like doing calculations and is related to the instrumental domain. By

clearly establishing the difference between arrows (a) and (b) on the one hand and (c) on the

other hand, the different character of structural and technical mathematical skills is evident.

Adding the translations between the rest of the world and the physical-mathematical model

gives a revised modelling cycle for physics [5]. All processes of the original modelling cycle

are present, but they are arranged differently, allowing focus on the structural skills for

conceptual understanding of physics through mathematics.

Figure 5. Revised Modelling Cycle, based on Physical-Mathematical Model [5]

Reprinted by permission from Copyright Clearance Center: Springer Nature,

Science & Education, Modelling Mathematical Reasoning in Physics

Education, Olaf Uhden, COPYRIGHT 2011.

The formulation by Uhden et al. [5] in terms of conceptual understanding underlines the

importance not only of conceptual understanding in physics but also in mathematics. Plenty of

research in PER has focused on student difficulties with physics concepts, and the impression

that ‘using mathematics’ opposes‘understanding the concepts’ leads to a struggle between an

emphasis on conceptual understanding and the use of mathematics. However, given the

underlying conceptual position on the role of mathematics in physics education, this opposition

is a paradox and conceptual mathematical understanding is important too.

In his work, Sherin [16] focuses on understanding equations in physics, rather than

routinised manipulation of these equations. He argues that “we do students a disservice by

treating conceptual understanding as separate from the use of mathematical notations” (p.

482). Instead, the meaning of mathematical symbols should be blended with physics concepts,

and this has led to the notion of ‘symbolic forms.’ Each symbolic form associates a simple

conceptual schema with a pattern of symbols in an equation.

116 | De Cock M.

The last framework we discuss is the conceptual blending framework. Fauconnier and

Turner [17] originally introduced this framework, sometimes also called mental space

integration, to model how people create new meaning in linguistic contexts by selectively

combining information from previous experiences. Figure 6 shows a general schematic

representation of the framework. In its basic form, a conceptual blending network consists of

four connected mental spaces: two partially matched input spaces, a generic space, and the

blended space. Generally, a mental space is comprised of conceptual packets or knowledge

elements that tend to be activated together and has an organizing frame that specifies the

relationships, or connections among the elements [18]. Input spaces are small, self-contained

regions of conceptual ideas. The generic space provides the underlying structure to the input

spaces, identifying commonalities in content and structure [19]. Blended spaces are constructed

through selective projection from the inputs. Considering that mathematics can be used to carry

and relay information about physical contexts, the conceptual blending framework provides a

means to explore student understanding as they connect mathematics and physics concepts.

One important sign of physics students’ progress is combining the symbols and structures of

mathematics with their physical knowledge and intuition, enhancing both. New ideas and

inferences emerge after this combination. The conceptual blending framework emphasizes both

the new combinations of elements and the different ways that combination itself can be

constructed. Several authors in PER have used the framework to describe student

understanding and problem solving at the mathematics-physics interplay [18, 20–23].

Figure 6. Schematic representation of the blending framework [16]

https://commons.wikimedia.org/wiki/File:BasicBlendingDiagram.jpg

Brahmia [24] formulated beautifully why the blending perspective has the potential to be

used to study the combination of mathematical and physical knowledge in reasoning:

Seen through the lens of conceptual blending, we suggest that the math physics

blending may be tighter than has been previously discussed in theoretical models

proposed in PER. Rather than a back and forth between the math world and the

physics world, we find it productive to think in terms of symbiotic cognition in which

a homogeneous blended cognitive space, at a subconscious level, can be cultivated

and can catalyze cognitive flexibility; the physics informs the mathematical thinking

which informs physics reasoning. (p. 4)

Chapter 6 | 117

Several other models were developed to describe the role of mathematics in physics and

physics problem solving (e.g., [25, 26]). Although none of these models is considered a guiding

model to design teaching, by explicitly trying to describe the process, important aspects come

into focus and make us realize potential barriers. They explicitly focus on the link between

mathematics and physics and should make us acknowledge that physics expertise involves

flexible and generative understanding of mathematical concepts and ideas.

3. Mathematics in Physics: a learners’ perspective

Whereas the previous section deals with the (theoretical) description of the role of mathematics

in physics and physics problem solving, in this section, we focus on difficulties that learners

experience in combining mathematics and physics.

Empirical research on ‘mathematics in physics education’ is relatively small compared to,

for instance, the field of conceptual change. It is well established that conceptual understanding

is not an automatic outcome of traditional physics instruction, but research shows that the

nature of students’ difficulties also involves the use of mathematics [5, 27, 28]. Moreover, most

empirical research on the mathematics-physics interplay is done with university students.

Tuminaro [29] argues that the reasons why students struggle with mathematics can be

divided in two: (1) students lack the prerequisite mathematical skills to solve problems and/or

(2) they do not know how to apply or use mathematics in physics. Research in the first group

explores the correlation between mathematical competence and physics achievement, while the

second line of research seeks the causes of students’ difficulties when applying mathematics in

physics. Although for all educational levels we find statements that students lack mathematical

knowledge and skills to be successful in physics, it seems that the issue is more subtle. Redish

and Kuo [8], as teachers, were often surprised by how little mathematics their students seem to

know in their physics classes. They wondered why so many students seem unable to use

mathematics in physics, despite their success in prerequisite mathematics classes. This

indicates that the classical solution to teach students more mathematics, hoping they take this

with them when studying physics, is not sufficient [30, 31]. Even if students have learned the

relevant mathematics, they still need to be given the opportunity to learn a component of

physics expertise not presented in mathematics classes: tying those formal mathematical tools

to physical meaning.

In what follows, we present some main findings on student difficulties on the one hand

and discuss the role of student views on the other hand.

3.1. Student difficulties

There are many studies in PER that focused on students’ mathematical knowledge and how this

impacts achievement in physics [27, 32, 33]. Many of them show that mathematical ability is

positively correlated to success in traditional introductory physics courses that emphasise

quantitative problem solving, although the correlation has not been observed to hold

consistently. Meltzer [27] however, remarks that correlation with problem solving skill does

not necessarily also imply correlation with conceptual understanding. In his work, he studied

the correlation between learning gains on a qualitative test on conceptual physics knowledge

and both mathematical skills and initial level of concept knowledge. The results indicate that

students’ pre-instruction mathematical skills had a significant impact on their learning gains in

(conceptual) physics, while their initial level of conceptual knowledge in physics was unrelated

to these learning gains. In a more recent study, Burkholder et al. [34] also show that the

relationship between mathematics and physics performance should be treated with care: they

found no effect of advanced mathematics preparation on performance in Physics I, but a

118 | De Cock M.

significant correlation between vector calculus preparation and Physics II final exam

performance although for reasons that are not completely clear. It is well known that

proficiency in mathematics does not guarantee success in physics.

Whereas the above group of studies focusses on correlations between mathematics and

physics achievement, another set seeks better understanding of the causes of students’

difficulties when applying mathematics in physics.

A first group of studies aims to identify taxonomies to characterize student difficulties. As

an example, we might mention the research by McDermott and colleagues [35] and later

Beichner [36] that describes different categories of typical student mistakes on graphs in

kinematics. They identified six dimensions corresponding to different difficulties: graph as

picture errors, confusion between slope and height, variable confusion, non-origin slope errors,

area ignorance and confusion among area, slope, and height. Zavala et al. [37] recently

proposed a modified TUG-K (Test of Understanding Graphs in Kinematics) improving the

parallelism between the different dimensions in the original test by Beichner. Another example

where a taxonomy of student difficulties was proposed, based on the use of a quantitative

instrument, is the research by Barniol and Zavala [38] on understanding vectors.

A second group of studies tried to gain more insight into student reasoning on specific

topics, often using qualitative methodologies. Much of this research deals with college level

and university students, and it spans a large range of topics, from concepts related to linear

functions [39] via calculus related concepts [21, 40] to vectors [41–44]. The general finding in

these studies is that most students focus on the technical aspects and that it is primarily the

missing awareness of the structural role of mathematics in physics that causes the difficulties,

rather than deficiencies in the technical application. In the following paragraphs, we illustrate

this line of research by discussing a few studies on relevant topics for secondary education:

derivatives, differentials and integrations, and vectors. These studies are only examples, and

by no means an exhaustive list.

Roorda et al. [45] report on a longitudinal observation study with secondary school

students. In the study, they looked at how students developed their use of procedures to

calculate instantaneous rate of change as part of the concept of derivative. They explicitly frame

their research in an actor-oriented transfer perspective and find that prior activities in physics

or mathematics classes affect students’ work in the interview tasks. The direction of

relationships however is not that students first learn mathematics and consequently apply it in

physics. Instead, in line with results of Zandieh [46] and Marrongelle [47], they observed that

some students also use physics knowledge to give meaning to mathematics tasks. Although not

mentioned by the authors, we connect this finding to the description of the mathematics-physics

interplay using the conceptual blending framework, and more particularly the idea of

‘backwards projection’.

Lopéz-Gay et al. [48] describe different conceptions of differentials as used in physics: as

a merely formal instrument, as an infinitesimal increment, as an infinitesimal approximation

and as a linear estimate of the increment. They show that the students’ main conception in

physics contexts identifies the differential with an infinitesimal increment and that this

constitutes an obstacle to students’ ability to mathematize. Nguyen and Rebello [48] studied

student difficulties in using the concept of area under a curve in physics problems. They show

that even when students mentioned the concept, they were not always able to relate it to the

accumulation process.

As a final example, we discuss research on student difficulties with the vector nature of

many physical quantities [41–44, 50–52] Flores et al. [53] show that many students had

difficulty determining the direction of the difference between two velocity vectors, to find the

direction of the acceleration vector and to find the relationship between the separate forces and

Chapter 6 | 119

the net force acting on a subject, even after instruction in mechanics. Shaffer and McDermott

[54] also report on student difficulties with velocity and acceleration vectors in mechanics.

To find out whether student difficulties are purely caused by lacking mathematical abilities

or by applying mathematics in a physics context, a third research strand focusses on comparing

students’ abilities to solve problems in mathematics and physics.

From a mathematics education perspective, Jones [55] studied students’ strategies when

solving problems involving definite integrals both in the context of mathematics and physics.

He found that students more often rely on antiderivative or area-based ideas than on Riemann

sum-based conceptions. In the context of mathematics, the three conceptualizations were

shown to be equally effective, whereas for physics problems the adding-up-pieces

conceptualization was more productive, although underutilized. For physics problems, the

area-under-the-curve and antiderivative ideas seemed less suited to help students to make sense

of contextualized integrals. Doughty et al. [40] also report that only a few students link

integration to a process of summation and that this limited view on integration is likely to

prevent students from solving problems requiring integration in an intermediate E&M course.

Both Jones and Doughty and colleagues suggest paying attention to conceptualizations that are

productive for physics problem solving.

Whereas the aforementioned research on integration deals with university students,

findings from Ceuppens et al. [56] concern students in grade 9 (14–15 years old). They studied

student understanding of linear functions and compared initial position and velocity in 1D

kinematics and the 𝑦-intercept and the slope in mathematics. They found that student

performance was better on most mathematics items. Based on a qualitative analysis, results

show frequent interval point confusion in kinematics but rarely in mathematics, as one

example. They also report that negative slope in mathematics is rarely an issue, while negative

velocities are by far the largest pitfall in kinematics. These results once again confirm that

mastering concepts in mathematics does not guarantee successful use in physics.

Researchers at the University of Zagreb [57–

59] explored both high school and university students’ strategies when dealing with graphs

in mathematics, physics, and contexts other than physics. By using sets of isomorphic items on

the concepts of slope and of area under the curve, they also found that students’ strategies for

interpreting the graphs were context dependent and domain specific. It turned out that

mathematics items were more often answered correctly, and that physics was the most difficult

context, in line with other findings in the literature [56, 61].

Furthermore, for problems requiring vector manipulations, several studies investigated the

effect of a physics context both on student performance and their problem-solving processes.

Regarding vector addition and subtraction, the literature reports mixed results. Nyugen and

Meltzer [50] found that students spontaneously use the concept of forces on an object when

solving problems involving vector addition. Van Deventer and Wittman [42] and Barniol and

Zavala [41] discovered that adding a displacement or velocity context improves students’

performance on vector addition questions. On the other hand, Shaffer and McDermott [54]

reported worse results in vector subtraction when questions were posed in a kinematics context.

Consequently, the nature of the physics context seems to matter. Emigh et al. [62], however,

found that the types of incorrect reasoning students made were roughly similar for different

contexts.

Overall, results on student difficulties with mathematics in physics indicate that not the

competency in mathematics but blending mathematics and physics is often a major hurdle for

students.

120 | De Cock M.

3.2. Student views

Most empirical research we described in the previous section used the “difficulties” perspective

to understand why students struggle with mathematics in physics. It became clear that the cause

of this struggle often does not come from poor mathematics competence, but from not knowing

how to use/apply mathematics in physics. There is evidence that how students view the role of

mathematics in physics might influence their problem-solving strategies (e.g., [63–65]. Most

of these studies deal with university students and often indicate that many of them have an

instrumental view of the role of mathematics with a stronger focus on the technical role than

on the structural role [66, 67]. The main finding of Ataide and Greca [68] is that a close

relationship appears to exist between the way students solve the problems and the students’

epistemic view of the role played by mathematics in physics (and, by extension, the learning

and understanding of physical concepts, since problem solving is an important activity in the

physics classroom). The reason we mention this study explicitly is that it was carried out with

students in their final year of teacher training to become high school physics teachers. As the

authors mention, their views on the relationship between physics and mathematics will

probably dominate how they teach the discipline.

The observation that students might know the mathematics or physics needed to solve a

particular problem, but still get ‘on the wrong track’ led to the work of Redish [69] on

‘epistemological framing’. Redish proposed the term to connect the study of personal

epistemologies to the notion of framing form anthropology and sociolinguistics [70]. Epistemic

framing refers to the process by which a student pares down the set of all available knowledge,

(often subconsciously) selecting a subset of knowledge and tools that are useful for solving a

problem, constructing new knowledge, or evaluating what they know. Bing and Redish [71]

introduced four epistemic frames to describe students’ use of mathematics in a physics context,

namely physical mapping, calculation, invoking authority, and mathematical consistency.

Later work on student framing when combining mathematics and physics has explored the

differences between the conceptual physics, conceptual mathematics, and algorithmic

mathematics and physics frames [72]. It is argued that sometimes student difficulties may be

the result of unproductive framing rather than a fundamental inability to solve the problems or

the misconceptions about physics context: elements of mathematics knowledge might be

included in schemes other than those needed to solve physics problems, resulting in not

selecting these concepts and unproductive framing of the situation [73]. Moreover, preliminary

results in a study of Ryan et al. [74] suggests a correlation between question characteristics and

student epistemic framing.

To conclude, it seems crucial that the students acknowledge that the application of

mathematics in physics is more fundamental and deeper than just applying formulae to some

problems by rote and that they learn to switch between the roles of mathematics.

4. Representations

Representations play a crucial role in teaching and learning physics. There is no purely abstract

understanding of a physical concept or relationship: they are always expressed in some form

of representation–often mathematical–such as a graph, picture, free-body diagram, formula,

ray diagram, etc. Algebraic representations (formulae, equations) are perhaps the most

prominent, but graphical representations also play a special role. They seem to play a bridging

role as they are both iconic and at the same time abstract and symbolic. Therefore, skillful

interpreting and use of different representations and coordination of multiple representations

are highly valued in physics, both as a tool for understanding concepts and as a means to

Chapter 6 | 121

facilitate problem solving. The skills needed to benefit from external representations can be

roughly categorized in two groups [75]:

• Representational fluency, which involves the ability to build and construct

representations, as well as the ability to translate and switch between representations.

• Representational flexibility, which involves making appropriate representational

choices in a given situation.

Research concerned with representational issues has taken many approaches, in

mathematics as well as physics, chemistry, and recently statistics education, both more

theoretical and empirical. As one example, Geyer and Kuske-Janssen [76] present an adapted

model to classify representations in physics based on a general description of representations

from a cognitive sciences and semiotics viewpoint. They classify representations as purely

mathematical, verbal, pictorial, and objective. Gire and colleagues [77] present another

theoretical analysis of external representations in terms of organization of information,

conceptual referent and medium. They identify a set of nine structural features. Rodriguez et

al. [78] introduced the concept of graphical forms, an extension of Sherin’s symbolic forms. In

a more empirical context, a lot of the research that is mentioned in the context of student

difficulties earlier in this chapter also relates to the role of representations.

One specific aspect studied is student performance in particular representations, such as

graphical representations. Among these graphical representations, we might particularly

mention line graphs. Although they may have an advantage over numbers or formulae as they

visualize relationships and might contribute to reducing cognitive load, it turns out that reading

and interpreting graphs is difficult. Difficulties related to graphical representations have been

studied in detail in both mathematics and physics education, where topics in kinematics

received considerable attention, such as the aforementioned work of McDermott and

colleagues [79], Beichner [35], and more recently Planinic and colleagues [57–59, 80]. Results

of these studies seem to imply that interpreting and working with graphs require structural

insights. However, research on the use of modern digital media indicates that it is often possible

to foster reading and graph-making skills (e.g., [81–83]).

Besides student understanding of specific representations, the relationship between student

success and the representational format in which the problem is raised has also been

investigated, both in mathematics and physics. In PER, Meltzer [27] compared student answers

on isomorphic questions raised in four different representations. He found instances where

students performed significantly better in one representation than in another. Moreover,

students were not always consistent in their performance in a peculiar representation across

topics. Kohl and Finkelstein [84] also observed that the success rate in solving physics

problems shows significant differences for near-isomorphic physics questions presented in a

verbal, mathematical, graphical, and pictorial representation. Additionally, they found that

allowing students to choose the representation in which they solve a given problem for some

students increased and for others decreased the success rate. In a follow-up study, De Cock

[75] confirmed these effects by investigating the strategies used when presented with a question

in a verbal, pictorial, or graphical representation. By analyzing explanations students gave to

support their answer, it became clear that details in the representational format being used

influenced the chosen problem-solving strategy.

Ceuppens et al. [61] not only studied context (physics-mathematics) but also

representational dependence (algebraic-graphical) when high school students solved

isomorphic questions. This study confirmed that the success rate differed with the

representation that is used in the problem statement.

As every representation carries specific information [85], the whole picture of physics

requires several complementary representations. Ainsworth [86] discusses the benefits of

122 | De Cock M.

multiple representations (MR), the change between them and their potential problems for

inexperienced learners. Research evidence in MER shows that the use of MR can contribute to

knowledge enhancement [87, 88]. However, it seems that this benefit only holds when students

can interpret the representation, know how it connects to reality and other representations of

the same concept, and have the skill to choose among representations. The relationship between

MR and problem solving has also been investigated in science and physics education [89–92].

Results here show that students studying physics in a learning environment that focuses on the

use of MR are more inclined to construct several representations to solve problems themselves.

This supposes that students should be fluent in switching between representations. Studies such

as Ainsworth et al. [88], Duval [93] and Kirsch [94] specifically identify the transitions between

representation as a key task in learning and problem solving. In that context, Ceuppens and

colleagues [61] developed a test for representational fluency of high school students in the

context of 1D kinematics and linear functions. The test consists of multiple-choice items and

includes graphs, tables and formulas as representations and mathematics and physics as

contexts. Each item is formulated in one representation and students are asked to translate the

description to another representation. The results show a main effect of representation and

indicate that transitions involving formulae are significantly more difficult. Moreover, function

types with negative values for either 𝑦-intercept or slope result in significant lower mean

accuracies, a result already mentioned in [95]. A similar study of Van den Eynde et al. [96]

reports similar results with both students in an algebra and calculus-based course.

Recent work by Brahmia and colleagues draws our attention to all the different types of

‘negativity’ in physics [24].

Overall, it seems that the problem-solving strategies and student results strongly rely on

details regarding problem representation and context. These findings support the epistemic

framing aspect that was discussed earlier.

5. Role of Teachers

Understanding the meaning of mathematics and its interrelation with the physical description

of the world is one of the most difficult steps in physics learning. Teachers, their stances, and

their teaching methods play a decisive role in learning. Hence, we are convinced that teachers

play an important role in imparting an appropriate view of physics and how it relates to

mathematics. However, little is known about teachers’ views and actual teaching practice.

Hansson and colleagues [97] developed a framework to analyze communication during physics

lessons and used it to explore the role of mathematics in physics lessons in secondary school.

They report that when a link to mathematics is made, the emphasis is often on the technical use

and that links emphasizing structural use are not frequent. A study of textbooks and lessons

using a refined framework hints at the importance of the role of the teacher and their use of

textbooks to shape interaction in the classroom, showing that teachers’ Pedagogical Content

Knowledge (PCK) is important [98].

PCK is the specific knowledge that teachers develop over time, and through experience,

about how to teach specific content in particular ways to enhance student understanding. Given

that mathematics-physics interplay is part of physics teaching, it seemed appropriate to

Pospiech and colleagues to establish a specific PCK model for Teaching Mathematics in

Physics [99]. The (theoretical) model relates the teachers’ views and their experience and

knowledge to curriculum, teaching principles and strategies and student ideas. They checked

whether the model is confirmed by interviews with experienced teachers. Although the number

of participants does not allow for generalizations, they found that the view of mathematics as

a tool or instrument is prevalent, but that the teachers also share a view that mathematics could

Chapter 6 | 123

contribute to understanding physics. However, with many teachers working as practitioners,

the views remained quite focused on practical teaching, and they saw a reduced awareness of

structural aspects in teaching. Teachers often see it as their first task to support technical

competences and procedural knowledge as a condition for more conceptual aspects.

Besides more foundational work on student views and difficulties, several instructional

strategies have been developed to support physics education in which mathematics also plays

a more structural role. We mention some initiatives on the interrelated treatment of physics and

mathematics at school level [100, 101], or initiatives that introduce digital media particularly

for this goal [83]. However, much more work is needed to develop teaching/learning materials

that can support teachers to go beyond the technical level and invite them to include more

structural aspects in their teaching.

6. Implications for teaching and teacher training

At the heart of this chapter lies our view that mathematics and physics are deeply connected,

and that mathematics is much more than ‘a tool’ for physics. This deep connection between the

two disciplines often makes describing physical phenomena in mathematical terms a challenge

for students as they not only have to master the mathematics but also should develop the

competence to make sense of the mathematics in physics. It is therefore important that teachers

design learning environments that support not only the development of conceptual

understanding but also the blending of mathematical and physical concepts. In what follows,

we list a set of recommendations or points for teachers to think about when designing their

teaching activities and that teacher educators should discuss with their students. Although the

list is based on the literature mentioned in this chapter, it is a personal selection and formulation

that cannot be matched to specific research results.

• Teachers should be aware of their own (epistemic) views on the role of mathematics in

physics. As we see that many students hold a rather instrumental view on this role, one

starting point will be to make student-teachers aware of their limited view by discussing

all the roles that mathematics can play.

• We should not only focus on students’ deficits in mathematics but actively support the

process of finding meaning: this takes time and requires explicit attention.

• Textbooks have an important influence on how teachers design their lessons. Focus on

an instrumental approach can invite teachers and students to follow it, highlighting the

importance that teachers critically analyze textbooks and their use and that student

teachers are provided with tools and frameworks to carry out this analysis.

• Teachers should discuss with their colleagues how mathematics is used in their fields

and try to agree on consistent use in their school where possible. They should explicitly

discuss with their students the similarities and differences between mathematics in

mathematics and mathematics in physics, based on concrete examples.

• Concerning particular mathematical concepts, it is important that teachers are aware of

students’ difficulties with these concepts and discuss different conceptualizations with

their mathematics colleagues, outlining which are most productive for making sense in

physics.

• Having insight into epistemic framing will give teachers an alternative explanation of

the difficulties students encounter when they ‘get stuck’ even if they can do the

mathematics.

• Teachers should pay particular attention to the role of representations. They should

think carefully about which representation to start with when teaching a particular

124 | De Cock M.

concept and how to connect representations. Moreover, they should provide a multitude

of situations and discuss advantages and disadvantages of different representations.

Although research on the role of mathematics in physics teaching is growing, there are still

many open questions and challenges. Here are some examples:

• Many student difficulties with particular mathematical concepts were identified, but we

need a better understanding of Quantitative Literacy [102]. In a recent paper, Brahmia

and colleagues define Quantitative Literacy as “the interconnected skills, attitudes, and

habits of mind that together support the sophisticated use of familiar mathematics for

sensemaking”. They report on the design and validation of a measurement instrument

to assess mathematical reasoning in calculus-based introductory physics. Their

instrument focusses on proportional reasoning, reasoning with negativity and

covariational reasoning. A similar instrument is needed for algebra-based courses in

secondary school and college settings as it would allow us to assess particular aspects

of mathematical reasoning and, as such, might stimulate the design of instructional

strategies and materials.

• There is still a substantial need to design and test teaching/learning materials that

support student learning in this context.

• It is not clear what role mathematics teachers can play in this context.

• Research on effective practices in physics teacher training is still missing.

• Research on integrated teaching of physics and mathematics is not conclusive. We do

not yet understand whether and how integration should be stimulated to facilitate

student learning.

Much more research and development of activities is needed so as to further support

students to blend mathematics and physics.

Acknowledgements

I gratefully acknowledge Paul van Kampen and Johan Deprez for the many discussions on the

mathematics-physics interplay that helped sharpen my ideas. Moreover, I would like to thank

both and Jan Sermeus for beta-reading the manuscript.

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129

Chapter 7

Physics Teachers’ Professional Knowledge and Motivation

Stefan SORGE, Melanie M. KELLER, Knut NEUMANN IPN – Leibniz Institute for Science and Mathematics Education,

Department of Physics Education, Olshausenstr. 62, 24105 Kiel, Germany

Abstract: In this chapter, we discuss the current state of research on physics teachers’

professional knowledge and motivation. For both, teacher knowledge and motivation,

respective models have underlined their relevance for the planning, enactment, and reflection

of physics instruction. Yet, most research on teachers’ content and pedagogical content

knowledge as well as on teacher motivation has not investigated the interplay between both

characteristics. To indicate the importance of accounting for the interplay between knowledge

and motivation, we summarize the findings of two major papers that have investigated the

interplay in pre-service physics teacher education and for the design of physics instruction.

1. Introduction

Physics instruction is focused on a thorough examination of natural phenomena through

scientific practices such as conducting experiments, developing models, and discussing

scientific evidence with peers and the teacher [1]. The selection of phenomena that spark

students’ interest as well as the implementation of diverse scientific practices relies on a series

of well-informed decisions and actions of the teacher in the physics classroom. Accordingly,

physics teacher education needs to provide future physics teachers with learning opportunities

that allow them to make such informed decisions about the design of physics instruction; and

enable them to act accordingly in physics classrooms. Hence, it is crucial for physics teacher

educators to have a sound understanding of the teacher characteristics influencing instructional

decisions and actions as well as how those characteristics can be fostered through physics

teacher education.

Research on physics teachers’ characteristics and their development has undergone major

shifts in research focus in the past 30 years. These research shifts become apparent by taking a

closer look at the sections on physics teacher characteristics from the two previous editions of

the ICPE handbook. In 1998, Gunstone and White as well as de Souza Barros and Elia focused

their chapters on physics teachers’ attitudes and how they impact instruction [2–3]. While

Gunstone and White do acknowledge that teachers’ understanding of physics also play an

important role for the enactment of instruction, “it is teachers’ view of teaching and learning,

the nature of science and the purpose of education that are of prime influence in shaping their

attitudes to classroom practice” [2, p. 1]. Yet, 10 years later in the second edition of the ICPE

handbook, there is no more reference to teachers’ attitudes in the chapters about teaching

physics. Instead, Grayson provides a concrete topic-specific example of the pedagogical

content knowledge (PCK) needed to teach electric circuits [4] and Carvalho highlights the

importance of communication skills for a change in classroom culture [5]. This comparison

between the first and second edition of the ICPE handbooks nicely illustrates the shift in

research on teacher characteristics from general teacher attitudes to topic-specific knowledge

and skills.

In the present chapter, we build on the chapters of Grayson and Carvalho [4–5] by

reviewing key research on science (and more specifically physics) teachers’ professional

knowledge and skills for planning, enacting, and reflecting quality physics instruction [for

130 | Sorge S., Keller M., Neumann K.

example, see 6–8]. Still, as Gunstone and White have pointed out, it is not only teachers’

knowledge that shapes physics instruction [2]. Rather and in addition to teachers’ knowledge,

it is motivational teacher characteristics like, for example, a love for physics or enthusiastic

teaching [9] that inspire classroom behavior – and ultimately impact students’ outcomes. In this

chapter, we want to introduce both teachers’ professional knowledge as well as teachers’

motivation, how these teacher characteristics develop, and how they mutually impact physics

instruction. The research introduced in this chapter should help physics teacher educators to

focus on key teacher characteristics throughout teacher education that have a strong impact on

physics instruction.

2. Physics Teachers’ Professional Knowledge

Research on teacher professional knowledge gained momentum following the seminal work of

Lee Shulman [10]. Therein, Shulman introduced a list of seven knowledge bases that serve as

a foundation for teacher reasoning: content knowledge (CK), general pedagogical knowledge

(PK), curriculum knowledge, pedagogical content knowledge (PCK), knowledge of learners

and their characteristics, knowledge of educational contexts, and knowledge of educational

purposes and values. Among those knowledge bases, Shulman directed the attention towards

PCK as the specialized knowledge base of teachers representing an amalgam of content and

pedagogy [10, see also 11]. In a similar vein, Etkina et al. introduced the term content

knowledge for teaching (CKT) and specified it for the domain of energy as “’residing’ at the

intersection of specific tasks of teaching with the student energy targets” [12, p. 4]. As such,

the knowledge of a physics teacher should go beyond the content knowledge they expect

students to acquire and should instead include a teaching-specific understanding of the domain

[12]. This teaching-specific focus on teacher knowledge can also be found in the model of

Mathematical Knowledge for Teaching from Ball and colleagues [13]. Here, Ball et al.

identified common CK, horizon CK and specialized CK as the different types of content

knowledge a teacher should have besides an understanding of PCK based on the analysis of

teaching practice. This distinction between different types of CK demonstrated that a general

understanding of the domain (i.e., common CK) is not sufficient for high-quality mathematics

instruction [13]. These different conceptualizations of teacher knowledge range from

representing a more static theoretical description of knowledge for teachers to a more practice-

based knowledge of teachers [see 14]. In addition to that, the role of CK differs among those

various conceptualizations: While Shulman clearly formulated that CK and PCK represent

distinct knowledge bases, Etkina et al., for example, took a more integrated approach

combining both perspectives into the CKT model [10, 12]. This leaves the question to which

degree CK is a unique knowledge base that teachers need to draw upon during teaching

processes or an integral part of PCK itself [e.g., 15].

In an effort to integrate the different perspectives on science teacher knowledge, a first

summit with experienced science education researchers was conducted in 2012. This summit

resulted in a new integrative model for teacher knowledge and skills, the so-called Consensus

Model of PCK [7]. This model incorporates two different conceptions of PCK, distinguishing

between broader professional knowledge bases for teachers that impact the personal PCK and

skills of a science teacher [7, see also 16]. Whereas CK has been identified as part of the broader

professional knowledge base, it is the personal PCK and skills that guide teachers’ decisions

when planning, enacting and reflecting on instruction. However, although successfully

integrating the different conceptions, the Consensus Model did not provide detailed

information on the individual facets of PCK itself. In response to this, a second PCK summit

was held in 2016 that resulted in the Refined Consensus Model (RCM) of PCK [17].

Chapter 7 | 131

The RCM includes CK as part of the broader professional knowledge bases but also

delineates three different and interconnected realms of PCK: collective PCK, personal PCK,

and enacted PCK [17]. Collective PCK represents the knowledge shared among a group of

professionals and includes the research from physics educators that is codified in research

articles and books. A possible piece of collective PCK could be that physics instruction needs

to be situated in meaningful contexts that spark a need to know among students [e.g., 18]. This

collective PCK forms one pillar of personal PCK that represents the cumulative knowledge and

skills of a single teacher that he or she can draw upon when designing instruction. Besides

collective PCK, the experiences teachers make when teaching a specific topic such as energy

to their 8th grade students can further enrich their personal PCK. In the moment of planning,

teaching, and reflecting on an energy lesson for 8th grade students, physics teachers utilize their

enacted PCK, which is specific to that very situation. In total, the RCM details a connection

between the knowledge that teachers utilize in a specific situation during class up to the

knowledge that is produced by physics education research. From this point of view, it is key

that pre-service teachers have the opportunity to develop broader knowledge bases such as CK

as well as to enrich their personal PCK.

2.1. Physics teachers’ content knowledge

There is no doubt that physics teachers need to understand, for example, Newton’s laws of

motion before they can teach them to students. In fact, prior research has shown that teachers’

understanding of the subject matter (i.e., their CK) forms the basis for understanding how to

address this subject matter in instruction (i.e., their personal PCK) [e.g., 19–21]. In Shulman’s

initial conception of teachers’ professional knowledge, he noted that teachers’ CK includes an

understanding of the main facts or concepts, how those facts are related to each other, and in

which ways new knowledge is produced in a domain [11, see also 22]. Yet, at which breadth

and depth do physics teachers need to acquire these facts and concepts?

A possible starting point to answer that question is that physics teachers need to have a

sound understanding of the content covered in the school curriculum (i.e., common CK) [13].

Grossman et al. also pointed out that this understanding of the school curriculum is likely not

sufficient and teachers need to have a CK that goes beyond knowing what students need to

know [23]. Teachers’ CK should rather enable them to follow future trends in the respective

domain and also allow them to adequately prepare their students for higher education courses

[23]. A more nuanced description of physics understanding was given by Woitkowski who

differentiated between school-related, deepened (i.e., advanced), and university knowledge of

physics [24]. While school and university knowledge can be distinguished according to the

level of complexity and mathematization, deepened knowledge is focused on misconception as

they are assessed for example with the force concept inventory [25]. A different classification

of science CK was provided by Nixon et al., who distinguish between core CK, specialized

CK, and linked CK [26, see also 13]. While core CK resembles school-related CK, specialized

CK comprises of knowledge about adequate representation and examples. Linked CK consists

of knowledge of the structure and relationship of facts in a domain. Bringing all those different

conceptions of CK together, we can conclude that physics teachers need CK that (1) includes

the knowledge covered in the physics curriculum, (2) goes beyond this school-related

knowledge to adequately prepare students for science college courses, and (3) covers

epistemological aspects of physics.

In an effort to assess and investigate the breadth and depth of pre-service physics teachers’

CK, Sorge et al. developed an instrument that covers the common topics of the school and

university curriculum: mechanics, electrodynamics, optics, thermodynamics, solid static

physics, atomic and nuclear physics, special relativity, and quantum mechanics [27]. To

132 | Sorge S., Keller M., Neumann K.

account for the depth of CK, the instrument covered basic facts and principles (i.e., declarative

knowledge) as well as knowledge about how, why, and under which conditions these facts and

principles can be used (i.e., procedural-strategic knowledge) [see 28]. Two sample items

covering different topics and types of knowledge are shown in Figure 1[PP1]. This newly

developed instrument was utilized in a cross-sectional as well as in a longitudinal study in order

to investigate the development of pre-service physics teachers’ CK during teacher education in

Germany. Based on that data, Schiering et al. were able to demonstrate that pre-service physics

teachers develop their declarative CK significantly between the first and second year of study

as well as between the second and third year of study [29]. Procedural-conditional CK,

however, did only increase significantly between the second and third year of study. This result

is in line with the finding from Woitkowski who also reported that physics students in Germany

mainly increased their factual knowledge during the first year of study [24]. The developmental

pattern indicates that pre-service physics teachers, first, learn new facts and principles and then

build upon those facts and principles to develop a deepened understanding of physics. Yet,

Schiering et al. were also able to show that acquired procedural-conditional knowledge can

also support the acquisition of declarative CK by making new principles and facts available to

pre-service teachers [29, see also 30].

A) Which of the following formulas applies to the magnitude of the gravitational

force F between two objects given their masses m1 and m2, and the distance r

between them? G represents the gravitational constant.

□ 𝐹 = 𝐺𝑚1∙𝑚2

𝑟

✓ 𝑭 = 𝑮𝒎𝟏∙𝒎𝟐

𝒓𝟐

□ 𝐹 =1

4𝜋𝐺∙

𝑚1∙𝑚2

𝑟

□ 𝐹 =1

4𝜋𝐺∙

𝑚1∙𝑚2

𝑟2

B) Heisenberg's uncertainty principle is commonly considered for small objects

like electrons or protons. Why is this principle not applied to larger objects?

□ Measurement uncertainties for large objects can be generally reduced by

more sensitive instruments.

□ Large objects do have a definite position and momentum which can be both

measured accurately.

□ For large objects, classical mechanics apply and uncertainty cannot be found

in classical mechanics.

✓ Generally, uncertainty principle can be also found in larger objects, but

uncertainties become small enough that they are negligible.

Figure 1. Sample CK items. A) shows a sample declarative CK item,

B) shows a sample procedural-conditional CK item [29].

Although there is evidence for the general effectiveness of physics teacher education for

the development of pre-service teachers’ CK, a particular variance can be found in the actual

design and implementation of teacher education systems [for an overview, see 31]. This

variance potentially influences the development of teachers’ CK. Two possible influencing

factors for pre-service physics teachers’ CK development are the quality of learning

opportunities in physics as well as the resources available to acquire the mathematical

foundations of physics. Indeed, Neumann et al. were able to demonstrate that for pre-service

Chapter 7 | 133

teachers who aspired to become physics and mathematics teachers, mathematical knowledge

had a significant impact on physics CK even when general cognitive abilities were controlled

for [32]. This study, thus, highlights the importance of mathematics understanding for the

development of pre-service physics teachers [see also 33]. To capture the quality of the learning

opportunities, Schiering et al. used a survey that covered key features of high-quality

instruction: cognitive activation, cognitive support, emotional support, and classroom

management [34]. From those features of high-quality instruction, only cognitive support

showed a significant impact on pre-service physics teachers’ CK development. This result

highlights the importance of individualized support as well as the clarity of learning goals (i.e.,

cognitive support) for the development of pre-service physics teachers’ CK. Thus, physics

teacher education needs to provide adequate cognitive support for their pre-service teachers as

well as learning opportunities in mathematics in order for pre-service physics teachers to

develop a sound understanding of CK and, consequently, provide a basis for the development

of personal PCK.

2.2. Physics teachers’ personal pedagogical content knowledge

The RCM identifies personal PCK as the reservoir of a teacher that he or she can draw upon

when planning, enacting, and reflecting on instruction [17]. Since personal PCK is the result

of all prior formal learning opportunities as well as personal classroom experiences, it is highly

dynamic and individual. One way to further describe this highly individualized knowledge is

through identifying key aspects of that personal PCK that guide the reasoning of teachers. The

most prominent model that identified key aspect of teachers’ PCK is the model proposed by

Magnusson et al. [35]. Magnusson et al. identified five aspects of teachers’ PCK: knowledge

of science curricula, knowledge of students’ understanding of science, knowledge of

instructional strategies, knowledge of assessment and literacy, and an overarching orientation

towards teaching science [35]. Friedrichsen et al. suggested that this general orientation

towards how science should be taught rather represents a conglomerate of interrelated beliefs

[36] and, thus, should act as amplifier or filters for theaching practices [7]. The five aspects of

PCK can be seen as a consensus among researchers as well [e.g., 37]. Kind and Chan also

highlighted that these different aspects represent the amalgam of content and pedagogy since

ideas from general pedagogy on how learning needs to be organized to be effective has to be

aligned with more content-oriented ideas on, for example, the difficulties students encounter

when dealing with a certain topic [38, see also 12]. Thus, it becomes possible to represent the

key characteristic of a teachers’ personal PCK by using the five aspects of the model from

Magnusson et al. [35], while teachers still can draw upon additional ideas from their

individualized knowledge.

These five aspects of teachers’ personal PCK can also be used to interpret the results from

studies using different types of assessment instruments such as: Content Representation tool

(CoRe) [e.g., 39–40], lesson observations and recordings [e.g., 41], performance assessments

[e.g., 42–43], and paper-pencil-tests [e.g., 27, 44]. The CoRe tool was developed by Loughran

et al. and is a set of questions oriented on key aspects of PCK (e.g., Why is it important for the

students to know this?) to elicit the collective understanding of a group of teachers (i.e., to

capture their collective PCK) [45]. However, other researchers have adapted this approach to

gain insights into the personal PCK on, for example, electric circuits from individual teachers

[39]. Seung used observational data to identify how physics teaching assistants’ PCK

developed when teaching an introductory course on the atomic and molecular nature of matter

[41]. She was able to demonstrate that teaching assistants first acquired the collective PCK,

then actualized it during the teaching experiences and finally internalized this new knowledge

as personal PCK [see also 43]. While this type of observational data allowed to draw direct

134 | Sorge S., Keller M., Neumann K.

conclusions from physics teachers’ actual teaching behavior, performance assessments

represent an approximation of practice by focusing on a standardized practice such as

explaining phenomena in mechanics [42]. Using a performance assessment, Kulgemeyer et al.

could demonstrate that the development of enacted PCK also depends on the foundational

personal PCK of teachers [46]. To assess the personal PCK, Kulgemeyer et al. utilized a paper-

pencil test [46]. Similar paper-pencil tests have also been developed by Kirschner et al. for the

topic of mechanics [44] and Sorge et al. covering eight different topics [27]. Based on this

developed paper-pencil test, Sorge et al. were able to find a significant increase of personal

PCK across initial physics teacher education. In addition, observations of experienced teachers

also had a significant influence on the personal PCK of pre-service physics teachers as well

[27, see also 19]. Overall previous research has shown that especially a combination of

assessment instruments allows to tap into knowledge exchange processes between different

realms of PCK. The investigation of the different realms of PCK has also shown that it is

important to acquire personal PCK during initial teacher education, which then can be refined

and enriched through purposeful designed practical experiences [e.g., 41, 47]. Yet, the RCM

also points out that other teacher characteristics such as teachers’ beliefs and motivation are

key amplifier and filters for the acquisition of personal PCK and for the actual behavior in

physics classroom.

3. Physics Teachers’ Motivation

Motivation is the motor that drives human behavior. Since the dawn of their discipline,

psychologists endeavored to understand why individuals behave the way they do. This decade-

long endeavor cumulated in a common understanding of motivation as “an internal state that

arouses, directs and maintains behavior” [48, p. 376]. For these different functions – arousing,

directing, and maintaining behavior – motivational theories have over time come up with a

plethora of constructs that may be somewhat overwhelming [for an entertaining read, see 49].

Yet, these motivational theories also are highly adaptable to describing motivational processes

in different contexts such as the teaching context. Motivation in teachers changes its shape and

function depending on their career phase and professional activity. Following, we highlight

some key findings from teacher motivation research.

Teachers’ careers start with high school students’ decision to become teachers.

Achievement related decisions are influenced by expectations of success and subjective task

values as postulated in the expectancy-value theory [50]. Based on this framework, Watt and

Richardson developed the FIT-choice model to describe the motives underpinning choosing

teaching as a career [51]. Thereby, students’ choices for teaching as a career are powered by

strong intrinsic and social utility values (such as shaping and guiding the future generation,

making a contribution to society, etc.), whereas – contrary to lay-beliefs – extrinsic motives

such as having time for family or even choosing teaching as a fallback career seem less

important [52–53].

According to expectancy-value theory, expectations of success are central to motivational

processes, and in teacher motivation research this facet is approximated most often by teaching-

related efficacy. Efficacy refers to teachers’ beliefs that they – as individuals or as a group of

teachers (i.e., self- and collective efficacy) – are able “to bring about desired outcomes of

student engagement and learning, even among those students who may be difficult or

unmotivated” [54, p. 783]. Efficacy in teachers is a powerful predictor of a whole range of

outcomes [for a review see 55]; it was found to be related to facets of teachers’ occupational

well-being (e.g., decreased emotional exhaustion [56]; increased job satisfaction [57]),

classroom practices and instructional quality [58–59], and students’ achievement [60–61].

Chapter 7 | 135

On the more affective side of teacher motivation, teachers’ interest and enthusiasm

describe an individual’s inclination towards an object or activity [62]. Teacher interest has been

associated with general effectiveness as perceived by students [63], and in differentiating

subject, didactic and educational interest, Schiefele and colleagues found that all three forms

of teachers’ interest relate to higher students’ interest, but only teachers’ educational interest

further related to mastery oriented instructional practices and students’ own mastery goals [59,

64]. This finding is mirrored in findings by Kunter and colleagues that enthusiasm for teaching

is the more powerful predictor of classroom practices compared to subject enthusiasm [65].

Further, teaching enthusiasm is related to occupational well-being [66], mastery oriented

classroom practices [58], and students’ achievement [67], interest [68] and developmental

trajectories of students’ interest [69].

Coming from the notion that teachers’ occupational activities are situated in an

achievement arena, Butler adopted the approach of achievement goal orientations also for

teachers [70]; she separated mastery goals (i.e., teachers’ striving to acquire and develop their

competence), achievement goals (i.e., striving to demonstrate high abilities or avoid

demonstration of poor abilities), and work avoidance goals (i.e., striving to invest as little effort

as possible). She found that only mastery orientations predict autonomous help-seeking

behaviors, whereas work avoidance related to a more passive approach to help seeking by

preferring others to provide assistance. This finding is corroborated by further studies

evidencing the adaptive effects of mastery orientations and detrimental effects of achievement

avoidance and work avoidance goals [71]. Teachers’ goal orientations impact classroom

practices in a way that teachers’ own approach to achievement stressing mastery vs

achievement is reflected in creating mastery vs achievement oriented learning environments

for students [72–73]. Although studies provide evidence about the superiority of teachers’

mastery goal orientations, it seems that teacher education programs at universities rather stress

achievement goals which increase during pre-service teachers’ time spend at universities [74].

Even though these findings demonstrate that teachers’ own take on learning shapes the

type of learning environments they create for students, not all in school and in classrooms is

about achievement and learning. Being a teacher is also a social job and forming social bonds

with students is key to effective classrooms [75] – and, as we saw earlier, also a driving motive

for why individuals choose teaching as a job in the first place. To account for this facet to the

teaching profession, teachers’ achievement goals are complemented by a relational goal

teachers strive for in the classroom which was found to relate to mastery-oriented classrooms

and social support as perceived by students [76].

Teachers’ goal to interact with and connect to their students also makes sense from a basic

needs perspective. In a more humanistic approach to motivation, Deci and Ryan argue that

humans have basic needs – the need for autonomy, competence, and relatedness – and what

drives (i.e., motivates) us is to satisfy those needs [77]. Self-determined motivation in teachers

is related to occupational well-being and students’ own self-determined motivation [78].

Specifically, the extent to which teachers see their need to form meaningful bonds with their

students satisfied is related to their work engagement and well-being [79].

In sum, a considerable body of research has demonstrated that teacher motivation matters

– to teachers’ themselves, their instructional practices, and ultimately students’ growth. Yet

what teacher motivation is, and which processes it influences heavily depends on teachers’

career phase. In other words: at universities where teacher students are mainly learners in an

achievement-environment who aspire to teach but seldom do, achievement motivation (for

instance in the expectancy-value theory) predicting achievement behavior and choices is a

suitable framework. However, in-service teachers mainly teach and forming social bonds with

students and direct social interactions in the classroom features strongly in their professional

activities; thereby, motivational theories applied to in-service teachers need to also account for

136 | Sorge S., Keller M., Neumann K.

these social activities and interdependencies between teacher motivation, instructional

behavior, and student outcomes.

4. Relationship between teachers’ professional knowledge and motivation

Up until this point, we have treated teacher knowledge and teacher motivation as separate

phenomena when in fact they are interdependent as they are developed and shaped during

teacher education as well as when they conjointly influence instructional practices and students’

outcomes. During teacher education pre-service teachers are learners themselves and, thus,

their motivational characteristics impact their knowledge acquisition as well as the success in

knowledge acquisition can subsequently influence the motivational characteristics [80]. When

designing and providing a classroom environment conducive to learning and inspiring for

students, in-service teachers rely, as we have shown earlier, on their professional knowledge as

well as on their motivational orientation. Acknowledging this interdependency of teacher

knowledge and motivation and their conjoint effects on instruction and students’ outcomes,

professional knowledge and their motivational characteristics are seen both as part of teachers’

professional competence [67, 81]. In the following section, we will detail two studies that have

investigated the interplay between professional knowledge and motivation during physics

teacher education and physics instruction to highlight the potential for combining both

perspectives.

4.1. The interplay of motivation and professional knowledge during teacher education

The first study by Sorge et al. investigated the relationship between pre-service physics

teachers’ professional knowledge, their self-concept, and interest during teacher education [82].

While previous research has indicated a positive association between professional knowledge

and motivation [83], the nature of this association has not been investigated in much detail. In

addition to this, pre-service teachers are expected to develop CK as well as PCK, which are

also expected to be intertwined [27]. One way to account for the interdependence of

achievement and motivation in multiple domains is through the use of the generalized

internal/external frame of reference model (GI/E model) [84]. The basic assumption of the GI/E

model is that individuals’ motivational characteristics such as their self-concept or interest in

multiple domains are based on social and dimensional comparisons of their achievement in

those domains [see also 85–86]. For example, a student will use external social comparisons to

relate his/her understanding in physics to the physics understanding of his/her peers. A high

understanding will then result in favorable social comparisons which ultimately lead to a high

self-concept for the domain of physics. Additionally, this student can also use an internal frame

of reference to compare his/her achievement in physics and English. If this student has below

average abilities in English and average abilities in physics, he/she will perceive the own

abilities higher in physics and lower in English – resulting in a higher/lower self-concept in the

respective domains [86]. While there is ample evidence for the validity of the GI/E model for

school students [87], only Paulick et al. used the GI/E model in the context of pre-service

biology teachers’ professional knowledge and self-concept before [88]. Sorge et al. extended

this previous investigation to pre-service physics teachers and also included pre-service

teachers’ interest as a possible outcome of comparison processes [82].

The results showed that indeed pre-service physics teachers with a high CK or PCK had a

high self-concept in the respective domain. Furthermore, there was also evidence for internal

comparison processes since pre-service physics teachers with a low CK level had a significant

higher self-concept of their PCK. The same internal comparison could not be identified for

PCK on CK self-concept and there were also no direct effects from pre-service teachers’

Chapter 7 | 137

knowledge on their interest. Still, additional analysis revealed that pre-service teachers’ self-

concept mediated the influence from professional knowledge to pre-service teachers’ interest.

These results highlighted that pre-service teachers base the assessment of their own PCK

abilities not only on their actual abilities but also on their abilities in CK and that these

comparison processes transcend to pre-service teachers’ interest in CK and PCK.

4.2. Effects of physics teachers’ PCK and motivation on instructional behavior and students’

learning and interest

As discussed in the preceding section, pre-service teachers’ motivation and knowledge are

deeply intertwined – something that is also true for in-service teachers. Yet, teacher knowledge

and motivation are rarely considered in conjunction as determinants to instructional behavior

and student outcomes. In the following, we summarize the findings of a previously published

study on physics teachers’ PCK and motivation influencing instruction and students’

achievement and interest in physics [89].

As has been argued earlier in this chapter, teachers’ PCK is at the heart of their professional

knowledge, and together with motivation they constitute key aspects of teachers’ professional

competence [67, 81]. It is assumed that conjointly they contribute to students’ learning

outcomes. However, as PCK is crucial in implementing content in the classroom in a way that

makes it accessible to students, teacher motivation should become visible to students,

impacting their own motivation in the subject. Therefore, it was hypothesized that on the one

hand, teachers’ motivation in the form of interest in teaching physics would positively influence

students’ interest in the subject [e.g., 68] – transmitted by enthusiastic teaching behaviors in

the classroom [e.g., 90]. On the other hand, it was hypothesized that teachers’ PCK would

influence students’ achievement, mediated by cognitively challenging but well-structured tasks

and learning opportunities in the classroom (i.e., cognitive activation, [67]).

In the study N = 77 high school teachers and one of their 10th grades physics classes (N =

1614 students) in Germany and Switzerland participated. Teachers provided information on

their PCK via a written test and their interest in teaching physics via a questionnaire at time

point T1, at which also students’ baseline interest in physics and achievement regarding

electricity was assessed which was repeated at a later time point T2 (for further information on

the student achievement test, see [91]). In between the two measurement points, a 90 minute

instructional unit on a fixed topic was videotaped and analyzed via trained raters regarding the

level of cognitive activation apparent in the questions and tasks teachers provided for their

students. The nested data (students in classes) was analyzed via multi-level modelling. The

findings of these models are shown in Figure 2.

In support of the hypotheses, teacher motivation positively influenced students’ subject

interest, and teachers’ PCK positively influenced students’ achievement (Figure 2[a]). The

effects were partially mediated by the respective instructional features, i.e., enthusiastic

teaching and cognitive activation (Figure 2[b]). However, neither did teacher motivation

impact students’ achievement, nor did teachers’ PCK impact students’ interest. This finding

implies that when both students’ achievement-related as well as motivational outcomes are

considered, it’s not either-or with teachers’ PCK and motivation, but and: teachers need to

know how to provide adaptive but challenging learning opportunities and they need to be

motivated to teach and interact with their students in order to optimally foster students’ growth

and learning.

138 | Sorge S., Keller M., Neumann K.

Figure 2. Physics teachers’ motivation and PCK influencing students’ interest

and achievement, without (a) and with (b) instructional behaviors as mediators,

on the class level. Standardized estimates are shown; dashed lines indicate

effects with p > .05; oval-shaped variables were implemented as latent

variables, rectangular-shaped as manifest variables in the model [see 89].

* p < .05. ** p < .01. *** p < .001.

5. Conclusion

Teachers’ professional knowledge, skill and motivation (i.e., competence) is widely considered

the prerequisite for quality teaching and hence student learning. Historically, in science and

physics education respectively, there has been a strong focus on teachers’ professional

knowledge, in particular teachers’ PCK [cf. 2]. Recently, evidence that non-cognitive aspects

of teachers’ professional competence play an important role for both the development of

teachers’ professional competence [e.g., 82] and teachers’ practice [43] has been growing. One

particular intriguing finding is that teachers’ knowledge and motivation affect different aspects

of instruction and are related to different learning outcomes [89]. The findings presented in this

chapter suggest that motivational aspects need to be attended to in teacher education. In line

with their role as amplifiers and filters that the RCM ascribes to motivational aspects, Sorge et

al. reported that pre-service teachers’ self-concept mediate the influence of pre-service

teachers’ knowledge on their interest [82]. This finding highlighted the importance of

supporting pre-service teachers in developing a strong self-concept. The role of motivational

aspects as amplifiers and filters is further corroborated by findings from Stender et al. that the

impact of teachers PCK on the quality of their teaching scripts is moderated by their motivation

[43] and findings by Keller et al. that it is the teachers’ interest in teaching the subject that

determines students’ interest in the subject [89].

The findings highlighting the importance of teachers’ motivation for their knowledge

development, as well as promoting students’ interest, raise the question of how to foster

motivation in pre- and in-service physics teachers in the first place. Interestingly, despite the

evidence suggesting that teacher motivation matters, there is little research on how to foster

teachers’ motivation [cf. 92]. The possibilities of how to foster teachers’ motivation, however,

will be highly dependent on the structure of teacher education. In countries such as Germany

with a dedicated teacher education, it can be assumed that students enter a teacher education

program with high motivation to teach. So, one challenge is to preserve this motivation while

educating them in the subjects they chose to teach [93]. In countries such as the United States,

where students decide to become a teacher after completing education in the subjects, the

challenge is to win the best students over to become teachers; that is, fostering a motivation in

them to teach [94]. Hence, we call for research not just examining how to support pre- and in-

service teachers in developing the professional knowledge they need but also in how to foster

Chapter 7 | 139

their motivation to teach. Furthermore, we note a lack of research, examining the mutual

interactions between professional knowledge and motivation development. In order to best

support students, we need to understand the mechanisms by which teacher knowledge and

motivation interact in their development and, even more importantly, how they jointly

influence teaching behaviors and student outcomes. We suggest that future research on physics

teachers attends to both teacher knowledge and motivation, and in particular the interplay

between them. We need to understand how teacher knowledge and motivation co-develop as a

function of teacher education and professional development. Plus, how can we support pre-

service physics teachers in developing beyond professional knowledge the motivation to teach

their subject? And how can professional development activities be designed to beyond

providing teachers with new knowledge, fuel or refuel their motivation? We envision teacher

education and teacher professional development of the future to equally pay attention to both

aspects to fill physics classrooms with knowledgeable and motivated teachers who design and

implement physics instruction in a way that helps students develop knowledge and interest as

well.

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Part IV

Experimentation and Multimedia in Physics Education

145

Chapter 8

Experimentation in Physics Education

Elizabeth J ANGSTMANN

School of Physics, The University of New South Wales, NSW 2052, Australia

Manjula D SHARMA

School of Physics, The University of Sydney, NSW 2006, Australia

Abstract: Physics is an experimental science; theories and knowledge are grounded in

experimental evidence. A cornerstone of physics is the quest for better ways of ‘seeing and

detecting’ with instrumentation and measurement at its heart. The novel techniques physicists

utilize to take measurements have tremendous impacts on other disciplines and society as a

whole. Physics education and curriculum seeks to embed an appreciation for measurement

through laboratory programs, practicals, experimentation, hands-on activities as well as

demonstrations. This chapter traces how experimentation has been approached in physics

education over time as well as our research and findings. We begin by considering inquiry as

a pedagogy in a school setting, describing the role of inquiry and how it can be measured.

Following this we consider labs in a tertiary setting. Throughout we provide examples of how

these ideas can be implemented.

1. Introduction

With the harnessing of fire and creation of tools for survival, humans in antiquity had started

experimenting! One could say that the goal of such developments was to ‘enhance’ their lives

and improve chances of survival. With trial-and-error, observations of patterns as well as

iterative attempts based on experiences, a naïve form of theorising was interwoven with

experimentation. As the quest to understand nature deepened, experimentation underpinned the

growth of navigation, astronomy, and natural philosophy. Communities for sharing were

established and schools for comprehensive education as well as research-based universities as

we know them, appeared. The goal of experimentation was to provide evidence as theories

solidified. In parallel with the industrial revolution, learned societies developed, the

educational model of an apprenticeship training under an expert dominated. The very few

aspiring novice scientist-to-be apprentices stood out from the rest, often funded by wealthy

amateurs or those intrigued with science. The novice scientist in an apprenticeship model,

would observe, be taught one-to-one the delicacies of methods, techniques, and

experimentation. One could say that the goals of experimentation were to discover, provide

evidence for theories and aid development of technologies to advance human societies.

The mid to late 1800s saw widespread development of experimentation in the form of

physics practical classes and laboratory work in both schools and universities [1–8]. The

experiments were predominantly confirming knowledge, what one would now label as

cookbook exercises, to be performed by individual students as assigned by their instructor.

Pickering [3] observed that “[t]he excellence of the work done by many of the students led to

the hope that valuable results might be attained by assigning to different students the

experiments in a research [project]...”. The seeds for questioning the goals of experimental

work were being sown. Questions about the desired balance between discovery

experimentation where the answer is unknown and refining the delicacies of methods and

techniques were surfacing [9, 10].

146 | Angstmann E. J., Sharma M. D.

Post-World War II saw the development of the cold war and the space race. The industrial

revolution saw factories with labourers being replaced by those who needed to operate

machinery and processes. In place of a selected few studying science, mass education was

becoming the norm. The notion of ‘education’ rather than ‘training’ was at the forefront of this

revolution. The ‘crisis in science education’ led to a consensus that the goals of science

education were to produce graduates with defined abilities and aptitudes. Experimental work

was seen as being important in the development of these abilities. The pendulum was swinging

towards experimentation underpinned by ‘inquiry’ and away from a recipe-based approach.

The apprentice model is a mainstay in PhD programs and in recent times, undergraduate

research has gained traction, students in later years of their study working with experts in the

apprenticeship model. It is in experimental fields that the apprentice model becomes

particularly important, as students develop discipline in executing detailed, repetitive tasks,

maintain attention on observations, record and analyse data. The balance between recipe and

open- ended components needs to be considered for individual experiments with students’

progression within the curriculum, and associated development of skills accounted for. The

introduction of ‘projects’ in secondary and university education as well as integrated STEM

projects, design-based activities, and the incorporation of digital technologies in parallel with

individual experiments seeks to find an appropriate balance [11–13]. The goals of

experimentation continue to be critiqued, as is the place of experimentation in its various guises

in the curriculum.

This paper probes the goals of experimentation in physics curriculum; exploring the

tension, balance and nuances in experimentation which can range from the more open-ended

project or discovery type experiments to the more recipe type where the focus is on honing the

techniques, the art, and craft of measurement. The probing of this tension is critical because

there is discourse around whether experimentation within a coherent laboratory or practical

program is justifiable [14–19]. What are the goals and how do they serve the learning of physics

as a discipline [20, 21]? In parallel, industry and employers are expressing a need for science

graduates, including physics graduates who have well developed project management and

generic skills [eg. 22]. Much of these are taught and learnt through laboratory programs. On

the other hand, those teaching science face practical tensions and dilemmas ranging from space

and resources to the gradual takeover by simulations and computer tools which are ‘not messy’,

to meeting diverse student needs [23–25]. Under the circumstances, it is a challenge to provide

quality learning experimental teaching programs.

The stalwarts, none-the-less, pursue teaching experimentation in the belief that there are

substantive learnings and benefits in terms of developing soft skills, working with messy data,

and handling equipment that defines the discipline of physics. After all, physics is about

measurements and experimentation, ranging from ‘looking’ at the beginning of time and

universe to ‘detecting’ the tiniest things around us. Curriculum designers, teachers and

researchers continue to strive to incorporate the notions of developing and using instruments,

the apprentice model, and inquiry in its various guises to unravel the complexity of skills

required in experimentation [26–28]. Evaluation of whether experimentation and lab programs

are effective are also ongoing [29–31].

This paper starts off with a section on schools which discusses inquiry as a pedagogy

underpinning experimentation. We elaborate on the various guises of inquiry within curricula

as well as the generation of the ASELL Inquiry Slider. Two physics experiments are used to

illustrate experiments in which features of inquiry can be varied. The second section is on

experimentation in university physics education. Here, we provide examples of open-ended

projects and ways by which inquiry can be fostered as well as what to consider when designing

experiments and laboratory programs. The conclusion comments on where we are at and

suggests future directions.

Chapter 8 | 147

2. Experimentation in schools: Inquiry as a pedagogy, and its various guises

In the school context, experimentation ‘neatly fitted’ into the teaching of content in the syllabus,

with the goal of supporting the learning of content. Post-World War II, saw the questioning of

the purpose of running practicals as well their pedagogical basis; what is taught, how is it taught

and what should students learn through experimentation? Schwab in 1962 [32] captured a view

widely held by scholars of that era, that science is “taught as a nearly unmitigated rhetoric of

conclusions in which the current and temporary constructions of scientific knowledge are

conveyed as empirical, literal and irrevocable truths”. If this is the case, then experimentation

is not required. A rationale and goal for experimentation, broader than simply supporting the

learning of content, was needed. As constructivist learning theories gained popularity, science

educators sought to utilise hands-on experiences and practicals to support conceptual

understanding, creating dissonance with the purpose of supporting conceptual development,

beyond understanding [eg. 33]. Perhaps a turning point was provided by the book, Children’s

Ideas of Science, edited by Driver, Guesne and Tiberghien [34]. Gradually, building further on

constructivism which was rapidly becoming the pedagogical basis of school education, the idea

of learners discovering through experimentation gained traction: discovery leaning with the

mantra ‘learn by doing’ [35]. Debate and deliberations are often polarised; at one extreme one

cannot discover all that needs to be learnt and on the other, learning only the established is void

of the processes [36–38].

2.1. Background on inquiry in school education

Given that questions were being raised about the goals of experimentation and whether

experimental programs were fit for purpose, Schwab (1960) [39] proposed linking laboratory

work with inquiry; seeking to provide a balanced approach “…curriculum can serve the needs

of teaching as inquiry… The laboratory is easily converted to inquiry ... The laboratory ceases

to be a place where statements already learned are merely illustrated and where perception of

phenomena occurs within the restrictive structuring of terms and concepts already laid down.

It ceases, too, to be preoccupied with standardized techniques. It becomes, instead, a place

where nature is seen more nearly in the raw and where things seen are used as occasions for

the invention and the conduct of programs of inquiry. … The laboratory manual which tells the

student what to do and what to expect is replaced by more permissive and open material.”

Schwab [39] called for three levels of inquiry with Herron [40] formalizing these and

developing the Herron scale for ascertaining the levels of inquiry. Since then, various types of

scales and levels of inquiry have been developed as well as a range of teaching approaches,

pedagogies with specific goals and purposes. For example, Bell, Smetana and Binns, p. 33 [41]

describe the 4 Level Model of Inquiry as follows:

- Confirmation - Students confirm a principle through an activity in which the

results are known in advance

- Structured - Students investigate a teacher presented question through a

prescribed procedure

- Guided - Students investigate a teacher-presented question using students’

design/selected procedure

- Open - Students investigate topic –related questions that are student formulated

through a student designed/selected procedure

Basically, each experiment can intentionally be slid from being more teacher directed to

more student directed according to the levels of inquiry, aligning with the goal of the

experiment.

148 | Angstmann E. J., Sharma M. D.

However, while the levels of inquiry provide an overarching framework, in practice each

experiment contains features. One example is that produced by the National Research Council

(NRC) p. 25, [42]. Each experiment has ‘essential features of classroom inquiry’ which are

listed as:

- Learners are engaged by scientifically oriented questions.

- Learners give priority to evidence, which allows them to develop and evaluate

explanations that address scientifically oriented questions.

- Learners formulate explanations from evidence to address scientifically oriented

questions.

- Learners evaluate their explanations in light of alternative explanations,

particularly those reflecting scientific understanding

- Learners communicate and justify their proposed explanations.

Bybee, p. 60 [43] generated the 5 E’s Model which has been popular in teacher education

programs:

- Engage - Learner engages in scientifically oriented questions

- Explore - Learner gives priority to evidence in responding to questions

- Explain - Learner formulates explanations from evidence

- Elaborate - Learner connects explanations to scientific knowledge

- Evaluate - Learner communicates and justifies explanations

It soon became apparent that each feature can also be slid from being teacher directed to

student directed. For example, a teacher can provide a well-defined topic or question, students

design/select the procedure, a teacher directs the analysis of which there may be several,

students formulate explanations while a teacher assists with connecting to a scientific

explanation. Hence, in practice, how the experiment is and can/be run does not fall neatly into

the levels of inquiry. This does not mean that the levels of inquiry are not useful. Rather, they

need refinement. NRC p. 29 [42] goes on to provide how each of the features can slide with

respect to ‘amount of learner self-direction’ as well as ‘amount of direction from teacher or

material’.

In summary, while the level of inquiry suggests that an experiment can be ‘classified’ [40,

41] the features of an experiment may also be at different levels of inquiry [42]. The sliding of

both the entire experiment as well as the features can assist the teacher in being more specific

with the goals of the experiment within their program and within the curriculum.

2.2. Inquiry slider, development and implementation

As part of a national project with the directive to facilitate the embedding of inquiry-based

learning in secondary school classrooms through teacher professional development (PD), we

sought to implement what has been described above. The project, Advancing Science and

Engineering through Laboratory Learning (ASELL) Schools, sought to utilise a three-pronged

approach drawing on (1) lessons learned in education research with (2) extensive consultation

with teachers and experts and (3) curriculum requirements [44]. Through an iterative process

we generated the key ASELL Schools pedagogical tool, called the ‘ASELL Inquiry Slider’ (see

[44] for more detail). The slider and a few example experiments are described below.

The NRC ‘essential features of classroom inquiry’ [42] and 5 E’s Model [43] formed the

basis of initial consultation with teachers. The fact that conducting an experiment or hands-on

activity was not explicit was identified as problematic. The act of experimentation was implicit:

not visible. This posed a problem as hands-on experimentation was mandatory in the syllabus,

embedded as learning outcomes. In essence, hypothetically, the question could be generated by

the learner, passed onto someone who generates a final table of evidence which the learner

Chapter 8 | 149

continues to work with. Working with teachers, academics and experts and in view of the

curriculum documentation in our state of New South Wales [46] as well as the Australian

Curriculum: Science [47], we set out to refine the features. The idea was to succinctly include

setting up, conducting, using instruments to take measurements, data recording and analysis

within the features. We converged on the following as the features of an experiment [45]:

- Learner engages in scientifically oriented questions and predictions.

- Learner plans how to carry out investigation and collect data.

- Learner conducts investigation, recording data.

- Learner processes and analyses data.

- Learner uses scientific reasoning and problem solving to link evidence to science

concepts.

- Learners communicate, and justify findings based on evidence and scientific

reasoning.

We note that teachers were insistent that planning should also pre-empt data handling and

that conduction should include data recording. Their point was that, while data is central, it is

often overshadowed by the ‘doing’. It was a challenge to constraint the number of features. The

features ended up being double barrelled, and we had to group them meaningfully. Teachers

also noted that ‘secondary data analysis’ which falls within the remit of experimentation will

not focus directly on the second and third feature. However, the presence of the second and

third features predicate teachers and learners to consider the source of data; interrogate the

‘trustworthiness’ of the providers of the data and the mechanisms by which the data were

obtained including biases. Teacher consultations lead to the features being better aligned with

the curriculum and learning outcomes.

During our consultations we also brainstormed and considered how each of the features

could slide with respect to ‘amount of learner self-direction’ as well as ‘amount of direction

from teacher or material’. What emerged was that teachers wanted explicit transition from

teacher to learner, rather than the approach adopted in the works described above which use

only student/learner when describing actions. Another important aspect that teachers argued

for was the inclusion of an ‘experiment’ which entailed showing or demonstrating phenomena.

They presented the case that oft times it was not possible for students to do experiments, even

if the experiments were prescriptive and confirmatory in nature. The reasons ranged from the

technical such as safety issues, limited resources, fragile equipment, paperwork to technical

staff support. Time pressures both in terms of time taken by students to do experiments and

time available to do experiments within the syllabus were discussed; with teachers optimising

by choosing to run experiments in different formats ranging from demonstrations to the more

open-ended. Behaviour and engagement as well as the differentiation within each class with

regards to confidence, risk taking, and competences meant that teachers had to balance their

strategies. Teacher expertise was also discussed honestly by teachers, with some seeking help

from peers when certain experiments were run or hesitating to do experiments in certain topics.

Sometimes, school policies and practices were a hurdle as well. Teachers presented the case

for exposing students to more experiments, argued for different forms of experiments,

including ‘demonstrations’ as a viable form of inquiry. They argued that the learning outcomes

of demonstrations as a form of inquiry aligned with meeting student needs within the syllabus.

Figure 1 shows the final ASELL Inquiry Slider, with five levels of inquiry and six features.

Demonstrated inquiry continues to be the most contested and debated, catching attention which

results in increased engagement, both cognitive and emotional. Some argue that demonstrated

inquiry can be framed with a question and have a conclusion, while others are happy to leave

it as a show and tell exercise. For our purposes, we were keen for teachers, academics and peers

to engage with inquiry-based learning as was the directive for our ASELL Schools project.

150 | Angstmann E. J., Sharma M. D.

Intense discussions suggested that teachers were engaging, and possibly reflecting on their

practices, which aligns with our goal of facilitating the uptake of inquiry-based learning.

Question

Plan

Conduct

Analyse

Reason

Conclude

Level of

inquiry

Figure 1. Advancing Science and Engineering through Laboratory Learning

(ASELL) Schools Inquiry slider; from [45].

By including ‘demonstrated inquiry’, we have sought to aid teachers who are often

challenged by comments such as “Question of time, energy, reading difficulties, risks,

expenses, and burden of the subject need not be rationalizations for not teaching science as

inquiry” Bybee, [43]. Bell, Setana and Binns, [41] state that “The inquiry scale should be seen

as a continuum, so ideally students should progress gradually from a lower level to higher

levels over the course of a year”; a sentiment our teachers generally affirmed but with

qualifiers. Given the range of activities which fall within experimentation, it is the features

where student progression can be mapped. Experimentation can range from demonstrations

with equipment, learning a practical skill, practical work, fieldwork, projects, problem-based

design activities, first-hand to second-hand investigations. The ASELL Inquiry Slider can be

used to frame experiments with learning outcomes such that students gradually progress along

the scale. Of course, as students’ progress through the years, the experiments become more

sophisticated. Richardson, Sharma and Khachan [30] report that, even if the experiment stays

simple, students’ approach increases in its sophistication.

2.3. Examples from schools

Two examples of experiments based on the ASELL Inquiry slider are presented below.

Example 1: Vampire Power [48]: This experiment was strategically designed with two-

steps. The first step was ‘prescribed inquiry’ and the second step was more open. The first step

was an exercise in which students working in teams of two or three were provided with a recipe

for a simple version of the experiment in which they took one reading. This step was timed and

each team was required to enter their reading on an EXCEL sheet which was displayed to the

Chapter 8 | 151

class. A class discussion was conducted around; setting up and taking measurements, the

readings and what they meant in terms of the science as well as the aim, and what other

questions/aims could be explored given a larger set of equipment on another table. The teams

were then asked to agree on a question and write their question on a white board. They were

told that they could modify their question on the white board. The reminder of the lesson was

spent on students exploring; they were asked to draw a sketch of their setup, records results,

and enter their results on a spreadsheet which could be displayed. In this experiment, the

analysis was hidden so that the experiment could be completed within the 70 to 90 minutes

double class dedicated to science experimentation, i.e., analyse was ‘demonstrated inquiry’. At

the end each team was asked to very briefly ‘respond’ to their question on the white board using

artifacts from their work as prompts. The experiment has been implemented with Grade 5 to

Grade 10 students, 10 to 16-year-old, in schools with a range of socio-economic backgrounds.

In earlier Grades, students were more involved in the act of measuring and recording values on

the spreadsheet and in higher grades, students got more involved in understanding the ‘model’

in the spreadsheet. Teachers noted that all students could achieve something and had something

to share; even those who normally do not effectively engage in experimentation. The two-steps

facilitated classroom differentiation as, in the second step, students explored quite nuanced

questions, from more physics-oriented, more equipment/measurement based, to more ‘energy

saving’ based. Some teachers used this experiment as a project for their students to do further

online search closely related to content leading to better learning outcomes. More detail on the

experiment is provided in Kota, Cornish and Sharma [48].

Example 2: Science in your pocket [49]: This experiment involved students from Grade 5

to Grade 10, 10 to 16-year-old, working in teams using an APP to ‘measure light’. Downloading

an APP was negotiated with schools in advance. We followed two steps where the first step

was finding a spot, taking a measurement and writing the measurement as well as the spot down

a whiteboard. In earlier Grades, students were told that they were to focus on how the numbers

change, patterns, and that the ‘what and how of the measured values’ would be covered in later

years. For higher grades, students were able to consider units as well as light from different

shapes and types of sources. The second step was again open-ended, students were asked to go

through the same process as in the above example. Here, the focus was on analysis, patterns,

different ways of representing and communicating. As each teams’ data emerged, contour

diagrams, measurements around corners and what does one get as you cut a line perpendicular

to contour lines were seeded. Higher graders could also be involved in log graphs. The sharing

of results at the end was phenomenal as each team tried to explain what they did to get their

patterns and what the patterns meant. Teachers reported that this led to projects where some

students were engaged in the differences between types of phones to how phones are getting

more sophisticated as well as detectors on phones. Other students explored types of light

sources and yet others explored ‘dark and light and measuring colours’. More detail on the

experiment is provided in Gordon, Georgiou and Sharma, [49].

3. Experimentation in undergraduate Physics

In the university context, once again, experimentation continues to ‘neatly fit’ into the teaching

of content in the syllabus, with the goal of supporting the learning of content. Changing the

status quo is compounded by the fact that most academics do not have a background in

education [50]. Given the competing demands on academics, research teaching nexus, often it

is not viable to adequately upskill [51]. Also, while school physics education is for a broader

cohort of students, university physics education is more focused on specialising in disciplinary

152 | Angstmann E. J., Sharma M. D.

skills and knowledge, albeit sometimes for allied service disciplines. Hence there is hesitancy

to detract from what are viewed as necessary ‘disciplinary knowledge’.

When comparing pedagogy in school physics education with university physics education,

it is fair to say that inquiry-based learning has not had the impact that it has had in schools.

What has had some penetration, are the more open-ended projects, including undergraduate

students working with research groups as suggested by Pickering [3]. Nevertheless, there have

been shifts towards incorporating processes and embedding development of skills, particularly

in experimentation. This is partially due to the questioning of the goals of running practicals,

their pedagogical basis as well as querying measurable learning outcomes. There are

aspirations to prepare work ready graduates to drive economies and contribute to the nation.

Hence, a focus on soft skills and what employers seek has emerged, driving mapping of

graduate qualities and attributes. In the Australian context, Threshold Learning Outcomes [21]

have been produced pointing to inquiry, generic skills and processes underpinning

undergraduate physics education.

Gradually, the goals and purpose of experiments and laboratory programs have been

shifting. Working under constraints such as limited space and resources, a gradual takeover by

simulations and computer tools which are ‘not messy’ and attempting to meet the diverse

student needs, academics are striving to provide quality teaching and learning experimental

teaching programs. Here, we provide a broad overview of undergraduate laboratory and

experimentation, including some examples of ways in which experiments can be designed with

specific goals in mind.

3.1. A glimpse of open-ended and guided experiments in first year university physics

Ideally, the purpose of the laboratory component in a given course informs the types of

experiments, more inquiry based, more guided, or a mix. The purpose is also reflected in the

assessment of the laboratory component; constructive alignment between learning outcomes

and assessment will increase student engagement with the laboratory activities [52]. If one

considers content, there is some evidence that laboratories do not improve examination

performance on conceptual questions related to the experiments [23]. This again raises the

question of whether laboratory programs are fit-for-purpose for teaching content unless, they

are specifically designed to teach content. In many laboratory programs, teaching content

including concepts is not the primary purpose. Often the learning outcomes are stated as

learning concepts and/or confirming theory; it is a good idea to explicitly articulate the goals

of each experiment as well as the laboratory program by clearly stating the skills and process.

It is important to note that measuring student development/progression in learning skills and

processes is significantly more difficult to ascertain. This compounds the issue of justifying the

existence of laboratory programs [53].

Common learning outcomes for laboratory programs and experiments in introductory

physics courses include data analysis, designing experiments, applying models,

instrumentation or consolidation of theoretical understanding [20, 21, 54]. This is where

students have the most opportunity to clarify misunderstandings as well as be supported

through the ‘messy processes of experimentation’; from setting up equipment, making sense

of unsteady dial numbers on instruments, recording to analysing and connecting with science.

To support student learning through the ‘messiness’, in many undergraduate physics courses,

the laboratory is the place with the highest staff to student ratio. Inquiry, reflective and practical

skills and behaviour can be encouraged by activities such as having students predict the

outcome of an experiment with reasons before performing it or having them derive an equation

for a certain situation. Together with activities, staff are critical in facilitating and guiding

students through the ‘messiness’. Similarly questioning and placing frequent check points

Chapter 8 | 153

throughout the experiments where students need to check-in with staff promotes interactions.

If the checkpoints are placed strategically, staff can prompt with questions and comments to

foster deeper thinking and engagement.

When we consider the more open-ended experiments which often are longer term projects,

the ‘amount of direction from teacher or material’ maybe restricted [55]. However, support

needs to be carefully managed through the ‘messiness’; students need choice and space for

reflective thinking and pre-empting outcomes of their choices. This is where adequate and

skilled staff presence is critical. When it comes to working with research groups, one needs to

be cautious. In the case of students working with research groups, it is possible to have

substantive teacher direction with no student choice, largely because the undergraduate

students are novices in quite sophisticated research. On the other hand, there are projects where

students are more self-directed and can still use the equipment from the labs as well as have

access to other equipment which they can request. We provide two examples below, one of

open-ended projects which are more learner self-directed and a guided experiment.

Example 1: Open-ended projects [13]: Projects are included in the course to give students

the opportunity to foster their natural curiosity, design and carry out a simple investigation,

develop experimental skills, work with a team and develop communication skills. Students

work in teams of six. During the first half of the semester students spend small amounts of time

choosing a suitable project and developing a plan. During the second half of the semester

students have three three-hour laboratory sessions in which they perform the experiment. The

following week students present their experiment orally to the class, submitting a written report

the next week. Students are marked on their two proposals, the oral presentation and the written

report. Team members determine the weekly participation marks for each member of the team.

Teams submit weekly progress reports summarizing what has been achieved that week, plans

for the following week and the contribution of each of the group members. The project mark

forms 15% of the course mark. More detail on the experiment is provided in [13].

Example 2: Guided experiment: The ideal gas law experiment was introduced to give

students the opportunity to experience the relationships between PV graph and processes

firsthand after it was noticed that students struggled with giving a physical description of the

different processes, for example a quick process is adiabatic because there is no time for heat

to flow. Before the class students complete a prelab exercise, which involves watching a short

video summarizing the equations involved and showing the equipment and then answering

numeric and conceptual questions. During the lab students use a syringe containing pressure

and temperature probes connected to a computer. They measure volume from the side of the

syringe. In the first part they measure pressure, volume and temperature as masses are slowly

added to the syringe, changing the pressure. In the second part they take the gas in the syringe

through a cycle, a quick compression followed by a slow expansion. Students are provided

with instructions but are asked to justify a number of the steps eg. “Why is it important that the

syringe reaches thermal equilibrium with the surroundings when you add the masses onto the

syringe?”. In the first part students are asked to plot a graph to calculate the number of mols of

gas in the syringe, they need to determine which quantities to put on each axis. In the second

part students are asked to draw a PV graph as accurately as possible for the cycle. They

calculate the heat transferred, work done and change in internal energy for each process. There

are checkpoints throughout the lab, when students reach these, they need to discuss their work

with a demonstrator, they have the opportunity to fix mistakes before it is graded. The lab is

marked out of 10 determined by how much of the exercise students complete correctly. The

prelab quiz forms 25% of the lab mark, the mark for this experiment is 2% of the student’s total

grade.

154 | Angstmann E. J., Sharma M. D.

3.2. Working within constraints: What to consider when designing undergraduate physics

experiments

3.2.1. Staffing

The most critical aspect of experimental programs is staffing; from technical support, tutors

who are sometimes called demonstrators and can be casual academics as well as PhD students

performing their first teaching role, to academics who are present during the sessions or oversee

the laboratory program. For those who are recruiting staff, it is utmost critical that staff have

appropriate skillsets, from communication, knowledge, technical expertise to approach. It is

not common, but entry tests and interviews have been known to make profound differences to

the teaching, student learning and laboratory work environment. Providing adequate training

at the beginning and ongoing mentoring and networking supports staff and results in an

improved experience for students while also introducing the next generation of academics to

evidence based pedagogy [56–58]. The call for professional development is not new, it has

been echoed over time by Schwab (1960) [39], Driver (1978) [33]. A couple of projects with

useful resources for demonstrator and tutor training are the Learning Assistants Alliance [59]

and Periscope [60].

3.2.2. Prework

As laboratories are expensive to run it is important to ensure that students get the maximum

possible benefit from the learning experience. Prework can assist with this. However, prework

needs to be carefully designed [61] taking into account the goals; not just focus on content.

Students coming adequately prepared for their experiments means that more time can be spent

on active learning such as discussions, taking measurements and analysing data. It can be useful

to place teacher-directed parts of the experiment into prework, online videos followed by

questions can introduce students to the equipment and the theories involved. Often, minimal

marks associated with prework leads to students being better prepared. Online prework with

automated feedback and marking can lead to more favourable outcomes than students investing

laboratory time answering prework questions. With online prework, one can also develop

question banks or random allocation of certain parts of prework to address issues of plagiarism.

3.2.3. Repetitive tasks

Laboratory experiments designed to maximise the time students spend developing skills

identified in the learning outcomes can aid in providing a cohesive program [52]. It is important

to also account for student interest which can be incorporated in a range of ways such as using

colourful stories [62]. Tedious and repetitive laboratory exercises disengage students [63].

While it can be important for researchers to repeat the same measurement numerous times,

time in teaching laboratories is limited so carefully consider which measurements need to be

repeated and why. There are creative ways around reducing the time spent on repeated

measurement. The obvious one is some form of automation. Another way is to repeat one set

of results giving students a way to judge the size of the uncertainties, it is then reasonable to

assume the uncertainties would be of a similar relative size in further data sets. One could also

consider different teams sharing their results, repetition is across different teams which can

lead to interesting discussions around sources of uncertainties. Such strategies mean that

students have the benefit of analysing the data to estimate uncertainties while avoiding the

tedium of numerous repeats.

Chapter 8 | 155

3.2.4. Lab notes

“Cook-book” experiments have a bad reputation [63], on the other hand, some students need

more guidance than others to complete the experiment. There is a tendency to skim over long

sets of notes, so a shorter set of instructions may be more effective and/or appropriate.

Optimising the detail in notes is critical. Furthermore, for students to reflect and think about

why certain steps are included in the method, it may be appropriate to have a series of prompts

where students are asked to discuss and explain why some steps are included as in the example

above.

3.2.5. Technology

Another aspect to consider when designing laboratory exercises is the level of technology

needed to support the learning outcomes. There is much debate around doing certain tasks by

hand as opposed to automating them. Generally, the act of plotting a few graphs by hand helps

internalise ‘graphing’ and other forms of representation [64]. Hence, integrating the plotting of

straight-line graphs by hand not only helps learning but also helps staff evaluate student

competence at such basic skills. Of course, when considering the learning outcomes, it is

important to consider if this skill is necessary in your context? If not, time can be saved by

providing students with suitable software, which in itself is an important skill to be developed.

This can free up time for other skills such as working out how to parameterize the data to get

a straight line. In terms of technology, data loggers allow students to obtain more data in a

shorter time period. This extra time can be spent on a more detailed analysis of the results or

can reduce the pressure on students to finish quickly giving them more opportunities to ask

questions of each other and staff. In many laboratory programs students are not working alone.

Sometimes this is due to a limited number of sets of equipment but working in small groups

can have benefits for students [13, 65, 66].

3.2.6. Submissions

Another aspect to consider is what do students do after their experiment. The frequency of the

laboratory sessions will play a role in answering this question. If labs are held every week

students may not have much time to write up their experiment out of class and it may exceed

the time expected to spend on core physics learning out of class. If on the other hand labs are

held every two or three weeks, it may be appropriate for students to analyse their data out of

class and submit for marking. Consideration needs to be given to whether the submissions are

individual, group, support provided for accessing assistance with analysis during the process

as well as the plethery of issues associated with such submissions ranging from plagiarism to

contract work. Careful thought needs to be given to the nature of the submission, will it be a

formal report, journal, portfolio or a logbook? This critical decision may ease the issues

encountered as well better capture the progression and development of processes learnt.

Finally, it is important to ensure that the submission aligns with the learning outcomes [52]

which is likely to be a more effective use of student’s time. Independent of the nature of the

submission, rubrics can help students identify what you consider to be important parts of the

submission and will also help reinforce the learning outcomes. If the submissions are not worth

a lot of marks, they could hit a soft spot of, students investing enough time (not too much and

not too little), not using problematic ways of getting the work done and reinforcing learning

outcomes. Table 1 shows a detailed rubric developed by the Director of First Physics Studies

at the University of New South Wales (first author) in consultation with colleagues for the

logbook students submit, at three points during the semester, which stresses development of

skills. Students submit all experiments which allows them to address different criteria in

156 | Angstmann E. J., Sharma M. D.

different experiments enabling students to demonstrate that they understand the skill and are

developing competency. The example rubric is used for all experiments, providing a scaffold

for aligning with learning outcomes. Students in this course have weekly labs. The exercises

vary in the level of inquiry with students developing their own methods some weeks while

completing guided exercises other weeks with the opportunity to extend the experiments. They

paste the rubric in their logbook, the staff uses it to provide feedback and assign marks.

Table 1. Example rubric which provides a scaffold for aligning development of

skills with learning outcomes.

High Distinction (HD) Distinction (D) Credit (CR) Pass (PS) Unsatisfactory

Uncertainties - Steps taken to minimize uncertainty in method

- Calculated correctly for all available data

- Final results presented correctly with uncertainty

- Results presented with correct number of significant figures

- Most uncertainties calculated

- Steps taken in method to minimize uncertainties

- Final results presented with uncertainty

- Calculated some uncertainties correctly

- Taken steps to minimize uncertainties

- Some uncertainties are calculated

- Many mistakes or many uncertainties not calculated

Graphs - Included wherever appropriate

- Fully labelled

- Units included

- Neatly drawn/or neatly done on computer

- Suitable fit chosen

- Suitable quantities on each axis

- Included wherever appropriate

- Fully labelled

- Units included

- Suitable fit chosen

- Suitable quantities on each axis

- Most data collected presented in an appropriate graph

- Most graphs labelled

- Most graphs include units

- Suitable quantities chosen for each axis.

- Some graphs suitable graphs included

- Graphs very hard to interpret

Reflection - Reflected on how results of experiment are related to what is taught in lectures.

- Explained whether results do or do not agree with theory and why, explanations detailed and thoughtful

- Reflected on how results of experiment are related to what is taught in lectures.

- Explained whether results do or do not agree with theory and why

- Some connections drawn between the lab and lectures

- Some explanation of whether results are what was expected

- Short discussion of whether results were as expected or not.

- Not much connection between lab and lectures presented in lab manual

Write up - All data in fully ruled tables

- Units included everywhere

- Neat

- Easy to follow

- Data in fully lined tables

- Most units included

- Neat

- Data in tables

- Most units included

- Most units included

- Not easy to follow

- Messy

Extension - Discussed and performed suitable extensions to experiment.

- Shown some intuition and original thought

- Detailed method for own experiment given

- Discussed and performed suitable extensions to experiment.

- Small amount of suitable extension work performed

- Very little extension work

- OR extension work not very suitable

- No extension work

Conclusion - Written for each experiment

- Clearly related to aim of the experiment

- Summarizes results

- Precise

- Written for each experiment

- Clearly related to aim of the experiment

- Summarizes results

- Written for most experiments

- Related to aim

- Little relationship between conclusion and aim

- Not done

Completeness - Experiments completed with adequate data; all questions well addressed

- Experiments completed with adequate data; most questions addressed

- All data collected, one or two small points missed

- Most data collected

- Missing data or answers to questions

Chapter 8 | 157

3.2.7. Success in assessing and providing feedback to students

This rubric underwent iterative updates over a number of years and is now in a format which

is deemed to be successful in the School of Physics. The markers circle the relevant cell and

write specific comments in the logbook relating to the circled cell as well as hints for

improvements. This helps students identify what was not done well as well as how to improve.

The feedback is used by students to improve in the next set of experiments, and progress in

most students’ development of skills is noted during the semester. Since the rubric is used by

several markers, the team have checked the consistency with which the rubric is used by the

different markers. Rather pleasantly, there is internal consistently amongst the team of markers.

Since the use of the rubric contributes to 20% of student marks, internal consistency and

improvement in skills indicates that the rubric and the way in which it is used leads to an

adequate assessment tool.

3.3. Physics experimental labs in the online environment

With COVID-19 impacting our lives, online laboratory programs have had to be created. It is

possible to have meaningful laboratory components in online courses. Students can make first-

hand measurements in the real-world using household equipment. Many people have now

experienced online laboratory programs from lockdowns due to COVID-19. Sensors on

smartphones are able to make fairly accurate measurements. Students can demonstrate

creativity and troubleshooting when working how to get an experiment to work with the

equipment available to them. Below are some examples of labs in the online environment

drawing on both teaching and research undertaken by us. We also comment on maintaining

learning outcomes.

Example 1: Online laboratories in an online course [67]: Everyday Physics is a completely

online algebra-based physics course which has been running prior to COVID-19 with around

500 students a year. During this course students complete investigations at home with

household equipment before designing their own experiment to investigate physics of interest

to them. Some of the experiments students conduct at home include measuring the speed of

sound using resonance, calculating the coefficient of static friction between different surfaces

and using a kettle to measure the specific heat of water. Students are supported through the

process of designing their own experiment with early feedback on the appropriateness of their

method provided by tutors and a peer review activity before they submit their final report. More

detail is provided in Ng and Angstmann [67].

Example 2: Online laboratories designed during COVID-19 for calculus-based courses: In

the calculus-based courses, there were three types of ‘experiments’. The first were ‘data

analysis experiments’ which contained a set of videos illustrating how data were taken and data

sets were provided for students to analysis asynchronously. Second were ‘at-home experiments’

adapted from Everyday Physics which can be found on the Australian Council of Teaching and

Learning repository [68]. These two constituted the bulk of the laboratory program. Third, were

carefully chosen simulations to complement the ‘data analysis experiments’ and ‘at-home

experiments’. The entire laboratory program was supported by ‘drop-in help sessions’ where

students could consult with a demonstrator. Between the three types of experiments, most of

the learning outcomes could be addressed for courses which covered topics such as thermal

and mechanics. However, for courses which covered electromagnetism and quantum, more

learning outcomes could not be addressed.

Example 3: Examining engagement with face-to-face and online labs: This research study

was in progress during 2019 and continued through 2020 allowing us to capture student

158 | Angstmann E. J., Sharma M. D.

engagement in different types of teaching. We need to be careful as the rapid transfer to online

teaching resulted in online teaching which was not specifically designed nor optimised for

online teaching. The first study showed that, students reported more positive and less negative

emotions with face-to-face teaching in comparison to blended prior to COVID-19, with the

COVID-19 online teaching somewhere in between [69, 70]. When looking at laboratory work,

historical colourful stories were inserted as the first page of student lab notes without affecting

the content or activity. Our findings were that, for most students, the stories provided a

mechanism to catch and hold interest, affecting the mood and ambience as well as students’

emotional engagement [71].

Example 4: Examining affordances and constraints of COVID-19 online labs across three

universities: This particular research retrospectively examined the ‘what and how’ of the rapid

transfer to online COVID-19 labs [72]. While there were overwhelming similarities across the

three universities, differences reflected what was already different during the face-to-face

teaching such as when and how submissions were made and organisation of student teams. The

similarities arose from common learning outcomes and how they were maintained, as best as

they could be, in COVID-19 online labs. Communications, efficient and effective Learning

Management Systems, maintaining staff-student ratios and adequate teaching resources and

support were more critical in COVID-19 online labs. In terms of affordances and constraints,

COVID-online labs were suited to developing students’ data analysis skills while face-to-face

labs were suited to developing trouble shooting skills as well as becoming accustomed to ‘real

life messiness in experimentation’[72]. When considering student feedback on open-ended

questionnaires, the most popular themes for COVID-19 online labs were ‘data handling’ and

‘understanding physics’ [73].

4. Discussion and Conclusion

Given that physics is an experimental science; where knowing and knowledge are embedded

in data, concepts and theories as we strive to model and understand nature as well as develop

technologies, the continuation of experimental programs in school and universities is

paramount. In this Chapter, we have presented our perspective on a brief history of

experimentation in physics education and how this is manifested in curriculum in schools and

universities, covering laboratory programs, practicals, experimentation, hands-on activities as

well as demonstrations. We have considered inquiry as a pedagogy in school settings, and

highlighted the increasing use of inquiry in university settings [39–45]. Through examples, we

have illustrated when and how the ideas are implemented, hopeful that these could be helpful

to others.

4.1. Implications and consequences for future teaching and for enhancing student learning

First and foremost, this Chapter argues for continuation of experimental laboratory programs,

particularly with a focus on hands-on experiments as argued by Schwab [39]. The balance

between the different levels of inquiry needs to be carefully considered to meet student needs;

that is, there are times for more student driven activities and there are times for less student

driven activities [45, 55]. In all instances the goals of the experimental program should be

essential to any decisions [25, 28]. Assessment and feedback need to underpin the design of

laboratory programs and individual experiments such that the goals of the experimental

program are delivered, appropriately influencing student learning and development of skills

and competencies. Online is most powerful as a way to help students prepare for labs so they

get most out of the time spent in face-to-face labs as well as in undertaking data analysis [72–

Chapter 8 | 159

73]. However, online labs cannot replace the hands-on components where critical skills such

as setting up and troubleshooting are being developed. The messiness of laboratory work is a

core and often underestimated learning in itself as this reflects real life occurrences. A word of

caution in that the online labs being referred to are COVID-19 online labs, nonetheless, we

tentatively offer that our finding is relevant more broadly.

4.2. Implications and consequences for future research

The goals of laboratory programs have been an area of ongoing study and there is a need to

continue this endeavour [16–19]. Our argument is that, as society evolves, the broader purpose

of why labs continue to be relevant need to be interrogated. This will not only provide sound

and defensible justification under pinning the continuation of experimental laboratory learning,

but also keep laboratory programs ‘fit for purpose’. The importance of examining goals is also

important due to infrastructure, staffing and financial consequences of continuing laboratory

programs [24, 57]. Research into evaluating laboratory programs and their efficacy for different

contexts, cohorts would aid in improving student learning [13, 50, 53, 61, 67]. Research based

individual experiments incorporating modern technologies as well as take home labs are

particularly important [25–28, 48, 49, 68] for continual revival and rejuvenation as it is not

uncommon to uncover staid and static laboratory programs. Student learning in the labs in

terms of skills development, not just within a semester or year, but longitudinally over three

years are rare and need to be undertaken [30–31]. This applies to not only physics specific

skills, but also generic skill development. Finally student research into engagement, from

emotional, cognitive to behavioural is sorely needed [62, 69–73].

In conclusion experimentation plays a vital role in physics and so should be utilized within

physics education. When designing laboratory experiences for students in primary, secondary

or tertiary settings it is useful to consider the desired level of inquiry for each aspect of the task

in order to best meet the learning outcomes for the task. While experiments tend to be expensive

to run, in many cases, they are the part of the course which is most memorable to students and

elicits the most positive feedback.

Acknowledgments

The authors would like to acknowledge the many grants funded by the Australian Federal

Government as well as their respective Universities. Without these, the authors works described

in this Chapter would not have been possible. Over the years, an extensive team of colleagues,

students and collaborators have contributed to the development of ideas crystallised in this

Chapter. In particular, the Sydney University Physics Education Research (SUPER) group and

mentors Ian Sefton and Brian McInnes have been influential and the Physics Education

Research for Evidence Centred Teaching (PERfECT) group at UNSW. Last but not least,

colleagues contributing in various ways to laboratory learning, in both schools and universities,

students and research participants have made this body of work possible.

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163

Chapter 9

Multimedia in Physics Education

David SOKOLOFF Department of Physics, University of Oregon, 1371 E 13th Avenue, Eugene, Oregon 97403, USA

Abstract: With the rapid development of computer-based multimedia beginning in the 1980s,

many new, exciting multimedia materials have become available to physics educators.

Paralleling this has been the development of research-validated active learning strategies that

effectively engage students in the learning process. The incorporation of multimedia into these

strategies has led to new approaches, many of which have resulted in documented, dramatic

improvements in student learning. This chapter will examine the principal multimedia

materials that are available and present examples of their applications in active learning of

physics.

1. Introduction

With the advent and now wide availability of personal computers since the 1980s, multimedia

materials have become ubiquitous and widely useful in enhancing student learning of physics.

Multimedia representations of physical situations are now available in most areas of physics,

and many of these also incorporate tools for careful analysis. A curriculum designer today has

a palette of tools to work with, and to incorporate with research-validated active learning

strategies. For these new approaches to be successful in improving learning, it is important that

the combination of multimedia resources and active learning strategy effectively engages the

students in the learning process. This can be achieved in a number of ways. Well-designed

multimedia resources incorporate the necessary simplicity of user interface, richness of content,

clarity of displays, and flexibility of analysis tools to encourage and support student

interactivity and enhance learning. Of course, as for any new approaches to physics education,

formal, research-based assessment of the multimedia/strategy combination is required to

demonstrate improved learning.

The rapid implementation of virtual, online approaches to learning--necessitated by the

2020 COVID-19 pandemic--is an excellent illustration of the curriculum development process

made possible with the ever-growing availability of multimedia. In a short period of time,

essentially all learning at the secondary and university levels around the world was transformed

to distance learning of some form. One immediate, pressing question was whether active

learning could be supported in these newly required, less-than-ideal learning environments.

One attempt was the author's exploration of the possibility of converting Interactive Lecture

Demonstrations (ILDs) [1, 2]--an inherently live, in-class learning strategy--to a form that

could be used by students online at home. The rapid development of these Home-Adapted ILDs

[3] was only possible because of the years of multimedia development that had preceded 2020.

The incorporation of a wide variety of multimedia resources within the ILD strategy will be

used in this chapter as an overarching illustration of this active learning curriculum

development process, enabled by multimedia, and as a vehicle for illustrating some of the

features of the multimedia resources.

The principal categories of multimedia resources available to curriculum developers today

and used prominently in the Home-Adapted ILDs include (1) Interactive Physics Simulations,

(2) Data Logging Tools (AKA Microcomputer-Based Laboratory tools--MBL), and (3)

Interactive Video Analysis. This chapter briefly describes these multimedia resources and the

164 | Sokoloff D.

characteristics and design features that make them useful for active learning. Examples of how

they have been incorporated into active learning curricula will also be presented. The goal of

the chapter is not to provide an exhaustive description of all multimedia available for physics

education, but, rather, only an introduction to the most prominent and effective forms of

multimedia available today is included. The incorporation of these multimedia resources into

the Home-Adapted ILDs will serve as a repeated example of the usefulness of multimedia in

the active learning of physics.

2. Interactive Physics Simulations

Interactive Physics Simulations consist of computer-based models of physical systems allowing

results to be displayed in easily understandable ways using well-designed graphics, with well-

designed user interfaces that allow students to easily make changes to input parameters. With

well-designed Interactive Physics Simulations, students are able to model a range of behaviors

of a wide variety of physical systems. The two largest collections of physics simulations are PhET

(or Physics Education Technology) [5–7] and Physlet Physics [8–10]. There are also a number of

other sources of physics simulations, including CMA Coach [11–13].

Well-designed interactive physics simulations provide the following advantages for

student learning:

1. If written in Javascript, Flash or HTML5, they can be run online or downloaded to

a computer and used anywhere in the world.

2. In addition to experiments that are easily done in the laboratory, they can be used

to do those experiments that are very difficult or impossible for students to do.

3. They can be used in classrooms where real experimental apparatus is either

unavailable or impractical to use.

4. It is easy to change input parameters in response to student questions that would

be difficult or impossible to change with real apparatus.

5. They can illustrate the invisible (e.g., sub-atomic particles, fields) and explicitly

connect multiple representations.

6. Students can run them on their own computers at home at their leisure, to repeat or

extend their work during class time and/or to clarify and strengthen their

understanding.

PhETs are open-ended, game-like simulations with an intuitive interface and minimal text,

appropriate for a variety of class settings. They are interactive simulations with sophisticated

graphics on the high end of the complexity scale, and each has required many person months

of development and testing. They were developed principally by Carl Wieman, Katherine

Perkins and Wendy Adams and their colleagues at the University of Colorado beginning in

2002 [5–7]. They are based on research into how students learn in general, student

understanding of specific physics concepts, and user interface design. They are available online

and free to use.

The characteristics listed above are well illustrated by the PhET simulation "Circuit

Construction Kit" [14]. (See Fig. 1 (A).) Portions of this simulation were used as a resource for

students in the "Introduction to DC Circuits" Home-Adapted ILDs [4]. Students are easily able

to construct simple DC circuits of their choice by dragging circuit elements (bulbs, wires,

batteries, switches, meters, etc.) into the workspace. Once the circuit is constructed and closed,

current flows according to the structure of the circuit and Ohm's law.

Chapter 9 | 165

Figure 1. (A) Simple series DC circuit with two light bulbs of different

resistance connected in series with a battery, set up in the PhET "Circuit

Constriction Kit" as used in the Home-Adapted ILD "Introduction to DC

Circuits." The simulation enables students to construct simple DC circuits of

their choice by dragging circuit elements (bulbs, wires, batteries, switches,

meters, etc.) into the workspace, and to observe the currents and voltages. (B)

Excerpt from the Prediction Sheet used by students for this ILD.

An excerpt from the Prediction Sheet for this ILD is shown in Fig. 1 (B). Students first

make predictions about the currents in this circuit. They then construct the circuit, and observe

the currents flowing, the bulbs glowing, and meters measuring the currents flowing through

the two bulbs. Unlike real circuits, students are able to see electrons (represented by blue

circles) as they move around. A significant percentage of students will predict that the current

through the right bulb should be larger than that through the left, thinking that some current is

"used up" as it flows through the right bulb. Viewing the electrons moving and, simultaneously

viewing the meter readings reinforces the idea that current is not "used up." Noticing that the

right bulb is brighter than the left demonstrates that, in a series circuit, the bulb with the larger

resistance consumes more power.

Research studies carried out with students using the "Circuit Construction Kit" in

conjunction with other well-designed curricula and/or strategies (e.g., in-class Interactive

Lecture Demonstrations [7] and Tutorials in Introductory Physics [15, 16]) have shown better

gains in students' understanding of circuit concepts than doing real demonstrations or

experiments using real equipment. However, as the PhET developers point out, there are also

many goals of hands-on labs that simulations do not address, e.g., specific skills relating to the

choice, set up and functioning of equipment. Effective use of PhETs in modern physics has also

been demonstrated [17, 18].

A)

B)

166 | Sokoloff D.

The first Physlets were developed by Wolfgang Christian as Java applets in 1995, and their

development has continued principally under Christian, Mario Belloni, Anne Cox, and Melissa

Dancy. [8–10] They are small, flexible, single‐concept simulations that help teachers facilitate

students' learning of specific physics concepts. The original Physlets were scriptable with

JavaScript and embedded in HTML pages. Thus, instructors could customize the Physlets by

writing their own individual exercises, creating interactive simulations to support virtually any

pedagogy. Beginning in 2003, with the release of Physlet Physics 2E, scripted exercises

accompanied the 800+ Java applets. This is one important way in which Physlets differ from

PhETs. With the release of Physlet Physics 3E [9] and Physlet Quantum Physics 3E [10], the

over 800 Java applets have been ported to JavaScript/HTML5, so that they now run on any

platform on a JavaScript-enabled browser, including smartphones and tablets. The entire

collection of Physlets is now available for use free of charge on AAPT/Compadre [9, 10]. As

an example of the use of Physlets, Fig. 2 shows some excerpts from Physlet Physics Chapter

35, Lenses [19], and how they were incorporated as resources in the Home-Adapted ILD

sequence "Image Formation with Lenses" [20]. This ILD sequence uses photos of the apparatus

from the original, in-class ILD sequence [2, 21], two flashlight bulbs as point sources on the

object and a large acrylic lens. (See Fig. 2 (A, B).) The righthand side of Fig. 2 shows two

screenshots from the Physlet that are used to complement the light bulb displays showing (C)

a large number of rays (in actuality, an infinite number or cone of light) originating on a

movable point source on the object and focused by the lens to an image point, and (D) the ray

diagram for this situation. The excellent graphics in this Physlet complement the observations

from the original ILD.

(A)

(C)

(B)

(D)

Figure 2. (A), (B) Photos of apparatus for original, in-class Image Formation

ILDs: two flashlight bulbs and a large acrylic lens, used to illustrate image

formation by a converging lens. (C) Simulation of movable point source on the

object in the Physlet "Lenses." (D) Ray diagram for the same situation in the

same Physlet.

3. Computer-Based Data Logging Tools with Graphical Displays

Data logging tools first became available as microcomputer-based laboratory (MBL) tools for

use in secondary and college level physics teaching in the mid 1980s [22, 23]. Today, the three

Chapter 9 | 167

most-widely-used commercial versions of computer-based data logging tools are Vernier [24],

PASCO [25] and CMA Coach [11]. These systems consist of a variety of sensors transferring

data to a computer through an interface. The collected data are most often displayed in

graphical form, typically some physical quantity vs. time. The most common sensors are sonic

motion detectors, collecting position vs. time data for moving objects, and sensors for force,

temperature, pressure, light intensity, sound intensity, current and voltage and magnetic field.

The Vernier system also incorporates a heat pulser for transferring known amounts of heat to

systems through a heating coil, to enable heat transfer and calorimetric experiments.

These computer-based tools have the following characteristics and features that enable

their use to enhance student learning from observations of the physical world:

1. They provide for real student-directed exploration of the physical world while

simplifying the time-consuming drudgery associated with data collection and

display.

2. Data from real experiments are plotted in easily understandable graphical form in

real time so that students get immediate feedback, stimulating discussion with their

peers.

3. Students are able to change display parameters (axis units and scale, time scale,

etc.) after data are collected to make the results more understandable.

4. They enable students to spend the majority of their laboratory time observing

physical phenomena and interpreting, discussing, and analyzing results with their

peers.

5. The hardware and software tools are independent of the experiments.

6. The variety of available sensors use the same interface and the same software

format, allowing students to focus on the investigation of many different physical

phenomena without spending significant time learning to use complicated tools.

7. The tools dictate neither the phenomena to be investigated, the steps of the

investigation, nor the level nor sophistication of the curriculum, thus, they are

usable with a wide range of students from elementary school to college level.

The significance of these features is that these sensors and software are experimental tools

for students, enabling them to collect data from a variety of real experiments and display them

in ways that can be easily understood and used as valuable support for their learning. The ease

of use and clarity of displays are the most essential features to support active learning. Effective

tools have enabled the development of curricular materials like the active learning introductory

laboratory curriculum, RealTime Physics [26, 27] and the active learning introductory lecture

materials, Interactive Lecture Demonstrations [1, 2]. They are also used extensively in

Workshop Physics [23]. Student activities based on computer-based data logging tools

combined with all three of these curricula have been demonstrated to result in significantly

improved student learning at the college and university levels [1, 23, 26].

As an illustration of how computer-assisted data logging tools can be used to promote

active learning, Fig. 3 shows a screen shot from a computer-based video incorporated in the

Home-Adapted ILDs "Introduction to Heat and Temperature" [28]. The video shows a heated

piece of brass being stirred in an insulated container of cold water. In the accompanying

graphical display produced with two Vernier temperature sensors and Logger Pro software, the

temperatures of both the brass and the water are displayed as they come to thermal equilibrium.

A relatively recent development in the area of computer-based data logging is the "smart-

cart," a self-contained cart that uses an optical encoder connected to its wheels to record its

movement and also has a built-in force sensor to measure forces applied to it. The device

transmits collected data to a computer using RF or Bluetooth. The first of these to be developed

was the IOLab [29, 30], quickly followed by Vernier [31] and Pasco versions [32]. A major

168 | Sokoloff D.

difference in these is that in addition to motion and force data collection, the IOLab includes

sensors for light intensity, atmospheric pressure, sound, temperature, 3D accelerometer,

magnetometer and gyroscope, and connections for electrical measurements. As with other data

logging tools, the key to improved student learning is the ease of use by students, the clarity

and ease of manipulation of graphical displays, and the ease of use of analysis tools. When

RealTime Physics Mechanics labs were adapted for use with IOLab, significantly improved

learning gains were achieved in college and university introductory physics labs as compared

to traditional labs [30].

As examples of the graphical displays produced by the IOLab software, Fig. 4 shows the

IOLab device and two displays of collected data (A) for it pulled along by a hanging mass (from

Home-Adapted ILD "Force and Motion-Newton's 1st and 2nd Laws" [33]) and (B) for an

asymmetrical collision between two IOLabs (from "Force and Motion-Newton's 3rd Law" [34]).

Figure 3. Graphs of temperatures of a hot piece of brass (blue) and cold water

(green) as they come to thermal equilibrium from Home-Adapted ILD

"Introduction to Heat and Temperature."

(A)

(B)

Figure 4. Graphs recorded for (A) an IOLab accelerated by a falling hanging

mass (modified Atwood's machine) and (B) asymmetric collision between two

IOLabs, from Home-Adapted ILDs "Force and Motion-Newton's 1st and 2nd

Laws" and "Force and Motion-Newton's 3rd Law," respectively.

4. Interactive Video Analysis

Interactive Video Analysis originated as stand-alone software packages in the early 1990s (e.g.,

VideoPoint). Today, it is included as a feature in Vernier Logger Pro [24], PASCO Capstone

[25], and CMA Coach [11]. It is also available in the popular, open-source program Tracker

Chapter 9 | 169

[35]. Video analysis is an easily usable tool, especially since the ubiquitous smartphone has

made video recording of physical phenomena accessible to all (and has mitigated the issues of

dropped frames that plagued earlier attempts to capture video in or for the classroom). The

availability of high-speed cameras has also broadened the range of phenomena that can be

analyzed [36]. Or, more commonly, clips from the vast libraries of pre-recorded physics videos

can be analyzed [37–39]. Regardless of the specific program used, video analysis has the same

basic features.

1. A video camera is used to "collect" a video of a moving object, thereby recording

position and time data.

2. Position data are retrieved from the video by clicking the cursor on the locations

of the object as the video automatically advances to each successive frame of the

clip, and the time data from the number of frames per second.

3. These data are simultaneously recorded in a table and then used to represent the

motion graphically.

4. The position can be scaled from pixels to meters by measuring a known distance

in one frame of the video (e.g., the length of a meter stick).

5. Velocity and acceleration are calculated and can also be displayed graphically as

functions of time and analyzed.

If the mass of the object is known, other quantities such as kinetic and potential energies

and momentum can be calculated. More sophisticated features include translating the origin in

the video, and for videos with multiple objects, locating and analyzing the motion of the center

of mass and measuring and graphing the distances between selected objects.

Among the advantages of video analysis are:

1. Even with standard recording rates of 30 frames per second, students are able to

record positions of an object fairly precisely in time.

2. Such methods as computer-based sensors are not suited to collecting and analyzing

data for two-dimensional motions--recording both the horizontal and vertical

motions.

3. Students are enabled to analyze the motions of virtually any object(s), even ones

that they cannot access in the lab, e.g., the launch of a rocket ship or the motion of

a sports figure, but for which videos are often readily available.

(A)

(B)

Figure 5. (A) On the left is a frame from video with 2-D positions of a tossed

tennis ball marked. On the right are the graphs of x-velocity (red) and y-velocity

(blue) plotted from the video data in Vernier Logger Pro.

(B) Prediction sheet for the Home-Adapted ILD "Two-Dimensional Motion:

Projectile Motion."

170 | Sokoloff D.

To illustrate how video analysis works, Fig 5 shows a frame from a now standard video of

the trajectory of a tennis ball tossed in the air as it is used in Home-Adapted ILD "Two-

Dimensional Motion: Projectile Motion" [40]. The individual locations of the ball that have

been marked with the cursor on successive frames by a student are represented by the blue dots

displayed persistently on the screen on the left side of Fig. 5 (A). The right side of Fig. 5 (A)

shows graphs of the x and y velocities of the ball as functions of time, calculated from these

data and the number of frames per second. (Note that the position data have been converted

from pixels to meters.) In the video used in the Home-Adapted ILD, the motion of the ball and

the graphs play out simultaneously. Fig. 5 (B) shows the Prediction Sheet for this exercise.

Video analysis of this type was first used for projects in Workshop Physics [41–43].

Besides its current use in Workshop Physics and the Home-Adapted ILDs, video analysis has

been made a standard part of a number of active learning curricula, for example, RealTime

Physics: Active Learning Labs [27] and Interactive Lecture Demonstrations [2]. While

Interactive Video Analysis is often thought of as a multimedia tool only applicable to analyzing

motions of objects, it has actually been applied to a wide variety of physical phenomena.

Figure 6. The video shows a charged ping pong ball at the end of a rod being

moved horizontally towards a hanging ping pong ball with the same sign of

charge. Video analysis (in Vernier Logger Pro) is used to record the positions of

the two charged balls in successive frames. (Red and green dots.) The data are

analyzed to "discover" Coulomb's Law. (Graph a lower right.)

Fig. 6 shows how it has been used in both RealTime Physics [27] and Workshop Physics

[42] to explore Coulomb's Law quantitatively in the introductory physics laboratory. The video

shows a charged ping pong ball at the end of a rod being moved horizontally towards a hanging

ping pong ball with the same sign of charge. By recording the positions of the two charged

balls in successive frames, the data can be analyzed from the position of the hanging ball and

the distance between the balls' centers (r) to examine the relationship between the force exerted

by the left ball on the right one and r--Coulomb's Law. A collection of videos in many areas of

physics, created by the LivePhoto Physics project, with classroom tested materials to guide

students through analysis of these videos is available [44].Other fairly recent examples of

interactive multimedia are the LivePhoto Physics Group's development of Interactive Video

Vignettes (IVVs) [45, 46] and Interactive Video-Enhanced Tutorials (IVETs) [47]. The IVVs are

web-based video activities that contain interactive elements and typically require students to

Chapter 9 | 171

make predictions and analyze real-world phenomena. They are designed to be used by students

at home, e.g., as part of homework assignments. They often make use of the common elicit-

confront-resolve technique, first eliciting a prediction from the student, then confronting the

user with an experimental result, and finally helping the user to resolve any differences between

them. The basis of the resolution is a clear video and analysis using video analysis or computer-

based sensors. Sometimes students are invited to perform analysis themselves. Similarly, the

vignettes developed so far include instructor-led presentations, “person-on-the-street”

interviews, discussions between students and instructors, and stories played out by student

actors. The IVETs use similar technology but are aimed at teaching problem-solving skills.

Both are web applications written in HTML5 and JavaScript, so they work on devices likely to

be used by students (laptops, desktops, and tablets). The group has also developed a free, open-

source authoring app, Vignette Studio, that anyone can use for creating vignettes and tutorials.

Fig. 7 shows portions of the video clips incorporated in the "Newton's Third Law" IVV.

These include (A) a clip showing an interviewer asking the participant to make a prediction

about the forces in a collision, (B) a clip of an asymmetric collision between two real cars, and

(C) a clip of a collision with carts and computer-based data logging, showing the equal and

opposite forces, but the greater damage to an occupant of the smaller car [45].

(A)

(B)

(C)

Figure 7. Excerpts from the "Newton's Third Law" IVV. (A) Clip showing

interviewer asking participant to make a prediction about the forces in a

collision. (B) Clip of an asymmetric collision between two cars, showing more

damage to smaller car. (C) Clip of collision with carts and computer-based data

logging, showing evolution of graph comparing forces (equal and opposite), and

the effects on toy vehicle "passengers."

5. Conclusions

There is an abundance of well-designed multimedia resources available today for use in

enhancing students' mastery of physics. The serendipity between the emergence of these

resources and the development of a variety of research-validated active learning strategies in

the last 20–30 years has dramatically changed the teaching of physics during this period,

especially in the area of conceptual learning. The rapid development and deployment by the

author of a set of Home-Based ILDs is ample testimony to this. For this project, it was possible

to find quality multimedia to support online versions of almost all of the in-class ILDs that have

been published [2], covering the majority of topics in the introductory physics course.

While not much used in physics education currently, emerging new multimedia

technologies like Virtual (or Augmented) Reality (VR) and Artificial Intelligence (AI) should

provide resources for exciting new pedagogical developments in the next decade. For example,

VR affords the advantages over standard simulations of immersing users in an environment

and allowing them to maneuver in three dimensions, even in micro-worlds, for example, where

charged particles interact with electromagnetic fields. [48] And kinesthetic learning, originally

advocated by Arons and Laws, [43, 49] could be enhanced using VR to study more complex

phenomena like three-dimensional angular momentum. [50] The relatively high cost of quality

172 | Sokoloff D.

VR has prevented it from being researched or tested extensively in the physics classroom to

date, but an increasing number of projects have explored its use. [51–53]

As with all new technologies, potential users will face a learning curve, and there will be

inertia to overcome before implementation is widespread. But the research and implementation

of multimedia resources over the years have been strongly supported by at least two important

factors. First, the international community of multimedia developers and users is a vibrant

group supported by the international organization, Multimedia in Physics Teaching and

Learning (MPTL) [54]. Since 1996, MPTL has evaluated multimedia resources and organized

an annual conference, often jointly with GIREP and/or ICPE, for a total of 24 since its

inception. Secondly, a number of prominent online PER resource collections have been brought

online over the years. These include Compadre [56], PhysPort [57] and PER Central [58].

Further implementation of current and future multimedia resources by educators will be

enabled by the wealth of free resources available at these sites.

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Chapter 9 | 173

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Part V

Designing and evaluating classroom practices

175

Chapter 10

Research-based design of teaching learning sequences:

description of an iterative process

Jenaro GUISASOLA, Kristina ZUZA, and Paulo SARRIUGARTE Department of Applied Physics, University of the Basque Country (UPV/EHU) and Donostia Physics

Education Research Group (DoPER-STEMER)

Jaume AMETLLER Department of Specific Didactics, University of Girona. Spain.

Abstract: Many studies have analyzed the process of constructing teaching-learning

sequences as a research activity. This line of research aims to increase the impact and transfer

of educational practice. In this chapter, we are presenting a proposal to design and evaluate

teaching and learning sequences for introductory physics courses at College and University.

We will connect our proposal to relevant contributions on the design of teaching sequences,

we will substantiate it in the design-based research methodology, and discuss how a designed

teaching and learning sequence is evaluated and redesigned.

1. Introduction

Many studies have analyzed the process of constructing teaching-learning sequences as a

research activity. Meheut and Psillos [1] define the term Teaching/Learning Sequence

(henceforth, TLS) as:

(…) both an interventional research activity and a product, like a traditional

curriculum unit package, which includes well-researched teaching-learning activities

empirically adapted to student reasoning. Sometimes teaching guidelines covering

expected student reactions are also included (p. 516).

This line of research aims to increase the impact and transfer of educational practice. This

requires constructing design theories and principles that guide, inform and improve both

practice and research in educational contexts [2]. TLS focuses on an educational intervention

concerning specific curriculum topics that cover several lessons which coherently incorporate

the learning objectives and sequencing of activities.

Over the last three decades, various didactic proposals have been published to connect

theory and research results with TLS design in several contexts [3, 4, 5, 6]. This TLS design

research tradition started at compulsory secondary education level (12–16 years) in an attempt

to improve learning in science with a constructivist and social-constructivist approach to

theories of learning. The results obtained showed greater learning on specific topics in the

science curriculum [7, 8]. Subsequently, investigations were extended to High School, College

and University [9, 10, 11, 12, 13]. At these levels, rigorous content analysis and the need for

teacher preparation have been key factors in experiences with positive and encouraging results.

These investigations have implied improving the existing didactic material, by means of

designing didactic activities based on the investigation results.

However, TLS proposals often lack details on how theory and research outcomes have

been articulated in their design. Furthermore, not all TLS proposals include an evaluation in

terms of learning outcomes and very rarely are these learning outcomes specifically related to

176 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

the design process. This lack of detailed information on the design and evaluation of the

proposed TLS makes it difficult to evaluate their potential effectiveness properly or to discuss

and systematically improve their design. The Design-based Research (DBR) methodology

emerges in an attempt to overcome these weaknesses, aiming not only to empirically adjust

“what works” from a TLS, but to develop classroom intervention theories [14, 15]. Beyond

simply creating designs that are effective, a design theory explains why the TLS designs work

and suggests how they can be adapted to new circumstances. Although some authors have

questioned the benefits of DBR in educational research [16], many studies show how DBR

provides a basis for a scientific focus in scientific education research by making the designed

TLS more reliable and by producing new educational knowledge [17, 18]. DBR is a research

methodology to generate and prove general teaching-learning theories [19].

In this chapter, we are presenting a proposal to design and evaluate teaching and learning

sequences for introductory physics courses at College and University. We will connect our

proposal to relevant contributions on the design of teaching sequences, we will substantiate it

in design-based research methodology, and we will discuss how a designed teaching and

learning sequence is evaluated and redesigned.

2. From general theories to the design process of Teaching Sequences

The general theories that uphold our example of TLS design come from cognitive psychology,

epistemology of Physics and the outcomes of science teaching research. Regarding how

students learn, our approach is based on the social-constructivist theory of learning [20, 21,

22]. This choice will lead our objectives to include the idea that to learn physics, it is necessary

to participate in knowledge building activities and in group work. However, these theories are

not sufficient to facilitate the design of our sequences on specific curriculum topics. We also

consider contributions from the history and epistemology of science. Our TLS design assumes

that knowledge on how explanatory ideas developed, eventually leading to the current scientific

model, can provide important information when determining fundamental issues in

constructing the concepts and theories of the topic to be taught, demonstrating, in turn, the

epistemological and ontological obstacles that had to be overcome and the ideas that led to that

progress [23, 24, 25]. In particular, this information provides arguments to justify the key ideas

that will become the TLS learning objectives (See Section 3.2). A third theoretical element

considered within our approach is the progress of research into science teaching. For this

chapter, various teaching proposals on the topic have been reviewed, and indications in the

literature that emphasize the integration of scientific concepts and practice have been

considered [26, 27].

In accordance with the aforementioned recommendations to apply the DBR methodology,

we have chosen four steps that guide the design process of a TLS and allow “fine analysis” of

the specific content to be taught:

A.- Analysis of the educational context for which the TLS is designed: physics curriculum,

students on the course, etc.

B.- Discussion on the epistemological and educational arguments on the chosen topic. All

this leads to the definition of learning objectives for the topic at the chosen educational level

(Section 2.2).

C.– Determination of the learning demands, in other words, the gap between these

objectives and the students’ difficulties (Section 2.3).

D.- Description of the resulting learning route and the learning activities (Section 2.4).

In the following sections, we will use an example to explain the application of each of the

aforementioned steps. Section 2.1 will show the application of step A. Section 2.2 will show

Chapter 10 | 177

the specific aspects carried out for step B, in the context of the example. For the chosen

example, the specific aspects corresponding to steps C and D will be carried out.

2.1. Educational Context

We will provide an example to illustrate the DBR methodology. In the example, we will focus

on the part of the program dedicated to charging and discharging a capacitor in RC circuits in

introductory physics for Sciences and Engineering at University [28]. Expected learning

includes understanding of the concept of capacitance and the relationship between charge and

potential in a capacitor. These relationships in an RC circuit depend on interactions between

the different parts (battery-medium-body to be charged) and the changes that take place (current

flows) in the circuit [29]. The potential electrical energy that the capacitor acquires as it gets

charged is due to the work done by the battery during the charging process. Comprehension of

the potential energy acquired by the capacitor helps us to determine a “mechanism” to explain

the new balance [30]. Consequently, we will look at an “RC circuits” topic that includes

comprehension of previous topics, such as current, potential difference and capacitance that

are necessary elements to understand the explanatory models of charging and discharging a

capacitor in dc circuits.

The TLS was developed for a transformed calculus-based physics course for first year

engineering and science students at the University of the Basque Country (UPV/EHU). At the

UPV/EHU, electromagnetism is taught during the spring term to a group of 50 to 60 students.

The number of students per class in first year engineering is similar in all classes: between 50–

60 students. In the experimental classes, teaching strategies compatible with this number of

students have been used, such as the Peer Understanding strategy. The traditional course format

is two hours per week of lectures and an hour and a half per week of problem sessions. In the

Electromagnetism course, electric current circuits are taught for two weeks. The lectures and

the problem-solving sessions cover electric current, resistance, batteries and Ohm’s law,

combinations of resistors, Kirchhoff’s Rules and RC circuits [28]. In the traditional courses,

students do not normally have the chance to participate actively and are limited to taking notes

from the teacher’s explanations, both in lectures and in the problem sessions. In the transformed

version, we use the same study program (in other words, we cover the same factual knowledge)

but, as we will explain, the course and the contents are organized differently.

2.2. Epistemological insights and learning objectives

In accordance with the discussion on historical and epistemological development, we identified

four key features of the electrical capacitance concept that we consider relevant in the current

theory and applicable to an RC circuit context on a university level introductory physics course

[selected from 31, 32, 33, 34]:

K1.- In the history of electricity, explanations on charging a body do not always fit a single

model. From Poisson’s work, the scientific community has assumed that in the process

of charging a body, the energy stored in it can vary. The explanatory model includes the

concepts of charge and potential electrical energy.

K2.- The previous model determines relationships between the concepts of charge and

electrical potential that define the concept of electrical capacitance for a body, that can

be measured macroscopically (by means of current and electrical potential difference) in

a circuit.

K3.- The explanation based on the charge/potential relationship (electrical capacitance model)

implies that the presence of other charged bodies around a body to be charged can

improve its charging process. Therefore, a system formed by two conductors close

178 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

together (with total influence) with opposite charges, in other words a capacitor,

optimizes its electrical capacitance.

K4.- Interpretation of RC circuits based on the electrical capacitance model leads to better

comprehension of how the circuit’s characteristic current and potential difference

magnitudes vary over time.

From an educational perspective, we cannot underestimate the epistemological analysis of

the controversy that led to an electrodynamic interpretation of the phenomena of charging a

body or a capacitor. Beginning with the introduction of the “electrical voltage” concept by Volta

and continuing with Poisson’s contributions on the potential function. This led the way to

introduce the electrical capacitance model for charging bodies and capacitors. Introduction of

the electrical capacitance model in teaching on RC circuits is relevant from an epistemological

point of view as it came at a time in the history of science when it was necessary to analyze the

concepts of charge and potential difference qualitatively and quantitatively, and their

relationship based on the concept of electrical capacitance.

To justify the learning objectives for the concepts and models contained in the topics of

electrical capacitance and RC circuits, we use contributions from the epistemology of science

(see Table 1).

Table 1. Epistemological justification of the learning objectives on RC circuits

Epistemology of physics issue Learning objectives

The electrical capacitance model was determined

to explain the processes of charging a body (K1

and K2).

O1.- Students can explain how, when charging a

body, it acquires energy due to the work done

by the environment-battery to charge it. It

includes the concept of electrical capacitance

as the relationship between charge and

electrical potential.

The explanation based on the charge/potential

relationship (electrical capacitance model)

demonstrates that a system formed by two

conductors close together (with total influence)

with opposite charges, in other words a capacitor,

optimizes its electrical capacitance (K3).

O2.- Students understand the influence of the

dielectric and geometric factors of a system

on its electrical capacitance.

Interpreting RC circuit situations based on the

electrical capacitance model leads to a better

comprehension of how the circuit’s characteristic

current and potential difference magnitudes vary

over time (K4).

Students understand the transitory processes of

current when charging and discharging a capacitor

in an RC circuit. Consequently:

O3.- Students interpret the transitory currents in

RC circuits according to the concepts of

charge, potential difference and electrical

capacitance. They use a macroscopic model

of potential difference to explain the current

in RC circuits.

O4.- Students can explain the influence of the

medium on the electrical capacitance of a

capacitor in an RC circuit.

O5.- Students can apply Energy and Charge

Conservation laws in capacitor associations.

Application of the macroscopic model of

potential difference.

We have previously proposed [35] a TLS for learning objectives concerning the concept

of electrical capacitance and capacitors (objectives O1 and O2). In this chapter, we are focusing

on objectives related to the context of RC circuits (objectives O3, O4 and O5). While objectives

Chapter 10 | 179

O1 and O2 on the capacitance of materials and capacitors are usually addressed in traditional

teaching in the electrostatics chapter [36], objectives O3, O4 and O5 are usually studied in the

electrodynamics topics when analyzing RC circuits [37]. Consequently, the physics program

justifies designing a TLS for objectives O3, O4 and O5, where objectives O1 and O2 are

considered as pre-requisites for good comprehension of RC circuits.

2.3. Student difficulties and Learning demands

To make progress in the didactic transposition from the defined learning objectives to the

learning activities in class, we use the “learning demands” didactic tool that defines the gap

between the students’ previous ideas and the learning objectives. Awareness of the size of the

gap to be breached to achieve significant learning will guide the design and review of teaching

strategies. This tool helps us to focus the study on students’ ideas towards ideas related to the

defined objectives.

As part of the design process, we review research on the students’ learning difficulties

related to the concepts of capacitance and RC circuits. Several studies show that undergraduate

students have difficulties analyzing the electrical nature of matter and the charging processes

for a body in conductors and dielectrics [38, 39, 40]. Furthermore, they demonstrate that most

students have difficulties explaining electrical polarization in the bodies. These studies show

students’ difficulties when learning objective O4. Reviewing the students’ ideas regarding the

defined learning objectives shows that they have some learning difficulties concerning the

basics of RC circuits. We will describe the main difficulties below:

D.1.- They do not consider the concept of the system’s potential difference to explain its

charging process. Consequently, they do not properly understand the concept of electrical

capacitance as the relationship between the charge and the electrical potential that it

acquires in the charging process.

D.2.- They cannot explain the influence of the dielectric in a capacitor and do not understand

the electrical polarization phenomena in RC circuits.

D.3.- They do not understand the explanatory model of RC circuits that uses the relationship

between the concepts of charge, potential and electrical capacitance. Consequently, they

cannot explain transitory phenomena in RC circuits.

D.4.- They find it difficult to apply charge and energy conservation laws to RC circuits.

The literature shows that there are large epistemic and ontological differences between the

learning objective and the students’ ideas and thus the learning demand is high.

2.4. Design of TLS activities

In this step of the DBR methodology, a series of tasks is designed (questions and problems)

that, considering the decisions made, should help students to achieve the learning objectives.

The sequence of tasks was developed considering two aspects that are incorporated repeatedly:

a) Content sequence; b) Teaching strategies and activities to help learning. The RC circuit

program is structured according to the following learning path:

- How does electric current work in charging and discharging a capacitor? Charge

and electric potential aspects in an RC circuit.

- Is it possible to improve the capacitance of a capacitor? The role of the dielectric

in the RC circuit capacitors.

- How does a circuit that associates charged capacitors work? Charge and energy

conservation laws in capacitor associations.

180 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

These questions structured an initial version of the TLS (henceforth TLS1) during the

2017/18 academic year with the following order of content presentation: I) Charging a

capacitor in a direct current circuit; II) Discharging a capacitor in a direct current circuit; III)

Energy balance model in an RC circuit; IV) The role of dielectrics in a capacitor in an RC

circuit; V) Associating capacitors.

3. TLS evaluation and redesign process

DBR methodology includes evaluation and feedback in the material design process. This section

presents and analyses the evaluation and consequent improvement of the TLS. We use two

dimensions that include a multi-aspect evaluation that is generally not considered [41, 42, 43]:

a) Analysis of the sequence quality in relation to its capacity to get the students working

on the activities. This includes issues such as: problems related to the clarity of the

activity in relation to what the students must work on, problems related to the time

required to carry out the sequence’s activities or unexpected problems related to the

teaching strategy.

b) Measurement of the student learning that includes aspects related to comprehension

of concepts, laws and models and measurement of the scientific skills they have

acquired.

Table 2. The first column shows the sequence of problems, which, as they are solved, address the necessary

knowledge for teaching and learning the TLS. The second column shows the learning objectives, and the third

column explains the strategies to help learning (scaffolding). The fourth and fifth columns list the activities and

how they relate to the skills to be worked on for TLS1 and TLS2. Each row presents the learning objectives and

teaching strategies connected to each driving problem as well as the activities proposed to address them in the

TLSs. O.3, O.4, O.5 refer to the learning objectives defined in Table 1.

Driving problems Learning

objectives

Strategies to

foster learning

TLS1. Activities and comments

Implementation and re-design

TLS2. Activities and comments

Implementation and re-design

How does electric

current work in the

charging and

discharging of a

capacitor? Charge

and electric

potential aspects in

an RC circuit

Is it possible to

improve the

capacitance of a

capacitor in an RC

circuit?

How does a circuit

associating charged

capacitors work?

O.3

O.4

O.5

A.- Familiarize students

with analyzing charging

and discharging

phenomena for a

capacitor in RC circuits.

B.- Organize empirical

information and propose

hypotheses on the charge,

potential difference and

capacitance relationships

in RC circuits. Apply the

energy conservation law

(Kirchoff’s 2nd law) in

an RC circuit.

C.- Propose hypotheses

on the dielectric paper

between the plates of a

capacitor. Explain

situations of capacitors

with dielectrics in RC

circuits.

D. Application of

macroscopic explanatory

models (Kirchoff’s laws)

to circuits that associate

capacitors.

Activities to build the

explanatory model of the RC

circuits at macroscopic level

(potential difference model): the

first 8 activities from TLS1

(strategies A and B).

Activities to define the role of

dielectrics in a capacitor

(strategies B and C). 6 activities

Problems to analyze RC circuits

and capacitor associations

(strategy D). 3 activities

Activities to build the explanatory

model of the RC circuits at a

macroscopic level (potential

different model): a) two

introductory activities, third

activities that includes a

simulation to discuss the

explanatory model of RC circuits;

b) 2 application activities

Activities to define the role of

dielectrics in capacitors from the

point of view of potential

difference and the electric field

between the plates (strategies B

and C). 2 activities and a

simulation of the analysis of the

variables V and E.

Problems to apply the potential

difference model in RC circuits

and capacitor associations

(strategy D). 3 activities.

Chapter 10 | 181

Our evaluation includes qualitative tools (teacher’s journal, students’ worksheets, class

observations protocols, etc.) and quantitative tools (pre-test and post-test questionnaires) to

obtain further information on how to redesign the TLS. The aim of this mixed-method

evaluation is to assess the quality of the TLS not only through the students’ learning outcomes

but also by evaluating the TLS implementation in class situations. The final decisions on the

TLS redesign must consider all outcomes, as the design decisions can affect more than one

problem set by the evaluation process. In this section, we are initially focusing on the

qualitative evaluation of the TLS quality and its impact on the redesign (Section 4.1). Secondly,

we will show some results from the quantitative analysis on the students’ learning (Section

4.2). The evaluation results indicate which parts of TLS1 and its implementation should be

improved. However, the specific changes from TLS1 to TLS2 also depend on the professional

knowledge of the researchers and teachers carrying out the project (see Table 2).

3.1. Outcomes from the first version and redesign

The first version of the TLS (TLS1) was tested during the second semester of the 2017/2018

academic year. Two of the authors implemented it in their classes. The time available within

the study plan for the topic “RC circuits” is 5 hours. Both the traditional teaching groups and

the experimental groups dedicated 5 hours to the topic, they followed the same study program,

and they had the same textbook [28]. In the two experimental classes, there were 111 students

in TLS1 and 110 in TLS2. There were 113 students in the control groups in the first year and

115 in the second year. In the TLS1 and TLS2 implementation, there were no problems with

the available time, although distribution of how long the activity lasted varied from the first

implementation to the second, due to modifications in the type of activities.

Working from the information included in the “teacher’s diary” and the student

workbooks, we observed that the students do not understand the role of the potential difference

between the capacitor plates in the flow of current. It seems that they talk about the potential

difference model, but when they choose an explanation, they tend to use the difference in the

quantity of charge between the battery and the capacitor. A significant proportion of the

students talk about the current stopping when the capacitor cannot take on more charge from

the battery. For example, in Activity A.2. of TLS1 (see Figure 1).

Figure 1. Extract from the teacher’s book for Activity A.2

“In Activity A.2: An initially discharged capacitor (see figure) charges when

switch S is closed. The results obtained are shown in the table,

Time 0 0.5 1 1.5 2 3 4 6 8 10

Charge on

plates

0 2.147 3.718 4.867 5.708 6.773 7.343 7.811 7.946 7.984

How does the current vary during the charging process?

Justify your answer depending on the charge and the

potential difference of the capacitor.

When will the current stop in the circuit?

The vast majority of students write in their workbook that the data from the table indicate

that the current decreases nonlinearly over time. However, they attribute the explanatory model

for this variation in current to the difference in charges between the battery and the capacitor.

They use an explanation from Coulomb’s Force Model and indicate that the growing

accumulation of charge on the plates (as time goes by) prevents current from passing through

V +

R

C

S

–

-

182 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

the circuit due to the charge from the capacitor repelling charges from the battery. Only a

minority uses a potential difference model and indicates that the current stops when the

potential difference for the capacitor and the battery are the same. However, as the other

activities (A.3-A.8) continue, the number of students using the potential difference model

increases.

Working from the teacher’s comments and the students’ notes (and the learning outcomes

that will be mentioned in the next section), it was decided to restructure the 8 activities and cut

them back to 5, including a simulation that will replace A.2. Activity A.3 in the TLS includes

a worksheet (see Figure 2).

Figure 2. Changes made to the learning path from the analysis of the transitory

electrical current in RC circuit (objective 3)

A.3. An initially discharged capacitor is charged by closing the circuit (see simulation).

A) How does the current vary during the charging process? Justify your answer depending on the charge and the

potential difference of the capacitor. Find the relationship between charge, current and potential difference of the

capacitor for three points in the charging process.

When will the current stop in the circuit?

B) Carry out a qualitative assessment on which aspects would change in the charging process, if the circuit

resistance were greater. R’>R.

C) Assess just qualitatively which aspects would be modified if the capacitor’s capacitance were C’>C.

Then check whether your estimations for Sections b) and c) are consistent with the outcomes of the simulation.

The new activity improved student understanding on what happens in terms of potential

difference. It is particularly interesting to understand that the maximum charge in the capacitor

does not depend on the electrical resistance and that with greater resistance, the charging

process slows down and the capacitor takes longer to charge. Furthermore, the maximum

current attained in the circuit is independent of the capacitor’s capacitance although the

capacitor with the greatest capacitance admits more charge with the same battery voltage (10V

battery in the simulation).

The students demonstrate persistent difficulties when applying the potential difference

model in RC circuits. This difficulty is demonstrated in the explanations on the influence of the

dielectric between the plates of a capacitor when the circuit battery remains constant. It was

necessary to reformulate the activities for objective 4 (see Table 2). Some of the activities were

re-written and simulations were added so that the students could check the analysis of variables

and use the potential difference model. For example, see Figure 3.

Chapter 10 | 183

Figure 3. New activities in relation to the students’ difficulties when relating the

electric potential model and the change of dielectric (objective 4)

A.6. Let's consider a capacitor with flat, parallel plates, area A and separation between them d, that are charged

up to a potential difference of V0 Volts, then the battery is disconnected.

a) Describe how the potential difference varies between plates, the electrical capacitance when a dielectric of the

same length, width and practically thickness d goes from entirely on the outside (x<0) to when it crosses it

completely and reaches the opposite part of the capacitor (x>2a). For this, please consider the generic positions:

1) x<0; 2) 0<x<a; 3) x=a; 4) a<x<2a; 5) x>2a, as shown on the diagram:

b) Check whether your analysis matches the results observed in the simulation

c) How do you think that the type of dielectric material (plastic, paraffin, porcelain...) inserted between the

plates might affect the capacitor’s behavior? In the simulation, compare the potential difference between plates,

electrical capacitance for two different dielectrics between plates.

Based on the data obtained from the teacher’s journal, the students’ exercise book, the

comments received by the classroom observers and the post-test results, we can refine the TLS1

sequence. The changes mainly involved reformulating activities to adapt them so that the students

understand their objective (metacognitive difficulty) and to stimulate production of hypotheses

and arguments for the conclusions. The data obtained indicates that the students have no difficulty

understanding the order in which the topic contents are presented, and no changes were made in

presenting the learning path (driving problems). The second version of the TLS2 applied in the

spring semester of the academic year 2018/2019 presents the re-written activities and the added

worksheets. Drafting new activities focused on promoting arguments on the conclusions in terms

of the potential difference in RC circuit model from the start of the TLS.

3.2. Results regarding students’ understanding

To see the improvement in the students’ learning against the learning objectives (Table 1), we use

pre-posttests. The post-test was applied to students from the experimental groups and the students

X x=0 x =a

x<0 x >2a

a

b

d r

184 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

from the control group in exam conditions and the result was included as part of the final course

mark. To decide whether there were significant differences between the experimental and control

groups, the Chi square (2) test was used for the usual confidence interval of 5% or less [46]. In

the pre-test, there were no significant differences in the experimental and control groups. The

same happens with the two experimental classes and the results were grouped as shown in the

tables. The pre-test and post-test questions were similar and had the same objectives. Posttest

questions are shown in the Appendix and their objectives in Table 3.

Table 3. Relationship between the aim of question and the learning objective

Questions Learning Objectives

Q1, Q2 O.3. The students use a macroscopic model of potential difference to explain the

current in RC circuits.

Q3 O.4 The students can explain the influence of the dielectric on the electrical

capacitance of a capacitor in an RC circuit.

Q4 O.5 Application of the macroscopic model of potential difference in capacitor

associations.

Regarding the conceptual and epistemic difficulty of the questions, they are all familiar for

the students in the academic context. However, questions Q3 and Q4 are not similar to

questions in the problems at the end of the textbook chapter. In these two questions, the students

must use more complex reasoning, where they have to apply the concepts of charge,

capacitance, current and potential difference in transitory situations (influence of the dielectric

in RC circuits in Q3 and circuit with two charged capacitors in Q4).

In Q1, the students have to explain that the electric current circulates as a consequence of

the potential difference between the battery terminals and the capacitor plates (macroscopic

model of potential difference) and that the current is variable and finishes when the battery and

the capacitor (that is charging) have the same potential difference. The students must use the

same potential difference model to explain Q2. In this case, the brightness of the light bulb will

vary due to a variable current that will stop when V=0 is reached between the capacitor plates.

The direction of the current in the circuit will follow the conventional current rule by

considering that the positive charges move towards the decreasing potential.

In Q3, the students must explain that inserting the dielectric represents a drop in the electric

field between the capacitor plates and consequently, a drop in its potential difference. This drop

will let the capacitor accumulate a greater quantity of charge on its plates, implying that its

capacitance increases. This requires students to use complex thinking to combine the dielectric

effect that, as a consequence of the polarization, reduces the potential difference between the

plates with reasoning based on the potential difference model (greater charge of the capacitor).

The level of epistemic difficulty is greater than in the previous questions.

Q4 assumes that the students must recognize that, according to the macroscopic model of

potential difference, the current (+ charges) moves anti-clockwise, as the V at which the top

capacitor has been charged is greater than the V at which the lower capacitor has been charged.

The students must explain that the charge associated with the plates joined by conductors is an

absolute value of 2Q, which is conserved, distributed proportionally to the capacitance of each

capacitor. A 2Q charge then passes through the wires, so the lower capacitor changes its polarity.

In this way, for the closed circuit, the sum of the potential differences between plates in both

capacitors is zero. Here, students must simultaneously apply the potential difference model in

both capacitors that explains the epistemic difficulty of the question.

To analyze the answers, firstly a preliminary set of descriptive categories was proposed for

each of the questions. Subsequently, the answers were re-read, and each answer was tentatively

assigned a category. When there was disagreement on a descriptive category or how the

answers related to a specific category, this was resolved using evidence of the student’s

Chapter 10 | 185

comprehension as a reference. The answers to the questions were grouped into the following

categories:

A. Correct answer and explanation for the question.

B. The answer includes reasoning based on the difference in the quantity of charge.

C. “Ad hoc” explanations that are limited to describing the phenomenon without

explaining it or using elements of the scientific model without logical consistency.

D. Incoherent or no answer.

Table 4 shows the frequency of the correct answers to the questions. Over the two years of

the experiment, the percentages of correct answers in the pre-test did not vary significantly, so

we have presented the average of the percentages in the first column. We are using the Chi

square statistic for data analysis, showing that there are statistical differences (p<<0.05) for all

implementations of TLS compared to the control groups for the four post-test questions. There

is also progression in learning from implementation of TLS1 to TLS2 (see figures 4 and 5).

Table 4. Percentages of the correct answer for all questions and the significance level (computed using the

chi square- the two-tailed Fisher exact test) of comparisons between the control and experimental groups.

Experimental groups in Spr. 18 (E-TLS1) and Spr. 19 (E-TLS2). Comparison groups in Spr. 18 (C-18) and

Spr. 19 (C-19). In all cases, the value of p<<0.005.

Question All courses Post-2017-18 Post-2019-20

Pre (N=334) C-18

N=113 E-TLS1

N=111 C-19

N=115 E-TLS1

N=110 Q1 15.0 28.5 63.5 27.0 73.0 Q2 13.0 25.0 68.5 19.5 70.0 Q3 8.5 22.0 65.0 18.0 75.5 Q4 7.0 17.5 57.0 15.5 61.5

Figure 4. Percentage of the answer categories in the four questions for the

control and experimental groups (Control 1, TLS1, Control 2 and TLS2)

Table 4 shows that Category A answers are more frequent in all the experimental groups

compared to the control groups, with statistically significant differences in all cases. The

following quotes illustrate typical answers in this category:

0

10

20

30

40

50

60

70

80

A B C D

Question 2

Control 1 TLS1 Control 2 TLS2

0

10

20

30

40

50

60

70

80

A B C D

Question 3

Control 1 TLS1 Control 2 TLS2

0

10

20

30

40

50

60

70

A B C D

Question 4

Control 1 TLS1 Control 2 TLS2

0

10

20

30

40

50

60

70

80

A B C D

Question 1

Control 1 TLS1 Control 2 TLS2

186 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

“The charging process starts because there is a potential difference between the battery

poles and the capacitor plates that have an initial potential of zero. As the current

circulates and the charge accumulates in the capacitor, its plates equal out the electrical

potential of the battery terminals. When they are equal, the current no longer passes.

As the potential differences vary over time, the current is variable.” (Q1, TLS2)

“By putting a dielectric between the capacitor plates, the field between the plates

drops due to the polarization of the dielectric. This implies that the potential

difference between its plates also drops, which generates a current between the

battery and the capacitor plates. The capacitor admits more charge for the same

potential. Its capacitance increases” (Q3, TLS1)

The answers in Category B are incorrect and their arguments show a current model in RC

circuits based on the difference of charge quantity between the circuit elements or by

considering the battery as a charge provider and the capacitor as a charge container. The

following quotes illustrate typical answers in this category:

“The charging process begins because the battery provides charge to the capacitor

that is empty. As the capacitor charges up, there is a greater repelling force to admit

charge and a time comes when the capacitor is full (depending on its capacitance),

and current does not pass.” (Q1, C-19).

The capacitor has charge that it will take from its positive plate to the negative plate

until it is neutralized. During this time, current passes through the light bulb that will

have variable brightness as the current is decreasing” (Q2, TLS1).

“The two capacitors have different quantities of charge, there will be a current until the

difference in charge equals out and each capacitor has a charge of 2Q” (Q4, C-19)

The answers from Category C are usually incomplete instead of completely incorrect or

descriptive without justifying what happens. There is an approach to applying the equations for

electric current or capacitance but no coherence to the answer. The following quotes illustrate

typical answers in this category:

“We know that in an RC circuit, the current obeys the equation i = i0 e-t/RC and

therefore, there will be variable current in the circuit over time. This current depends

on the resistor R and the capacitance of the Capacitor” (Q2, TLS1)

“This is an association of capacitors in parallel so the equivalent circuit will have a

capacitance C= C1+C2 and the final charge Q=Q1 + Q2. Current will circulate until

the two capacitors work as one equivalent capacitor” (Q4, C-19).

The percentages of Category B (Figure 4) show that the model based on the difference in

quantity of charge to explain how RC circuits work is favored by the majority among the

control groups (around half the students) while only a minority (around 10%) of students from

experimental groups use this model. Applying the innovative program means that students

evolve towards a scientific model based on the potential difference. The model based on the

quantity of charge also appears in prior research as an alternative interpretation by the students

of the scientific model [29, 30].

The second category with the highest percentage among the students from the

experimental groups is C (around 20%) and increases as the question becomes more complex,

from around 15% in Q1 and Q2, to 20% in Q3 and Q4. It seems that the learning progression

drops when the cognitive demand level of the questions requires complex reasoning. In these

Chapter 10 | 187

cases, students from Category C tend to answer with equations memorized during instruction

although lacking overall coherence.

4. Discussion and conclusions

This study aimed to show how it is possible to go from general recommendations from physics

teaching research to specific teaching proposals following a research-based design

methodology. In the example provided here, this methodology allows us to clearly show the

choices in the TLS design and its systematic refinement based on evaluation tools. The

assessment of the didactic material that allows its successive improvement is not usually

considered when proposing a new approach. Our application to the topic “RC Circuits”

indicated that the DBR methodology has had an impact not only on the final learning outcomes

but also on aspects related to the type of teaching strategies applied in a transformed

environment, work carried out by the students. Our design and evaluation of TLS is convergent

with approaches from other research groups that show that they achieve greater and better

learning based on empirical data from the classroom [47, 48, 49]

One novel aspect of this research is the didactic tools used in the design. We demonstrate

the usefulness of epistemological analysis as a didactic tool to substantiate and, when

appropriate, modify the curricular objectives to suit the educational level. Furthermore,

“learning demands” are used as a tool to guide the design of learning activities so that they fall

in the Vygotskian zone of the students’ potential development. We use guide-problems that

include a set of activities to drive learning and solve the problem. Carrying out these activities

implies promoting active teaching strategies such as TORA that combine conceptual content

and scientific practice.

Another novel aspect, regarding the chosen design principles, is the evidence we provide

that well-grounded material design is not enough. It should be compared in its classroom

implementation and the analysis of coherence between the TLS activities, the objectives and

the results obtained by the students. In addition, we show the need for a careful design that

makes it possible to guarantee success in the first implementation, as the DBR does not aim to

refine an initial TLS through successive implementations by trial and error. It is not acceptable

that it takes five years of implementation to guarantee teachers a successful TLS design in a

school environment.

One of the central ideas of the scientific paradigm is replicability; however, because DBR

on TLS design cannot handle school contexts, it is difficult to replicate the findings in contexts

where teaching strategies differ widely. Consequently, we think that our TLS design will not

work in teaching contexts where the students mainly listen to the teacher and take notes. For

example, students who have not picked up the skills of working in groups or who are not used

to arguing with data and defending their results with evidence, will not be able to follow the

sequence of activities. We think that these students are not familiar with learning concepts and

laws alongside practice of scientific procedures as required to solve the TLS activities. The

same happens with teachers. If they are not trained in stimulating students with questions that

help them advance from the activities, they will not be able to develop this type of teaching.

Development of teaching-learning sequences remains a common goal in the Physics

Teaching community. The application of DBR, and the example that is given here can provide

a guide for study plan designers and teachers beyond the description of mere “good ideas” or

applications without evaluation.

Acknowledgments

188 | Guisasola J., Zuza K., Sarriugarte P., Ametller J.

Part of this research was funded by the Spanish government MINECO Project No. PID2019-

105172RB- I00

Appendix

Q1. A capacitor is connected to a battery with potential difference V, until it is completely

charged (see figure). Explain how the capacitor charges. Justify your answer and draw the

direction of the current in the circuit.

Q2. The charged capacitor from the previous question is connected to a light bulb (see

diagram). Will the light bulb come on? If so, explain how the current happens in the circuit.

Justify your answer.

Q3. In the laboratory, it is seen that when inserting a dielectric with a relative dielectric constant

r between the flat, parallel plates of a capacitor, its capacitance increased precisely by this

factor (see figure). Explain what is happening in terms of charge, field and potential difference

between plates. Does the capacitor’s capacitance vary?

Q4. O.5- Two equal capacitors with capacitance C are charged under different voltages and

acquire charges of 3Q and Q. Then they are connected up as shown in the diagram. What will

the final charge of each capacitor be? Explain the current circulation, if there is one. Justify

your answer.

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191

Chapter 11

Designing curriculum to introduce contemporary topics to

physics lectures

Mojca ČEPIČ University of Ljubljana, Faculty of Education, Ljubljana, Slovenia;

Jožef Stefan Institute, Ljubljana Slovenia

Abstract. The article deals with the prerequisites and the activities required to introduce

contemporary physics in introductory physics courses in universities and to pre-university

education. Contemporary physics covers topics in physics that are currently being investigated

in fundamental research laboratories. When the results of these investigations are found in

everyday devices or objects of daily use, such as liquid crystals in displays or hydrogels in

diapers, the research is also relevant. Introducing a contemporary topic into physics education

requires close collaboration from researchers in fundamental research, educators, and

teachers-practitioners. The paper discusses various actions required to develop the module and

their timing. It also reports on the development of a real module, including the obstacles that

motivated collaboration among developers can circumnavigate.

1. Introduction

Physics is a subject that students either love or hate, not many are indifferent. The proportion

of students who love physics is usually small, and they are often seen as very talented but a bit

odd. Why is this? There are several reasons, which have been widely studied, and which can

generally be summarized in three groups. Physics is very abstract, using a language with its

own rules, often speaking in mathematical expressions and graphs, and drawing conclusions

from seemingly different premises [1]. Many students find it difficult to understand the

language of physics [2]. Simplifications, generalizations, neglecting and precision are another

problem. In order to use algebraic expressions that are accessible at an introductory level,

problems must be simplified, many everyday circumstances must be neglected, e.g., friction

and air resistance, and some laws contradict everyday experience, e.g., Newton's laws. From

experience, a student assesses force by the force acting on her/himself or caused by him or

herself, and therefore easily forgets the role of mass in the effects of force. Similarly, students

are aware of the forces they can cause one way or another, but easily forget forces that exist

"by themselves," such as static friction. All of this leads to the conclusion of an unhappy student

that physics and its reasoning do not correspond to daily life, so school physics teaches

something that is not true and is reserved for school knowledge, and that student learning has

a simple goal, which is to get a passing grade [3]. Finally, from a student's perspective, the

topics covered in a regular curriculum are very old, even historical. The most advanced

curriculum topics end up introducing elementary concepts of modern physics, which may

include the basics of special relativity, an introduction to uncertainty, the wave nature of

particles, and some nuclear physics (for example [4]). However, the discoveries related to these

topics, even if considered under the title of "modern physics", are more than a hundred years

old, which is an eternity from the perspective of young people, and they actually support the

irrelevance of physics to everyday life.

On the contrary, physics is a vivid and beautiful science. Thousands of researchers strive

to understand phenomena related to the dawn of time in the cosmos, but also to the properties

of new materials ([5, 6, 7], and references therein) and, surprisingly, even to everyday activities

192 | Čepič M.

such as knitting [8, 9], which hide problems that could help to design new materials, structures

or devices. Students' visits to scientific laboratories hardly register this perspective. Usually,

sophisticated equipment is shown and very often accompanied by explanations that are not

particularly easy to understand for a student with normal school knowledge. Physics is the basis

for most equipment we use every day. Physics is the eternal and, literally, the largest discipline.

We believe that the laws of physics have not changed in the past and will not change even in

the distant future. Physics phenomena span more than 60 orders of magnitude, from parts of

the atomic nucleus to the edges of the cosmos.

However, introducing physics, nowadays investigated in laboratories, into the classroom

involves bridging many gaps. It requires subtle knowledge of the topic being introduced and

an ability to adapt communication about the phenomenon to the appropriate level of the

students, providing the students with experience so that they can incorporate the new

knowledge into their existing knowledge network, the teachers must be trained because the

knowledge is new to them as well, the teachers have to be able to evaluate the effectiveness of

the teaching, and much more. This plethora of reasons seems to explain why it is rare to

introduce contemporary topics. However, there are some successful examples that make it

possible to formulate the introduction methodology framework [10, 11, 12, 6, 7].

Before proceeding, we must discuss one further issue. What shall we call the physics which

is active in research laboratories, whose new discoveries are published in scientific journals,

with which many researchers are engaged, and whose problems are actively discussed at

scientific conferences? There are several names that seem appropriate, but they are often

already in use. For example, "modern physics" is the common name for discoveries made at

the beginning of the last century, relativistic theory, quantum mechanics, nuclear reactions.

"New physics" is used in particle physics. The term "current research" might be too narrow,

since the real cutting-edge results often require a lot of background knowledge that is no longer

current. We suggest "contemporary" physics, which includes physics where research is still

active, scientific journals and conferences focus on it, but on the other hand, results of the topics

could be "contained" in devices that are familiar to the students, although the background to

understand the topics could be based on a few decades-old discoveries.

The contribution is structured as follows. In the theoretical framework, aspects necessary

to introduce new topics to the physics classroom are discussed. Then, the process of introducing

new scientific results is presented in subtle detail. Subsequently, one example is presented,

from content to results. Finally, the approach’s outreach possibilities are presented, plus the

interdisciplinary role that new, contemporary topics could play, especially in the social

sciences.

2. Contemporary physics topics and physics curriculum

In this contribution, we will focus on topics that we would like to call "contemporary physics

topics”. What properties must a topic have to be called a "contemporary physics topic”? Its

most important characteristic is that research on the topic is still active. This actually means

that the most enthusiastic students can address their questions directly to the researchers

involved in researching the topic. It also means that the topic is being researched on the

frontlines, where there are no answers to the questions yet, and students can taste the thrill of

the unknown, even if they are not able to understand all the details. They can learn that through

the known, you can reach the unknown. This perspective does not exist or is very weak when

discussing topics in classical physics.

Contemporary physics is defined more broadly than something one could call the "front-

end" or "current physics." It includes topics that have been studied in recent decennia. One

Chapter 11 | 193

characteristic of its content is that it was not included in physics teachers’ study programs or it

was merely mentioned during their studies without being covered in detail. Moreover, the

topics are usually familiar to students, they have heard the names, such as hydrogels [13, 14],

or they know that some everyday devices use the properties of recently developed materials,

e.g. liquid crystal displays [15] However, students usually recognize a name or a device, but

they do not have the slightest idea how these properties or materials are used. The contexts

provided by these circumstances are also motivating for students.

Contemporary physics topics also include topics that are fundamental to understanding

new findings. Thus, these particular topics are not entirely new, but because they are necessary

for understanding new findings, contemporary physics can serve as a motivator, e.g.,

aquaplaning in the context of friction and Newton's laws [16].

Finally, the name "contemporary physics topics" is distinctive, timeless and general

enough in content that it could be used in the future for new topics that emerge and become

interesting to be introduced in teaching. Because the name is not content related, it cannot fall

into the trap of "modern" or "new" physics, which were once modern or new but have aged and

became "old" years later.

2.1. The role of contemporary topics in the curriculum

The strictness of the curriculum varies by country. Some curricula leave a certain amount of

freedom to the teacher, in terms of content and/or time (e.g., [4]). The curriculum leaves the

choice of some topics to the teacher or allows the teacher to decide which part to teach

according to their own or the students' interests. In addition, many physics curricula encourage

teachers to teach and train scientific skills. Usually, skills such as measuring, designing

experiments, formulating scientific questions, drawing conclusions, planning investigations,

reporting results, and many others overarch the whole curriculum (e.g., [17, 4]). Contemporary

physics topics can be "used" to introduce scientific skills, as the content is completely new for

students. For example, to gain initial experience relevant to the contemporary topic, students

plan and conduct an investigation on the elastic properties of swollen hydrogels [5].

Contemporary physics topics can be used as a common thread running through the physics

program. The teacher demonstrates an interesting phenomenon during introductory physics

lessons and promises a certain level of understanding by the end of the physics course. Later,

the teacher returns to the topic a few times a year and adds a piece of information. For example,

liquid crystals in the cell between crossed polarizers, their colours and how the colours change

when heated are introduced at the beginning of the course as motivation and later revisited

when talking about phase transitions. Birefringence is demonstrated in geometrical optics and

polarization of refracted beams in wave optics. Finally, their dielectric properties are

demonstrated using the liquid crystal device in action. If students want to know more about

liquid crystals, there is plenty of material to enrich the physics lessons [18].

Contemporary physics topics can be taught as an elective topic. As the contemporary

research is brought into the classroom, these topics show that physics as a science is not old

and abandoned. When properly conveyed, students realize that physics is not merely reserved

for the brightest minds in the world. If the teacher is motivated, a few hints about contemporary

research can be included in any lecturing plan.

2.2. Teacher education and training

The physics teacher must address two great and difficult problems when teaching contemporary

topics to students. The first has already been mentioned. The contemporary topics were not

taught during the teachers' own study, because the teachers’ content knowledge usually ends

with modern physics. The second problem is related to the first. Since a contemporary topic is

194 | Čepič M.

not part of the regular curriculum, neither at university and certainly not in high school courses,

the teaching methodology has not been developed yet. For teachers who are willing to invest

in teaching contemporary topics, topic-specific training must be available. The training must

include the general content knowledge of the topic at the teacher's level with experiments that

enable teachers to observe and investigate relevant phenomena. Next, it should include the

methodology of teaching the topic with experiments that bridge the gap between regular

knowledge and new content and provide students with basic experiences. Finally, some

materials for experiments are not readily available, e.g., liquid crystals with phase transitions

near room temperature. Such materials need to be made available to teachers for further use.

For all activities, lecture notes, worksheets, detailed instructions for experimental setups, and

methodological advice must be constantly available to teachers. This means that the training

must include written materials for future reference and adaptation, or it must be available

remotely after the training. Furthermore, teachers must be able to permanently contact experts,

usually the course developers, if they have any questions. To prepare teachers for professional

education, researchers and educators must work together. In each subfield of physics and other

sciences, researchers develop specific, jargon-like professional language. Within the

community of the subfield, research methodology is known, the meanings of certain

expressions are clear, models and theories are understood.

However, communicating this knowledge outside the field is difficult even if the audiences

are researchers from similar but not the same field, as is clearly evident in the evaluation

processes of various projects, where it cannot always be guaranteed that reviewers are

exclusively from the same field. It is even more difficult to communicate the results to students

with different cognitive levels and to lay audiences. Moreover, researchers are usually not

familiar with the prior knowledge and understanding of students at different levels. I clearly

remember my experience as a young teacher taking students to a nuclear reactor. The scientist

explaining the physics was surprised that the second-year high school students were not

familiar with Cherenkov radiation.

In recent years, awareness of these problems has led to developing training courses on

communicating with lay audiences. Nevertheless, communication in public lectures is often

peppered with beautiful pictures and sometimes even astonishing experiments, but the

explanations are usually superficial and too quick for a layperson to grasp the reasoning. The

impression is made, but understanding is often lacking.

To avoid this trap, we propose that researchers, i.e., experts on the subject, work closely

with educators, who are experts on the methodology of physics education. Educators alone

cannot prepare the methodological background for teacher education since their knowledge of

the specific contemporary topic is rather superficial compared to that of the experts.

Nevertheless, their professional training allows them to understand the researcher, to recognize

when communication becomes too specific or jargon-like, and they are also independent

enough to dare to ask questions when phenomena are not clearly explained. The educator's

expertise builds the bridge between the researcher and the teacher and his students.

The role of this collaboration is as follows. The researcher and the educator jointly adapt

how the contemporary topic is conveyed to the appropriate level for the teachers. The teachers

are considered to be better educated in physics and also more motivated than the lay audience.

They jointly develop a topic-specific experimental support for teacher training. These are

demonstration experiments that accompany content lectures, laboratory experiments that

teachers perform individually to achieve a higher level of experience than expected of students,

tasks and exercises for teachers to brainstorm, written materials, etc. This part takes into

account teachers' content knowledge. Next, researchers and educators develop experiments for

demonstrations during teachers' classroom explanations, experiments for students’ practical

work, accompanying materials such as worksheets, and the like. Some experiments may be

Chapter 11 | 195

identical to the experiments for teachers, others are usually simplified to be available for the

practical work of several students in parallel or to demonstrate some of the studied phenomena

only by observation and not using detailed measurements. Finally, educators prepare

methodological support and advice for lectures and practical work with students. The

methodological materials are also reviewed by a researcher to avoid errors or oversimplified

conclusions.

The most serious problem with this process is the lack of interest in such extensive work

by fundamental researchers. As long as the value of research is measured only in publications

in high impact factor journals, it will be difficult to motivate them. Recently, however, outreach

has become a very important part of project proposals, and the experience of working with an

educator can be fruitful in planning outreach. One can hope, then, that motivation for

communicating contemporary research findings to a lay audience will increase in the research

community in the future.

One alternative to collaboration between researchers and educators is when the same

person is qualified as both a researcher in the contemporary topic and an educator, as was the

case of introducing liquid crystals at various levels of education. Unfortunately, such

combinations are extremely rare and often not appreciated even in the research community.

2.3. The role of preliminary knowledge, experience and experiments

When considering contemporary physics topics for introduction to the classroom, one must be

aware of their novelty. Unlike most regular physics topics, students' prior experience is

negligible. As studies have shown, students have heard some of the expressions related to these

topics, but the knowledge and experience stop at that point [14]. So, to promote the construction

of the new knowledge network and make connections with the existing ones, the prior

knowledge required to learn and understand the basics of the contemporary topics should be

examined in detail. The contemporary topic is placed at the level where prior knowledge is

already sufficient and little additional information is needed. For example, to learn about

hydrogels and the absorption of water, students should be aware of the concepts of polymers

and osmosis. Both these concepts could be refreshed when studying the properties of hydrogels,

but knowledge-building is better when students are already familiar with them.

However, the phenomena relevant to the contemporary topic are most likely new and being

experienced by students for the first time. Practical, inquiry-based experimental work by

students is most efficient in providing the missing experience. These inquiry type experiments,

in which students have some degree of freedom to investigate the properties of contemporary

materials or new phenomena, explore cause-and-effect relationships, or simply observe a

phenomenon that is important to the contemporary topic, are relatively time-consuming. On

the other hand, the time is not spent in vain, because it allows students, with support from the

teacher, to become familiar with completely new phenomena, to internalize a vocabulary and

language characteristic of the topic, to consider different aspects, and - last but not least - to

investigate and play under novel conditions. Students rely on these experiences later when the

contemporary topic is discussed. During experimentation, students are actively observing,

working, discussing, and designing; that is, they are learning. Active participation promotes

recall of the experience when it is needed. It is more effective than learning that occurs only by

listening and observing.

From what has been said, it is clear that researchers and educators must work together to

inspect the curriculum to find the best placement for the topic, but at the same time, they must

work together to develop introductory experiments that are not necessarily part of the

contemporary physics topics already, but provide the necessary experiences that students can

later rely on. For example, to demonstrate the birefringence of liquid crystals, a prismatic cell

196 | Čepič M.

filled with an ordered liquid crystal is used. Experiments that provide experience also include

the prism and rainbow indicating that waves with different wavelengths refract differently.

2.4. The choice of topics

Not all topics are suitable for introducing contemporary physics into the classroom. Many

topics, while interesting and motivating to students, must remain at the narrative level and

cannot actively engage students. This is true for many recent discoveries in astrophysics, but

the same problem exists for many topics in modern physics, which are not actually

contemporary anymore. In quantum mechanics, animation is helpful, but the relevant

experiments performed by students are hard to find. Understanding experiments in modern

physics that are relatively easy to perform, such as observing discrete spectra, usually requires

a great deal of knowledge about modern physics and understanding them is difficult in the

introductory phase of the new topic.

An important prerequisite for effectively introducing contemporary physics into the

physics classroom are experiments. The research methodology, i.e., the instruments used in the

laboratories, should be adapted to the classroom. In other words, it must be possible to make

observations and measurements with simple means accessible to the school with sufficient

precision to observe phenomena. Compared to research equipment, observations and

measurements do not need to be very accurate. The equipment should not be expensive, and it

is best if enough experimental equipment is available so that groups of students can work in

parallel. These requirements are important both to provide preliminary experience and for

exploratory learning of the topic itself.

Good contemporary topics are also related to daily life. Either novel materials are used in

devices, such as semiconductors or liquid crystals, or they are simply used in their pure form

as hydrogels. There are also topics that are not necessarily contemporary, but the phenomena

are interesting, even artistically beautiful, and can be easily observed and manipulated. One

such example is colors of transparent anisotropic material between polarizers [19].

Surprisingly, there are many phenomena that are not actually new, as they have always existed,

but were not recognized, such as multiple [20] and spreading [21] shadows of objects,

mechanically or thermodynamically metastable structures [22, 23], bistable or chaotic

pendulum behavior [24], mediated forces caused by surface tension [25], and many others that

encourage easy experimentation to gain experience but are still not recognized in everyday life.

Each of these requires collaboration from many people, researchers, educators, and teachers to

develop interesting and experimentally-supported learning units.

As mentioned in the introduction, the classical choice of topics in the curricula is quite old

from the students' point of view. Nevertheless, the teacher has to meet the expectations imposed

by the curriculum and consequently the expectations of students and parents in terms of student

performance in external assessments and in later stages of education. For this reason,

contemporary physics topics must support the learning of at least part of the regular curriculum.

3. Development of modules

To develop a module, a series of units leading to basic knowledge and understanding of a

contemporary physics topic, four questions must be clearly answered. Why would you want to

teach students this particular topic? What might students be expected to know at the end of the

module? In parallel, you need to think about the target audience. Who are the students who will

be studying the topics? And finally, what teaching methodology should be used for the topic?

All these questions are closely related to evaluation of the module, which should test and

evaluate the appropriateness of goals for the cognitive level and prior knowledge of the

Chapter 11 | 197

students, as well as the suitability of the teaching methodology to achieve this goal. The

relationship between the questions is shown in Figure 1.

Figure 1. The interplay of questions and associated tasks to consider when

designing a teaching module on a contemporary physics topic. The lower the

question or task in the diagram, the later it comes into consideration in the process.

Let us consider these four questions thoroughly, and how they relate to the content, the

method, the people involved in introducing the topic, and so on.

3.1. Why should you want to introduce a specific topic into education?

This question is probably the most difficult of all. Who is actually motivated to introduce the

contemporary topic into the classroom? A researcher from a physics lab? An educator? A

teacher? To put it bluntly, usually none of them.

Researchers care most about publishing in journals and giving talks at scientific

conferences. They are not even motivated to publish in their native language if it is not English,

the lingua franca of physics. A colleague of mine, a brilliant researcher and a born

communicator, once said on this topic, "It is not worth preparing something in Slovenian, it

takes as long as preparing an article for a journal and is worth nothing in the research

community." This clearly shows how miserable the situation is. As stated earlier, this situation

has improved in recent years, as project proposals often require outreach as an important part

of the project. The methodology for designing outreach activities has many similarities with

introducing the new topic to education, but it is freer, is usually not assessed and often remains

at the narrative level. However, it must be done in local languages if they are not English. As a

result, at least a national subject vocabulary develops.

In some cases, a researcher who is truly passionate about his or her field is intrinsically

motivated to communicate his or her findings to non-specialists. Since researchers are often

lecturers on physics courses, this communication usually ends up with them sharing some

results in introductory physics lectures, with the motivation that students later decide to join

the researcher in his field. Sometimes, this also leads to developing elective subjects in graduate

courses that provide more comprehensive knowledge to students who have already chosen a

research topic. In rare cases, some elements of contemporary topics have been introduced into

high schools, but for a very specific audience of the most talented students with the goal of

198 | Čepič M.

motivating them to study physics or physics-related studies, as reported in an editorial series in

Soft Matter [26]. In general, the researchers’ reports on these activities did not include an

assessment of student learning but were limited to suggestions about the content.

An educator, a researcher in physics education might also be interested in an introduction

to the topic of contemporary physics in the classroom. This is a new area of research in science

education because there are not many examples of such introductions, for example, one does

not have data on different topics that are more or less suitable to find their way into pre-

university education. There is a strong belief that information about contemporary physics

research increases students' motivation for physics, but how can one study the impact of such

topics when they are rare and not widely used? The physics education research is rich on the

learning and understanding of topics in classical physics, where students can usually draw on

everyday experiences. In contrast, many contemporary topics are completely new to students.

Thus, analyzing the learning of older students, where the entire experience is also new, is an

area that should be explored. Finally, testing, improving and adapting the content of specific

contemporary topics, investigating the consistency of these actions as the framework for

designing modules on contemporary topics in physics, and improving the framework is an open

research problem in itself.

However, educators do not usually actively work in research laboratories. They may find

a contemporary topic of interest to introduce, but they are not familiar with the fine details and

potential pitfalls already understood by researchers. For this reason, an educator must

collaborate with a researcher in the field during the process of adapting the content to the

students' prior knowledge and cognitive level. Without such collaboration, the unit can easily

become superficial and contain errors, or it may emphasize less important phenomena and

leave out important aspects.

Finally, why would teachers-practitioners want extra work? Many passionate teachers,

after years of work and repetition of regular lectures, seek new challenges, for their students

and for themselves. Some try experimenting with new methods, others decide to introduce new

assessment methods, still others want to pursue research in their subject but also inform their

students about it. Such teachers often take part in in-service training, and are willing to invest

their time and effort, as in the case of the teachers who participated in the workshop on teaching

liquid crystals organized as part of International Liquid Crystals Conference in 2011 [27].

Nevertheless, there are some examples that report introducing contemporary topics to pre-

university education and evaluation, but they are rare. To the best of our knowledge, two

examples [10, 12] have been found that span the entire study, and one is being prepared (Dziob,

unpublished).

However, many activities for lay public and younger students have been developed in

various projects but are rarely systematically studied and reported on. Nevertheless, various

international resources, e.g., ERASMUS+, support educators and teachers to try new

approaches and topics. Unfortunately, more important initiatives such as Horizon2020 have not

continued to support research and development in education in a similar way to FP7. One of

the examples from FP7 is the IRRESISTIBLE project [28], in which many contemporary topics

have been brought to a level that is a good start for introduction into the classroom and a good

source of ideas for other studies related to contemporary physics topics. The content of these

activities is not new from a scientific perspective, but from a science education research

perspective, evaluations are lacking, and basic science researchers are clearly not motivated for

such additional efforts. The best examples that can be found are presentations of

teaching/learning activities sometimes reported in journals dealing with high school physics,

such as Physics Education (e.g. [29]) or The Physics Teacher [30, 31, 32, 33].

Chapter 11 | 199

3.2. How should we choose the learning objectives?

Again, the researcher and the educator must work closely together, even better if teachers-

practitioners are involved. What are their roles? The researcher explains what discoveries,

reflections, and findings are most relevant to the chosen topic from the researcher's perspective.

Next, the researcher also discusses the history of the discoveries, which problems were difficult

to solve and understand and why, which problems were easy to solve, if any, but why they were

easy and what you need to know to solve those problems. Next, the researcher discusses the

prior knowledge needed to understand these discoveries, and the educator either tries to find

that knowledge in the curriculum at some level as existing knowledge or discusses how

students can acquire that knowledge without spending an inordinate amount of time on it. At

this point, the topic might become questionable or even inappropriate for introduction. If

students' prior knowledge is non-existent or too far removed from a regular curriculum, it

would be difficult to convince teachers, who are always pressed for time, authorities, who want

efficient teaching, and students and their parents, who primarily want to see learning value in

terms of preparing for final exams. For example, to understand why light-emitting diodes often

have a quasi-discrete spectrum, students would need to understand the existence of valence and

conduction bands and band gaps. Their occurrence and role could be explained with hand-

waving arguments, but this requires more details from quantum mechanics than a normal high

school student might understand. This does not mean that LEDs are unsuitable for introduction,

only that the goal of understanding how gaps occur, which is probably very important for a

researcher since manipulating them makes it possible to tune the frequency of the emitted light,

cannot be included in the learning objectives for high school students [31].

Finally, the teacher-practitioner reports on actual teaching. Not every topic included in a

curriculum is studied thoroughly enough for the needs of a particular contemporary topic. The

teacher discusses possible adaptations of the content to the sequence of topics in regular classes

and suggests the place in the curriculum, the level of the students and the time available for the

contemporary topic.

3.3. Who are the students to whom the contemporary topic is introduced?

Learning objectives are closely related to the level and prior knowledge of the students who

are the target audience. However, this issue must be handled flexibly. As previously stated, the

learning objectives for each pre-university level need to be thoroughly considered and the same

objectives cannot be achieved at all levels. However, some topics can be introduced at very

different levels from pre-school to university. Hydrogels, for example, are a very complex

topic, but even preschoolers can observe the growth of a hydrogel bead when it is submerged

in water, they can compare the properties of a full-grown hydrogel bead and a wet sponge, how

they respond to pressure, and they can discuss why they are used in diapers. Students can return

to hydrogels in cycles and gain further experimental experience until finally, towards the end

of pre-university education, they can understand the absorption of water, its dynamics and

hydrogen bonding in the polymer network. Adding experiences and knowledge at different

educational levels can increase motivation for science, or at least decrease the decline that

typically occurs as students become teenagers [1].

As discussed in a series of articles by Planinšič and Etkina on LEDs [30, 31, 32, 33], the

contemporary topic may play different roles at different levels. Devices using the new

phenomena can be used simply as devices, and students become familiar with their existence

and curious about how they work, e.g. a LCD; later their structure is studied, e.g. the shades of

different colors obtained only from red, green and blue: later still, the components of a LCD,

200 | Čepič M.

e.g. polarizers and liquid crystals, are included, and finally, when the response of a material to

the external electric field is learned, how a LCD works can be discussed in subtle detail.

3.4. How can we teach contemporary topics?

Contemporary topics differ from regular topics in their novelty. Novel materials and/or

phenomena have only recently been discovered and are not yet part of public knowledge. Since

they "come" from laboratories, students usually have no prior experience with them. Teachers

are also unfamiliar with these topics. Older teachers have not encountered these topics during

their studies because they had not been discovered. The same is usually true for younger

teachers. Teachers' content knowledge rarely extends to contemporary research. Such topics

are reserved for research-oriented graduate students. So, teachers also lack content knowledge.

This is an additional barrier to the inclusion of such topics in the teaching.

Problems related to the students’ lack of experience can be solved by using appropriate

teaching methods to deliver them. Here, we propose the inquiry-based learning approach for

introduction of basic phenomena relevant to each contemporary topic. In this part, the topic

does not need to be studied, but experiences are provided on which discussions can be

subsequently based. For example, one of the most important properties of liquid crystals is their

optical anisotropy. However, to get an idea of optical anisotropy, it is much easier to study its

effects with transparent adhesive tapes [19, 18]. This experience will be reflected later when

discussing the effects of liquid crystalline ordering on cell/display transparency.

The important task, then, where a researcher and an educator work together, is to devise

relatively simple experiments that make it possible to investigate properties or phenomena

individually and to gain initial experience. The educator judges the usefulness of experiments

because he is also a novice on the subject; the researcher, as an expert, decides whether the

illustration or analogy that conveys the experience is correct and not too superficial, and

whether it is relevant to subsequent teaching.

If you want to affect the students' knowledge, the best concept to use is "Hands on/Minds

on". Many lectures rely on narration, but students who just listen usually get an impression of

something interesting but are unlikely to be able to repeat the content later. Therefore, a set of

accessible experiments that explore the contemporary topic in more detail must be designed by

an educator who is supervised by an experienced researcher. These two people discuss the

adaptations, the simplification, the narrative, the students' work, i.e., the observations and

measurements, the conclusions they are expected to draw, altogether in terms of the learning

objectives. At this stage, the learning objectives are questioned, theoretically so to speak, as no

students are involved yet.

Next comes a detailed elaboration of the content of the units/modules. This includes all

information given to students, written materials such as the contents of a textbook, detailed

instructions for experiments, worksheets, discussion tasks, etc. This is more the responsibility

of an educator who is "supervised" by a researcher. The educator knows how to communicate

to students according to their level of prior knowledge and scientific vocabulary related to the

chosen topic, what instructions students need to receive in order to conduct experiments, how

they should be guided to draw the correct conclusions and how they need to be assisted in

reporting them, etc.

Finally, the researcher and the educator must decide together and prepare materials for

teacher training. Any teacher who decides to introduce the topic in his classroom needs a good

support. This support consists of theoretical lectures, an experimental laboratory at a more

sophisticated level than student experiments, method training that includes an appropriate

sequence for introducing the new knowledge, adapted explanations regarding students' prior

knowledge, demonstration experiments, student-performed experiments, and a thorough

Chapter 11 | 201

discussion of any written instructions for students. In many cases, teachers need to be provided

with at least some experimental equipment for both demonstration experiments and student

experiments. It is best if they use the same experiments during the training and take them back

to school at the end of the training. In addition, teachers need to establish a close relationship

with educators and researchers so that they can get support when problems arise.

In summary, three types of experts need to work closely together in developing a

contemporary science unit/module: the researcher who is an expert on the topic, the educator,

and the teacher. This combination of collaborators is difficult to achieve because these three

professional groups work at different institutions and their areas of work rarely overlap. Such

collaboration sometimes takes place during teachers’ graduate studies at institutions that

combine training of pre-service teachers with training of professionals. I believe that the

importance of such collaboration is the main reason why examples of introducing

contemporary science into science teaching are so rare.

3.5. Evaluation

Finally, the idea of introducing the class to contemporary science might be noble, the choice of

topic wise, the module thought through and developed in the smallest detail, but it still does

not lead to the intended goals. Students listen, play with the experiments, are satisfied with the

topic, but when they later share what they have learned, we find that the concepts are not clear

and understanding has not been achieved. Therefore, evaluation of the module/unit is crucial.

More so, evaluation must take into account all stages of development. Since the development

process is very complex, the methodology of educational design research [34], is also

recommended during the process. Finally, implementation of the module requires a review in

terms of fundamentals, time requirements, availability of experimental equipment, actual prior

knowledge of students, consistency of student observations and measurements, and the like.

This part of the evaluation is discussed with the teachers in advance when they are dealing with

the new topic and later when they pilot the unit. In addition, the teaching objectives should be

reviewed with the knowledge test. In addition to the short knowledge test beforehand, we

suggest two types of tests during the development process. A short test follows each unit of the

module to check whether certain objectives of the unit have been achieved. Another test should

be integrated into the regular knowledge test after a few weeks. The regular test provides

external motivation for students to check their knowledge of the brand-new topic. This second

test shows whether the learning objectives have been achieved and whether the students have

actually acquired new knowledge. It is administered shortly after completion of the module. A

long-term test could also be added to measure how much students remembered.

There remains the question of the cognitive level of the questions. As a researcher in liquid

crystal theory, I am willing to admit that it took me years to understand some of the problems

that allowed me to propose a theory for polar smectics [35]. This simply means that cognitively

demanding tasks cannot be expected to be accessible to students after a few hours of a module

on a completely unfamiliar topic. The main goal is for them to become familiar with the

phenomena, to remember a little more about the content than the title or the name of the

material/phenomenon. Consequently, the tests should remain at a less demanding cognitive

level. The main aim is for students to become aware of the new topic and for the whole module

to increase motivation for science, to relate to current research and to leave the impression that

it is accessible to everyone, not just the most able students. However, more cognitively difficult

concepts can always be debated with highly motivated and/or able students. Since such debate

is easily beyond the knowledge of the teacher, an established collaboration between researcher,

educator, and teacher helps with more challenging discussions. It is important to remember that

202 | Čepič M.

in almost every class there are one or two students who are more gifted than their physics

teacher, so questions from an inquiry-oriented student can easily become very challenging.

Let us briefly review the steps required to introduce a contemporary physics topic, which

are hidden behind the symbols in Fig. 1. The list is long and includes the following steps in a

quasi-temporary sequence

- Select the topic;

- Determine the level of students for whom the topic will be taught;

- Define the learning objectives;

- Determine the prior knowledge required;

- Investigate the curriculum in terms of student knowledge;

- Investigate the possible curriculum objectives to be achieved by the new topic;

- Determine the appropriate place in the curriculum for the topic;

- Decide on the teaching methods;

- Design experiments to gain experience;

- Design the teaching module (content, timing, experimental equipment, etc.);

- Prepare the accompanying materials for the students;

- Test and evaluate the module;

- Design the training and materials for the teachers, which include more

challenging experiments and lectures;

- Train the teachers;

- Provide the experiments for teachers to use in the classroom.

- Provide ongoing support to teachers from researchers and educators for

implementation, student questions, etc.

Although the list is long, it cannot simply be used as a guide and one line at a time checked

off as done. The path to developing a new module on contemporary physics topic is much more

curious, as I will show with a historical account of developing the module on liquid crystals.

4. Example of liquid crystals

My first experience of introducing a contemporary topic into the physics classroom was more

than two decades ago. During a Leonardo da Vinci project SUPERComet, we developed a

teaching module on superconductivity. The module was presented to teachers, but

unfortunately, they did not implement it in class. The training was quite short and the teachers

were encountering superconductivity for the first time. The subject was also extracurricular.

The reasons for this failure were not thoroughly investigated at the time, but today the problem

is understood better. However, in the follow-up projects SUPERComet2 and MOSEM, where

an experimental kit was developed [36, 37], superconductivity found its way into some schools

[38]. I have also been personally involved in developing modules on two soft matter examples:

Liquid Crystals and Hydrogels. As far as liquid crystals are concerned, preliminary research

has shown that the majority of students heard about them in their first year at university, i.e.,

shortly after leaving school, but beyond that, only a very small percentage of students had some

knowledge [15]. For hydrogels, this percentage was even lower. However, students also said

that they would like to know more about these topics because they encounter them frequently

in everyday life [14], which confirms the importance of context in motivating learning.

The motivation for introducing liquid crystals into the classroom was triggered by very

specific personal circumstances. I am a physics teacher by training with a few years of

experience serving in a high school. Since life works in mysterious ways, I got an opportunity

to work as a theoretical physicist in soft matter physics at the Jožef Stefan Institute. My PhD

training and later research work focused on theoretical modelling of polar smectic liquid

Chapter 11 | 203

crystals, which I still work on occasionally. After completing my PhD studies, I obtained a

position as a teaching assistant at the University of Ljubljana, Faculty of Education, an

institution that trains teachers of science subjects, mathematics, computer science, technology

and home economics, as well as fine arts, preschool and elementary school teachers, and social

and special pedagogy. The reader can imagine how many specialists from very different fields

work together in my institution. However, the focus of my work there was on the content

knowledge background of future physics teachers. After a few years, I started to work also on

the methodology of physics teaching, and later I took over lectures on the methodology of

physics teaching in addition to the introductory physics course and the physics lectures for

prospective physics teachers. So, I became a theoretical physicist and an educator all in one

person.

To return to motivation: theoretical physicists are often worlds apart from experimental

physicists. There is a hidden quarrel between the two of them, which can be summed up in a

joke. A theorist is a person who no one believes but himself. An experimentalist is a person

who everyone believes except himself. I have been fortunate to bridge this gap, having

established a very productive working relationship with experimentalists. This allowed me to

see and play with liquid crystals directly, observe changes in phase transitions, and also

partially understand the second part of the joke. Experimentalists have to make a lot of

assumptions to get data. However, this collaboration opened the door for me to the colorful

world of liquid crystals, their textures, and experimental observations. I was eager to share this

experience with my students. However, I found that my colleagues working on liquid crystals

at my institution were not interested. They strongly believed that this was too difficult for our

students. As a notorious optimist, I turned to my younger colleagues, who were still naturally

curious and wanted to learn new things, and we started to develop the module together.

The first attempts were fun, converting experiments from professional research labs into

hands-on experiments to explore what can be observed, how to adapt those experiments to

make them simple and repeatable, and so on, and how to explain the observation to newcomers

to the field. Fortunately, novice roles were happily played by my younger co-workers. Many

of these experiments were never included in the short module we developed, but detailed

instructions for many of them can be found in a book with the title ‘Liquid Crystals through

Experiments’[18] and many experiments are suitable for hands-on work by students in optics

and soft matter in general.

Next, we investigated prior knowledge and motivation of first-year students at the

University of Ljubljana [15] to engage with the topic. The students from very different courses

had something in common: most of them had heard about liquid crystals, but that was all. It

was obvious that no prior knowledge on the subject could be expected.

Based on these findings, we developed a module on liquid crystals for prospective

elementary school teachers. In its first year, this program taught the subject called ‘science’

consisting of three rather limited modules, biology, chemistry and physics, 60 hours of 45

minutes per subject. The hours included lectures, practical work and field work. The students

who participated in the program were very diverse and many of them had some aversion to

science. Their learning success in high school was also generally average. Therefore, this group

was considered a model group for high school students.

The module consisted of a 90-minute lecture on the properties of liquid crystals and their

use in liquid crystal displays, a 90-minute chemistry lab in which students synthesized MBBA,

a short name for N-(4-metoxibenzylidylene)-4-butylanylene, and then investigated its

properties in the 90-minute physics lab (Table 1).

Students' knowledge was tested in advance, before the lecture, immediately after the

physics lab, and finally as part of the regular exam 6 weeks later. Only the basic knowledge

that could be acquired in the lectures and laboratories was evaluated. The evaluation, which

204 | Čepič M.

included 85 students who took the pretest, the test immediately after the lectures and lab, and

the test 6 weeks later, clearly showed (Fig. 2) that even less motivated students picked up some

information, while the most motivated gained an overview of liquid crystals and their use in a

liquid crystal display.

Table 1. Contents of the module on liquid crystals. The left column cites the

topics from the lecture. The right column describes the contents of the labs.

Lecture Physics laboratory

Liquid crystalline phase, an

additional phase between the solid

and the liquid phase

Phases of a liquid crystal MBBA

synthesized in the chemistry lab:

solid, liquid crystalline, isotropic.

Students measured the transition

temperatures.

Properties of molecules forming

liquid crystals

Ordering of molecules and the

order parameter

Transmission of light through

polarizers

Students played with polarizers

and determined the transmission

direction using the Brewster

angle and the polarizer with a

known transmission direction.

Anisotropy

Structure of an LCD Assembling a liquid crystal cell

and its observation under a

microscope on heating

Properties of polarizers

Ordering and structure of liquid

crystals in an LCD

Transmission of light through a

wedge cell filled with a liquid

crystal and determination of the

polarization of two beams.

Effect of an electric field

Finally, encouraged by the success of the implementation, we tried to carry out in-service

teacher training. Slovenia has a good in-service training program for practicing teachers, which

is financially supported by the Ministry of Education. The Ministry usually covers half to three

quarters of the program fee, which is required to cover the cost of lecturers and materials.

Prospective training providers must submit an application each year describing the content of

the requested program, objectives, benefits to participants, list of lecturers and detailed costs

of the program. However, the program that proposed to introduce liquid crystals into education

was considered irrelevant because liquid crystals are not part of the curriculum and therefore

do not receive support. Consequently, the fee was high, principals did not allow teachers to

sign up for an expensive training program, and the training was not given. In my opinion, we

were dealing with the usual problem of premature ideas that are rarely supported institutionally.

Chapter 11 | 205

Figure 2. Distribution of students' success on the pretest (left columns in the

set), immediately after lectures and exercises (middle columns), and six weeks

later (right columns).

Fortunately, in 2011, the University of Maribor in Slovenia organized the European

Conference on Liquid Crystals and decided to have a day at the conference that was more

teaching oriented and open to teachers. This special day started with a plenary lecture on liquid

crystals in introductory courses by the well-known expert in the field, who has also developed

many experiments for teaching, Pawel Pieranski [39], continued with liquid crystals in nature,

focusing on spider webs, composed of polymerized ordered liquid crystals, followed by

lectures and workshops in the local language for teachers, and ended with lectures for all

conference participants interested in teaching about liquid crystals at a university introductory

level or higher, and teachers. More than half of the conference participants focused on

fundamental research attended the evening lectures on teaching liquid crystals. About 50

teachers participated in this event and almost half of them tested at least one or two experiments

during their physics lectures afterwards. Experts from both institutions, the University of

Maribor and the University of Ljubljana, directly supported the teachers in discussing liquid

crystals in the classroom and provided them with materials/equipment for the experiments if

needed. Later, most of them reported that training which included scientific background,

teaching methodology and personal experience gained through experimental work was crucial

for their ability to convey the topic to the students.

We have repeated the workshop for teachers in its shorter form several times at local and

international events and have established a collaboration with a Polish teacher and two

Slovenian teachers. The unit was adapted to secondary level and the results were very similar

to those of prospective elementary school teachers [40].

Currently we are working on hydrogels and the preliminary results show that students are

not familiar with the subject and are excited when they learn about and play with these special

materials. Several informal training sessions have been conducted nationally and

internationally through workshops and in-service trainings, pre-service teachers have tested the

activities, but we are currently working on preparing the materials, so hydrogels are still

considered a work in progress.

0

5

10

15

20

25

30

35

40

5 15 25 35 45 55 65 75 85 95

Per

cen

tage

of

stu

den

ts

Percentage of achieved points

206 | Čepič M.

5. Conclusions

Contemporary physics topics are often considered too difficult to be introduced to regular

physics classes. Even the inclusion of contemporary physics in introductory physics courses is

often met with skepticism by instructors. To overcome this hesitation, collaboration is needed

between a basic researcher, an expert in physics education, and a teacher from the field. More

representatives of these profiles are, of course, welcome in this group. Such a group seems

difficult to organize, and we believe that the lack of such collaboration is the main obstacle

explaining why contemporary physics is rarely introduced into the classroom. The unpublished

meta-study covering ten years (from 2007 to 2017) of science education journals, did not

unearth any examples, other than ours, that could be categorized as developing and testing a

module on a contemporary topic. Lecturers who publish in physics education journals usually

discuss new experiments or adapted explanations of various concepts, including current ones.

In most cases, they do not address developing tested materials in their proposals. Although

several projects funded by European funds focus on outreach, the calls for proposals that focus

on education usually concern only the exchange of good practices, but rarely educational

research. Researchers seeking to develop such topics are thus more or less left to “ethical fuel”.

However, introducing contemporary physics topics into physics education is important.

The most important thing is the bridge that is built between active research and school physics.

It is believed that information about current research can increase students' motivation for

physics. However, since there are not many topics that are thoroughly developed as mentioned

earlier, it is difficult to study the effects of such topics on student motivation. However, when

looking for ideas for potential current topics, you should also look at the results of various

projects in the classroom. There are examples of very interesting modules (IRRESISTIBLE,

2016, for example). However, the impact of contemporary themes on student motivation still

needs to be explored.

Moreover, contemporary themes offer other perspectives. There are many studies on the

development of concepts such as energy, electricity or magnetism in young children. However,

contemporary topics are introduced at a higher level when there is already some level of

knowledge. Therefore, they are an ideal setting for studies of how near-adult learners

incorporate entirely new concepts into their knowledge network.

Finally, it is well known that higher ability students are able to quickly incorporate new

information into their existing knowledge network and use this new information to make

predictions almost instantly. Therefore, with contemporary subjects where learning occurs

through hands-on, inquiry-based experimental work, I can identify gifted students who, for

whatever reason, are not successful in regular schoolwork. Such students are usually weak in

reading, reasoning, and arithmetic, but they may be able to quickly draw conclusions from

practical work and related results. Since experimental work does not usually require extensive

reading but more work on the problem, they may overcome weakness in intellectual skills, i.e.,

reading, writing, and arithmetic. These skills are usually a prerequisite for regular school

success, but students with problematic intellectual or/and social backgrounds in school may

have problems attaining a satisfactory level of these skills. Furthermore, migrants who do not

speak the language of learning and doubly exceptional students with learning difficulties may

also have a chance to demonstrate their abilities [41].

In conclusion, topical issues in physics are an important ingredient in a regular school

process. They can be used as a common thread to make the connection between school and

advanced science, they can simply introduce interesting new facts or concepts to study later.

All this can increase motivation, but also shows non-physics-oriented students, who later also

become taxpayers, that physics and basic research are not a pointless waste of resources.

Chapter 11 | 207

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Chapter 12

Inquiry approaches in Physics Education

Eilish MCLOUGHLIN

School of Physical Sciences & CASTeL, Dublin City University, Dublin, Ireland

Dagmara SOKOLOWSKA M. Smoluchowski Institute of Physics, Jagiellonian University, Lojasiewicza 11,

30-348 Krakow, Poland

Abstract. Despite EU recommendations over a decade ago that inquiry-based learning is an

effective strategy for learning science, this method is still uncommon in European schools.

Teachers express doubts about the feasibility and effectiveness of inquiry-based learning and

a lack of understanding of how to use inquiry approaches in their classrooms. This chapter

presents an overview of inquiry-based learning and discusses how an inquiry approach can be

utilised to develop both student and teacher learning in physics. An inquiry approach that

involves teachers conducting their own practitioner inquiry in the context of inquiry-based

learning in physics is recommended.

1. Introduction

A human being enters the world without any prior knowledge or experience. From that day on,

we start to develop our own experiences of the world and everything in it. We continue to

explore and develop our understanding of the world around us because we are intrinsically

curious [1] and inquisitive. And although for some of us, inquisition may carry pejorative

connotations, this is what we do to explore and discover the world around us – having a strong

intrinsic motivation [2] we constantly make inquiries throughout our lifetimes. We would not

survive in this world if we lacked the ability to construct our learning based upon our

experiences [3]. Accumulation of experiences, together with constant reflection, creates the

process of learning, ultimately leading to the progress of self-development. The lack of

curiosity puts humanity at risk and threatens the development of our open-mindedness,

independence, self-esteem, and respect for others and overall learning. Despite recent

international focus on promoting the development of core competencies, it is still quite

common that the focus of 'learning content knowledge to pass tests' prevails [4] and other

learning is either treated as a secondary need or moved to specialised courses. Accumulating

knowledge without the use of reasoning - learning by heart - appears to originate from the

Middle Ages when education was almost inseparable from religion [5]. Nevertheless, it is still

one of the most common methods of self-learning.

The challenges regarding student engagement and participation in science disciplines are

a matter of international concern. The 2015 report to the European Commission of the expert

group on science education [6] highlighted that ‘Europe faces a shortfall in science-

knowledgeable people at all levels of society and the economy’ (p. 6). This challenge was raised

in a previous European Commission report in 2007 [7]. The OECD [8] reported that in OECD

countries only 6% of new entrants to university choose to study natural sciences. Accepting

that it’s not essential that all students study science disciplines at third level, it is critically

important for society that all students engage in science studies to develop science literacy (EU

Key Competences, [9]) and an inquisitive mindset that develops the skills necessary to make

informed decisions on societal challenges such as climate change, food, water, and energy

shortfalls. While all the science disciplines face challenges engaging students, it is particularly

210 | McLoughlin E., Sokolowska D.

pronounced in the discipline of physics for a multitude of reasons, such as shortages of qualified

teachers, perception of being difficult, and gender stereotyping.

The OECD Learning Compass 2030 sets out an aspirational vision for the future of

education (OECD, [10]):

How can we prepare students for jobs that have not yet been created, to tackle societal

challenges that we cannot yet imagine, and to use technologies that have not yet been

invented? How can we equip them to thrive in an interconnected world where they

need to understand and appreciate different perspectives and worldviews, interact

respectfully with others, and take responsible action toward sustainability and

collective well-being?

The Learning Compass offers a vision of the types of interdependent competencies that

students will need to thrive in 2030 and beyond including the development of knowledge,

skills, attitudes and values, transformative competencies and a cycle of anticipation, action, and

reflection. The insufficient focus on the assessment of such competencies is an issue of global

concern. Learning goals are misaligned with XXI-century society demands and patterns of

behaviour, thus creating a dissonance between school (education) and learning for life.

Students’ intrinsic motivation for learning has been shown to significantly decrease at

around 10 years of age [11] and evidenced as a so-called fourth-grade slump that occurs not

only in reading comprehension [12, 13] but also in motivation for STEM education [14]. This

phenomenon appears to be quite common and needs proper addressing. The sooner that the

role of intrinsic motivation is recognized at schools and the longer this innate ability to explore

the world is cherished, the better prepared individuals will be for lifelong learning [15].

Thus, the use of engaging and active methodologies is urgently needed to influence

learners' attitudes and motivation for STEM, while at the same developing their skills,

understanding and knowledge of STEM. This chapter presents an overview of inquiry-based

learning and discusses how an inquiry approach can be utilised to develop both student and

teacher learning in physics.

2. What is Inquiry?

Inquiry is a natural process of wondering about the world, experiencing it with all senses, and

building human being’s own attitude towards the miracle of its existence and the beauty of its

structure. Inquiry starts any adventure and keeps the pace of any learning endeavour without

giving up. Inquiry-based learning (IBL) can be described as a process of constructing

knowledge through direct experience in authentic circumstances by the involvement of one’s

creativity. This instance comprises the ideas and works of the precursors of two pedagogical

streams: constructivism and progressivism. Constructivists were confident that learning is an

act of students who construct knowledge out of their experiences. For them, repeated exercises

of building knowledge needed creativity, and at the same time, enhanced it. Progressivists

argued that doing is more valuable than the result of doing. For them, the process combining

thinking, trying out, reflecting, and redesign - applied to the unknown, triggered motivation

and engagement, and resulted in natural learning.

In the early 1960s, Schwab [16] and Bruner [17] independently brought the concept of

inquiry-based learning, comparing it to any other act of life that leads to achieving

understanding. Just before, Bruner [18] argued:

Chapter 12 | 211

What a scientist does at his desk or in his laboratory, what a literary critic does in

reading a poem, are of the same order as what anybody else does when he is engaged

in like activities – if he is to achieve understanding. The difference is in degree, not

in kind. The schoolboy learning physics is a physicist, and it is easier for him to learn

physics behaving like a physicist than doing something else. The “something else”

usually involves (…) classroom discussions and textbooks that talk about the

conclusions in a field of intellectual inquiry rather than centring upon the inquiry

itself. Approached this way, high school physics often looks very little like physics,

social studies are removed from the issues of life and society as usually discussed,

and school mathematics too often has lost contact with what is at the heart of the

subject, the idea of order. (p. 14)

Bruner focused his idea of IBL around a concrete image of “acting like a scientist.” He

also drew attention to the fact that the school curricula did not promote such a learning

approach. The idea of reflecting a scientist’s way of approaching science problems at school

has evolved over the past 40 years. Several educators and researchers in education elaborated

Bruner’s concept by setting up principles [19]; describing conditions for successful

implementation [20, 21] and designing materials for schools, particularly relating to science

subjects [20, 22]. A new evaluation format at school, i.e., ‘assessment for learning’ [23] was

proposed to encompass the complexity of the learning outcomes, and on this basis strategies

and tools for assessing IBL were designed (e.g., SAILS, [24]).

Following the idea of Bruner, the IBL method is usually associated with a research cycle.

To date, a few different versions of inquiry cycles have been proposed [19]. A cycle is complete

because it mimics the entire unit of the scientific process of research. However, it is not a rigid

structure and should be implemented according to the learning purpose and class

circumstances. The IBL method is not uniform, and the IBL process can take place on at least

three levels, distinguished as structured, guided, and open inquiry [21].

3. What is Inquiry at the student level?

IBL is more than another didactic method. It is a way of thinking, behaving, and enhancing

attitudes and beliefs. It promotes holistic development by activating all three domains of

learning: cognitive, psychomotor, and affective – in one inquiry process. Students constantly

create, reflect, and design, thus gaining new knowledge and developing the knowledge already

acquired (cognitive domain). They act primarily by engaging their hands – manipulating,

connecting objects, moving them, matching them, and rearranging; they walk and carefully

observe (psychomotor domain). Learning occurs upon personal and collective effort. Students

interact with each other since communication and cooperation in groups lie at the heart of the

IBL. Dynamics of this interaction with others and emotions involved in the pursuit of

understanding constitute reinforcement of the affective domain of learning. For these reasons,

IBL approaches have been promoted in many national curricula over the past decades [7, 25].

Sokołowska [21] presents an extended model for an IBL process consisting of nine phases

of inquiry cycle, as shown in Table 1.

212 | McLoughlin E., Sokolowska D.

Table 1. Sequence of steps in the Inquiry-Based Learning cyclic process [21].

1. Setting the scene and generating ideas on a specific topic or problem initiates the entire process.

A general theme is selected at this phase. Questions arise: Why does this happen? What is the trend?

What if? The problem may be launched by students’ interests or observation. If a teacher initiates the

topic - it may remain not verbalized until students reveal it during the brainstorming.

When Generating ideas students spontaneously bring their experiences, examples from life,

associations and refer to their current knowledge. The teachers’ role is to ensure that everybody has a

voice and guide the group with minimal intervention. In this phase, teachers learn what their students

already know about the chosen topic. Thanks to that, teachers can still adapt the subsequent steps of

the process - avoiding elements already known to learners or diversifying experiments due to different

levels of students.

2. Formulating an inquiry question asks one or a series of qualitative or quantitative questions related

to the selected topic to narrow it down. It should be formulated considering the feasibility of doing the

investigation to search for the answer, i.e., specific conditions created during classes, i.e., class time,

availability of materials, classroom conditions, and student safety.

3. The next step is putting forward hypotheses/predictions on the outcomes of the experiment.

Students come with their hypothesis, reasoning based on their knowledge and prior experiences. It

may occur just after formulating the inquiry question or after establishing an action plan, but always

before students proceed to the investigation.

4. Planning investigation is an organization of research. Students divide themselves into groups and

agree upon the roles they take in each group (conducting experiments, taking notes, ordering collected

data, etc.). In this phase, students decide on selecting materials, tools, and instruments necessary to

perform the experiment and write an action plan. This plan may not be too detailed since students are

very likely to employ a trial-and-error procedure and modify their plan when experimenting.

5. Carrying out the investigation starts after making a hypothesis and setting an inquiry plan. Students

perform one or more experiments, recording their observations and experimental data.

6. Data analysis takes place after completing all stages of the experiment. Students organize their notes

on experiments and then analyse experimental data and observations. They transfer the results into

visual representations.

7. Based on the obtained results, students draw conclusions. They try to answer the inquiry question by

verbalizing arguments that support their reasoning. Students return to the hypotheses put forward at

the beginning and confront them with the experiment's outcomes.

8. After completing their investigation, the groups share and compare their results. Students learn how

to present their studies clearly and consistently within a given time frame, and ask constructive

questions to other research groups.

9. Developing the problem is a possible (not always present) closing phase of the IBL cycle and, at the

same time, a stage potentially opening the next inquiry cycle (an extension of the same problem, an

investigation of a related issue, etc.)

While doing an inquiry, students are constantly challenged by the undiscovered. So, by

practicing inquiry, students are likely to develop high-order skills for adaptation to any new

situation, not only in a school or any other familiar circumstances, but also in completely

unknown environments. Such experiences can build their independence and self-confidence

and equip them with the necessary skills for and the attitude of lifelong learning. Inquiry never

leads to any win or failure. Whenever one phenomenon or instance is understood, a few new

challenging questions open, and the inquiry process continues in another cycle. Whenever

anything goes the way the inquirer cannot understand, the result is the same – a new question

arises, and the iteration of a trial-and-error procedure continues. Individuals regularly learning

by inquiry will constitute a society ready to act creatively, think and reflect logically, form

coherent arguments, and address global challenges.

Despite EU recommendations [7] over a decade ago that the IBL is an effective strategy

for learning science, this method is still uncommon in European schools. The hesitation of

Chapter 12 | 213

teachers’ widespread implementation of IBL is rooted in teachers’ doubts about its feasibility

and effectiveness. Science curricula overloaded with content knowledge leave little space for

a time-consuming method of doing science. Also, the final standardized exams, evaluating a

narrow part of learning, solely related to content knowledge [4] do not encourage changing the

classroom practice from knowledge transfer to constructing knowledge from experience. Such

a construction of standard curricula and assessment in science education is not only in

contradiction to the nature of science, which should be reflected in the way science is delivered

at school, but also appear to ignore many findings reporting substantial or at least minor

positive effects of IBL approaches on students’ attitudes toward science (e.g. [26–28]) and

acquisition of the content knowledge [29–32], including medium- or long-term retention of

knowledge [33, 34].

It is difficult for teachers to remove the systemic obstacles that impede widespread use of

IBL. However, given the enormous benefits of inquiry [19], some teachers would introduce the

method if they knew how to. Harlen [20] argues that moving from more traditional to inquiry-

based teaching is likely to involve a shift in several aspects of teachers’ pedagogy (Table 2).

Table 2. Harlen [20] (p. 22): “Moving from more traditional to Inquiry-Based

Learning is likely to involve a shift in which teachers…”

…do more of this …do less of this

Having students seated so that they can interact

with each other in groups.

Having students seated in rows working

individually.

Encouraging students to respect each other’s

views and feelings.

Allowing students to force their own ideas on

others, not listening to others.

Asking open questions and ones that invite

students to give their ideas.

Asking questions that call for nothing more than

a one-word or short, factual response.

Finding out and taking account of students’

prior experiences and ideas.

Ignoring students’ ideas in favour of ensuring

that they have the ‘right’ answer.

Helping students to develop and use inquiry

skills of planning investigations, collecting

evidence, analysing, and interpreting evidence

and reaching valid conclusions.

Giving students step-by-step instructions for

any practical activity or reading about

investigations that they could do for themselves.

Arranging for group and whole class discussion

of ideas and outcomes of investigations.

Allowing students to respond and report

individually only to the teacher.

Giving time for reflection and making reports in

various ways appropriate to the type of

investigation.

Giving students a set format in which to record

what they did, found and concluded.

Providing feedback on oral and written reports

that enables students to know how to improve

their work.

Giving grades or marks and allowing students

to judge themselves against each other in terms

of marks or scores.

Providing students with a clear picture of the

reason for particular tasks so that they can begin

to take responsibility for their work.

Presenting activities without a rationale so that

students encounter them as a set of unconnected

exercises to be completed.

214 | McLoughlin E., Sokolowska D.

…do more of this …do less of this

Using assessment formatively as an ongoing

part of teaching and ensuring student progress

in developing knowledge, understanding and

skills.

Using assessment only to test what has been

achieved at various times.

4. What is Inquiry at the teacher level?

The lack of qualified and experienced teachers of physics in second-level schools is an urgent

matter of international concern. It is widely recognised that the quality of an education system

is highly dependent on 1) getting the right people to become teachers, 2) developing them into

effective instructors, and 3) ensuring that the system can deliver the best possible instruction

for every child. As a result of significant funding for national and international projects over

the past two decades, many excellent IBL resources have been designed and thousands of

teachers have been introduced to IBL approaches. However, even with the success of these

initiatives, the widespread and effective implementation of IBL, its long-term use in the

classroom and the sustainability and scalability of the teacher education offered by such

programmes is still an issue of major concern. Additionally, issues of teachers’ self-confidence

in using an IBL approach exist and further obstacles such as curriculum demands, and the

pressure of national assessments are hindering the use of IBL in schools.

To support the sustainable use of IBL in physics classrooms and enhance students’ interest,

motivation, knowledge, and skills in physics we need to consider what are appropriate

strategies and models for teacher professional learning. In 1986, Thomas R. Guskey presented

a model of teacher change through staff development programs. He highlighted that the purpose

of professional development programmes was to bring about changes in teachers’ classroom

practices, beliefs and attitudes and the learning outcomes of students [35]. Teachers’ motivation

to engage in professional development and teachers’ process of change are two critical

considerations in programme design. This model proposes that teacher change is a process of

learning that is “developmental and primarily experientially based” for teachers [35], p. 7. This

idea helps us to understand why teachers retain or abandon particular teaching practices.

Guskey [35] suggests that change in teachers’ attitudes and beliefs depends on collecting

evidence of positive influences changes in classroom practice has on student learning.

So, what does effective professional learning look like? Enhanced teacher knowledge and

skills is more likely to occur in professional development programs that focus on “hands-on”

experiences for teachers that are integrated into daily school life [36]. Penuel et al., [37]

advocate that the focus of professional development should be on general and specific forms

of content to support teaching practice. Active learning that supports student inquiry and

coherence in aligning professional development activities with the learning goals of

participants are critical for effective professional learning [37]. The authors propose a

framework for professional learning where teachers and colleagues from the school or area

work alongside each other. Timperley et al. [38] also advocate teachers’ involvement in a

professional community of practice with some external expertise preferable and an active

school leadership presence. Timperley et al. [38] suggest integrating different aspects of theory

and practice and pedagogical content knowledge in professional learning opportunities.

Including a variety of activities that are aligned with the intended learning goals where

understandings can be discussed and negotiated is important in facilitating effective

professional learning [38]. Teacher collaboration in the form of professional learning

communities and communities of practice are reported to address physics teacher isolation [39]

Chapter 12 | 215

and raise teacher satisfaction through sharing of practices and participation in learning

activities with colleagues [40].

Practitioner inquiry (PI) has been promoted as a model that empowers teachers to make

evidence informed professional judgements and changes in classroom practice that influence

their student learning [41]. PI or teacher inquiry is a form of professional learning defined as

the systematic, intentional study of one’s own professional practice [42]. It involves teachers

identifying problems, constructing inquiry questions, gathering, and analysing data to make

evidence-based conclusions and recommendations with respect to their chosen problem. They

engage in systematic reflection and take action for change by asking questions or “inquiries”,

gathering data to explore their inquiry, analysing the data, making changes in practice based on

knowledge constructed, and sharing learning with others as part of professional learning

communities [43]. Ownership is maybe one of the most important considerations for a

successful PI - the teacher must be willing to change his/her classroom practice!

Adopting a PI approach where the teacher acts as a reflective practitioner to inform their

own practice has been shown to lead to more sustainable pedagogical impact. In 1999,

Cochran-Smith and Lytle [44], investigated three conceptions of teacher learning (knowledge-

for-practice, knowledge-in-practice, and knowledge-of-practice) and used them to guide their

theoretical perspective of an inquiry stance. This idea describes the positions that teachers take

towards knowledge and is separate from inquiry as a project that comes to the end of a cycle

as it highlights the building of knowledge over a professional lifespan.

Teachers and student teachers who take an inquiry stance work within inquiry

communities to generate local knowledge, envision and theorize their practice, and

interpret and interrogate the theory and research of others. [43]

Dana [45] interprets inquiry stance as a continuous cycle of questioning, systematically

studying and improving practice while becoming a natural part of every-day teaching. She

highlights the tensions that exist between inquiry stance (a way of being) and the inquiry

process to produce practitioner research. In her illustrations of inquiry as a stance, data

collection becomes part of teaching, so that inquirer and teacher roles are integrated [45]. A

review of over 200 teacher practitioner inquiries, [46] identified patterns in the types of PI

questions raised by teachers and organised them systematically into six “passions”:

1. Helping the individual child,

2. Desire to improve the curriculum,

3. Desire to improve or experiment,

4. Beliefs about management, teaching and learning,

5. The intersection of teachers’ personal and professional identities and

6. Focus on understanding the teaching and learning context

The authors suggest that framing inquiry questions on one of these six passions can help

practitioners to focus on specific questions and potential solutions. Like IBL, the process of PI

involves a step-by-step process of asking a question about one’s own practice, formulating an

inquiry plan (usually following discussion and deliberation with other practitioners),

implementing methods, collecting evidence from practice, analysing data to find insights, and

changing practice or refining the question based on findings [45, 47].

Dyson [48] reported some of the difficulties that teachers encounter in their engagement

in practitioner inquiry. Firstly, practitioners may often have different interpretations of the

concept of inquiry - as a systematic or an informal process. Secondly, teachers felt a tension

between school leadership supporting them in their professional growth and a focus on student

performance [48]. Cochran-Smith and Lytle [49] highlighted that inquiries solely focusing on

216 | McLoughlin E., Sokolowska D.

student learning during the teaching period may in fact reinforce the notion of inquiry as a

project rather than an inquiry stance. Dana and Yendol-Hoppey [43] also expressed concerns

arising from a focus on high stakes exams over student learning outcomes as a barrier to inquiry

stance. In addition, [48] outlined concerns over mandating reflection in the PI process that is

contradictory to encouraging and facilitating reflective practice in the everyday work of

teaching. Rutten [50] recommends that future inquiries include the term 'practitioner inquiry'

as a keyword when describing systematic, intentional studies of their own practice, to

consolidate research in this area.

5. Practitioner Inquiry in the context of Inquiry Based Learning

Practitioner Inquiry (PI) can tackle various topics and challenges that a teacher is faced with.

This kind of inquiry is not limited to an educational setting. It is often used as a kind of action

research in organizations where employees (= practitioners) want to improve their professional

practice. In the ERASMUS + Project Three Dimensions of Inquiry in Physics Education [51]

project, two dimensions of inquiry, IBL & PI, reinforce each other by conducting PI in the

context of IBL. Though it is not a necessity, the project partners experienced an added value of

bringing the two together. Making PI more specific in the context of IBL, provides teachers

with a direction and focus and, at the same time, amplifies their teaching methodology of IBL.

The 3DIPhE project concluded that if teachers want to learn something about their

teaching, it is important to make students’ learning visible. Collecting data or evidence of that

learning is crucial. Teachers must become comfortable with using data and evidence as tools

in routinely and critically reflecting their own practice (through the process of Practitioner

Inquiry). However, teachers often have a misunderstanding about what is meant by this.

Collecting data is an essential part of a teachers' role and involves more than the collation of

results at the end of the school year. A teacher should begin by articulating what 'it' means to

them, then use the tools to enable them to explore the issue. A variety of quantitative and

qualitative strategies for collecting data (evidence) should be used, e.g., student work, test

scores, notes, interviews, questionnaires focus groups, pictures, journals. Data must be used in

a learning-oriented manner to realize any valuable improvement in the learning, as an ongoing

process: collecting, analysing, new learnings, changes in practice. Practice cannot be

considered effective unless it is responsive to the participating students and promotes their

learning. The worth of the co-constructed criteria in practice, therefore, needs to be judged in

terms of how students are responding and learning [52]. Students’ involvement in inquiry

makes it immediate, relevant, differentiated, active, and engaging, therefore it makes sense to

share it with the students they teach [53]. An example of PI in the context of IBL from the

3DIPhE Project [54] is presented in Table 3.

Table 3. Example of Practitioner Inquiry in the context of Inquiry Based Learning [54]

Margaret conducted a PI into how her students perceive IBL in physics

Physics teacher Margaret was teaching a group of 4 boys and 14 girls with a humanistic profile. The

course was introductory physics at basic level, only 1 hour per week for one school year. As this was the first

time the students got introduced to IBL a guided level of inquiry was adopted. Margaret wanted to find out

how her students perceive the IBL method during this physics course. Therefore, she applied inquiry-based

learning in two topics: The Moon and centrifugal force.

The students were very active in class, engaged in experiments, conducted research, discussed their

results, and formulated their own conclusions. After completing the two topics Margaret administered a test

and immediately after the test (when students did not know the results yet) students were asked honestly to

fill in an anonymous survey to answer the question: ‘Did the method of IBL help you in taking the test?’ It

Chapter 12 | 217

seemed that all students disagreed. An exemplary response was that ‘the IBL method did not fully help me

prepare for the test, although I like that we could come to some conclusions in physics lessons, and they were

not boring.’ Discussing these results with her students, it turned out that they did not believe they would learn

something using IBL. When preparing for the test, students resorted to using traditional methods: reading the

book or even searching the internet. However, what they had studied was not asked at the test, because the test

examined inquiry skills like drawing conclusions, interpreting physics phenomena and laws. In fact, the

students perceived they were lost during the test. The method of learning and the test were different from what

they were used to. However, when Margaret corrected the test, the results showed that the average student

grade was 72% which was higher than the average score of 60% obtained in previous traditional tests based

on facts and administered after traditional lessons.

Margaret discussed these results with a group of colleagues from her Professional Learning Community

(PLC) formed in the 3DIPhE project. She felt that IBL hadn’t worked in her class. During the discussion, the

group managed to convince her to continue using IBL, since it had worked, but somehow the students did not

realize it. Indeed, students were very surprised with the test results, they somehow realized (and were

convinced) that they had learned more when developing inquiry skills, not only acquiring content knowledge

as usual. The IBL method was implemented a second time in a topic about radioactive decay. After completing

the topic, Margaret asked the students again to fill in the survey about their perceptions of IBL and what they

learned. The change was enormous. Many students now agreed when they were asked if IBL supported their

learning. Again, Margaret was very surprised, this time positively. When she discussed this change of

perception with her students, they admitted that they needed more time to get used to the method. Exemplary

responses included 'learning by playing, better acquisition of content knowledge, teaches how to "be up to",

remember the lessons, doing experiments by themselves, cooperation between teacher and students.' A few of

the students pointed out weaknesses, such as a slight chaos, there were a few students doing nothing, some

problems with remembering part of the content.

Margaret finally concluded that whenever you start with IBL, you should not give up after the first trial.

If students are not used to the method, they may be very distrustful and lacking confidence in what they

acquire. At first, the method looks like only playing and having fun, and in a traditional school system of

teaching with the most common method of learning facts and laws by heart, "playing" is considered a waste

of time. Such an opinion is embedded also in students' minds. Only being persistent in using IBL can convince

students that they learn more with IBL than in traditional format. The method itself is so engaging and

interesting that sooner or later the students realize that they learn a lot.

6. Conclusions and Implications

Physics is often presented in schools as a discipline focused solely on “solving problems”,

which is often unappealing to students and results in students exhibiting resistance to learning

physics. On the other hand, physical phenomena are common in everyday life and vitally

important across many industrial and economic sectors. Thus, understanding physics

phenomena is one of the most necessary endeavours for today’s learners and society.

Addressing this challenge requires teachers and curricula developers to design and adopt new

approaches for learning and teaching physics that embody the true nature of this discipline.

Over the past decade, physics education in schools, colleges, universities, and physics

curricula have adopted learning goals towards developing student’s scientific abilities, skills,

and competences alongside physics-specific knowledge. It is less common, however, for

physics programmes to explicitly consider knowledge and skills associated with the application

of physics in interdisciplinary contexts and in the wide variety of career settings in which many

graduates find themselves (Phys 21: Preparing Physics Students for 21st-Century Careers,

[55]). Crosscutting, interdisciplinary connections are becoming important features of the future

generation physics curriculum and defines how physics should be taught collaboratively with

other STEM courses [56]. Studies report that an integrated approach to STEM education can

be effective in supporting students to develop transversal competences such as problem-

solving, innovation and creativity, communication, critical thinking, meta-cognitive skills,

collaboration, self-regulation, and disciplinary competences [57].

218 | McLoughlin E., Sokolowska D.

Inquiry Based Learning (IBL) is an active learning method based on a research cycle

employed by real researchers in their laboratories. As argued in this chapter, IBL has been

shown not only to be successful in raising student motivation and interest in physics and other

STEM subjects, but also has proven to be effective in student acquisition and long-term

retention of learning. IBL is recognised as an effective method for developing research skills,

collaboration, critical thinking and sustaining natural human curiosity. Indeed, IBL is promoted

as an important strategy for the reinforcement of positive attitudes towards cooperation with

others and lifelong learning.

Practitioner inquiry (PI) involves teachers carrying out systematic, intentional studies of

their own practice. Like IBL, PI involves a step-by-step process of asking a question about one’s

own practice, formulating an inquiry plan (usually following discussion and deliberation with

other practitioners), implementing methods, collecting evidence from practice, analysing data to

find insights, and changing practice or refining the question based on findings. PI has been

promoted as a professional learning model that empowers teachers to make evidence-informed

judgements and changes in their professional practice that influence their student learning. [52]

advocates that a PI needs to be judged in terms of how students are responding and learning.

Additional benefits have been reported when teachers adopt an inquiry approach of

carrying out a PI in the context of IBL. The findings from the PI example presented in this

chapter reminds teachers that persistent use of IBL can serve to convince students that they

learn more with IBL than in traditional format. The teacher in this example concludes that "the

IBL method is engaging and interesting to students and sooner or later the students realize that

they learn a lot". Using this type of inquiry approach can support teachers to develop an inquiry

stance - a continuous cycle of questioning, systematically studying and improving practice

while becoming a natural part of everyday learning and teaching. Developing teachers'

confidence and competence in using inquiry approaches can be supported through their

participation in professional learning communities with small groups of teachers sharing and

reflecting on their own PIs.

Many models of inquiry exist, so it is important to adopt an approach that achieves learning

outcomes in terms of knowledge, skills, attitudes, and value for both teachers and students.

Carrying out a PI in the context of IBL in physics education can serve to create an inquiry

culture in the classroom, with both teachers and students conducting and reflecting on their

own inquiries. Student engagement in IBL activities can develop their conceptual

understanding, inquiry skills and sense of belonging in physics while teacher engagement in PI

can provide them with evidence and insights to inform the design of future learning experiences

tailored to their own student’s needs.

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Part VI

Learning in informal context and inclusion in Physics

Education

223

Chapter 13

An Overview of Informal Physics Education

Michael BENNETT and Noah FINKELSTEIN

University of Colorado, Boulder, Boulder, CO USA 80309

Dena IZADI

Michigan State University, East Lansing, MI USA 48823

Abstract: In this chapter, we provide a survey of informal physics education with an emphasis

on research and design. Because informal learning is so embedded in our daily experiences,

programs that intentionally focus on partnerships with their communities are better positioned

for greater impact. We discuss informal physics education and provide some examples of ways

in which this focus can bear fruit, drawing both on our experience as informal educators and

on research being done internationally. Finally, we provide some considerations for educators

and practitioners looking to build their own informal physics programs.

1. History & Conception of Informal Physics Education

Much of this handbook has been dedicated to the extent to which physics learning takes place

in formal environments such as classrooms and labs. However, the time we as learners spend

in these formal settings pales in comparison to the amount of time we spent simply living our

lives: reading, socializing, visiting public places, watching television or YouTube, surfing the

Internet, etc. Physics education, unsurprisingly, happens in these spaces too: popular science

books and magazines written by physicists; “science on tap” events at the local pub or

microbrewery; museum installations in malls; shows and channels like PBS’s NOVA or

YouTube’s Science Girl. Following the characterization of the United States’ National Research

Council, we label these forms of learning as informal [1].

Informal learning has a number of characteristics to distinguish it from formal-space

learning. Participants span diverse backgrounds and social statuses, and predominantly direct

their own discovery while participating. This participant-led, “free-choice” nature and the lack

of need to assess or evaluate participants allows informal education spaces to focus

predominantly on participant agency, excitement, and interest, emphasizing curiosity and

exploration over simply content mastery. As a result, informal education programs and efforts

are seen as key opportunities to increase participant engagement with both the topic of interest

and the field at large -- a large body of research has connected informal science, technology,

engineering and mathematics (STEM) learning with increased interest in science careers,

identity formation, and career intentions [1–4].

1.1. Formats

In the interests of providing a common framing of various types of informal learning, we list a

brief selection of descriptions of the formats used in informal physics education. While formats

may have differing affordances or limitations, the reader should detect a common trend of focus

on interest/exploration. Henceforth, we will refer to any entity with an expressed purpose of

conducting informal learning as a “program” (these are distinct from other learning

opportunities , e.g., a science podcast, which may be products that support informal learning

but are not in and of themselves organized entities). In our consideration of the variation among

224 | Bennett M., Finkelstein N., Izadi D.

such programs, we draw from a preliminary examination of the characteristics of different

informal physics programs [5].

1.2. Museums and Science Centers

Perhaps the most easily-recognized form of informal learning, science centers focus on

bringing in participants to explore installations, exhibits, etc. Typically, museums are sponsored

by the community in which they are built and maintained, both through ticketing income and

through grants. Museums may also conduct research on the scientific topics they house,

including in partnership with institutions of higher education. Science centers can serve as an

important community hub for scientific activity, as they (usually) persist for a long time.

1.3. Camps

Camp formats include day camps, where participants (most normally children) arrive at the

camp in the morning then leave by the end of the workday, as well as sleepway camps, where

participants stay at the camp over the course of multiple days. Camps can be facilitated by a

number of parties; science centers, for example, often run camps that include their own exhibits

and offerings in camp curricula. Non-profit and for-profit organizations both also sponsor

camps, and may partner with organizations for space utilization; for example, a STEM non-

profit may partner with a local college campus to house a week-long STEM camp. Camp

programs can serve the dual purposes of providing science education for children (for example

when school is on holiday) and providing childcare for parents, who may need to work during

the day.

1.4. Afterschool Programming

Typically implemented on the campus of a primary or secondary school, afterschool programs

can provide regular, ongoing opportunities for students to explore STEM, conduct experiments,

and connect with facilitators. They may be sponsored by the school itself, or may be facilitated

by an outside partner, such as a university or non-profit. Programs may continue for a number

of weeks, a full semester or school year, or longer, and may provide a novel experience each

week or build on a single curriculum. Additionally, because programs are often staffed by the

same individuals at least in the short term, child participants can develop relationships with

facilitators, who may themselves be practicing scientists, providing a cultural experience as

well as a scientific one.

1.5. Lectures and Demonstrations

Participants gather at a public forum as one or more lead facilitators, typically practicing

scientists, discuss a topic of scientific interest, often with a “real-world” spin. Often these

lectures are accompanied by exciting and potentially hands-on demonstrations of physical

principles. Lectures typically have low overhead cost in terms of resources and labor, and may

therefore be an appealing option for, e.g., physics departments wanting to engage with the

community without committing researchers to much ongoing engagement efforts.

1.6. Traveling Shows

One or a group of scientists may create sets of thematically-linked demonstrations, for example

on a particular subfield of physics. These demonstrations and any accompanying lectures can

be “exported” around the community or even farther afield as part of a traveling show that can

Chapter 13 | 225

be repeated over and over to different groups of participants. Traveling shows can be used to

great effect to raise awareness in the community of the types of science being undertaken at

the parent institution. Many other types of informal physics education formats exist as well.

1.7. Scale

Along with the wide variety of formats of informal physics education, efforts at informal

learning happen along a tremendous spectrum of scales. Even for a given particular format,

resources and institutional support may allow for implementation at a much larger scale; or,

program goals may intentionally narrow the focus of the program’s efforts, operating at a much

smaller scale toward a specific purpose. As with the various formats, we do not here claim that

“bigger is better”; rather, the right scale for a program is the scale that allows it to achieve its

goals.

1.8. Local/Neighborhood Programs

It can be argued that a majority of informal programming efforts are undertaken at the most

local level: neighborhood astronomy clubs, local science centers, university campus

planetariums, etc., are all examples of programs operating at the local level. Operating at this

scale can allow modestly-supported programs to still have sizeable impact with a small group

of participants. For example, the authors have been affiliated with local efforts for over a decade

through a highly-successful afterschool program, which will be discussed as a case study later

in the chapter. Briefly, this program has, through an intentional focus on building relationships

in the community, has enabled institutional-level partnerships between the authors’ institution

and local K-12 schools, empowering them to take greater ownership over the program

direction.

Some examples of local / neighborhood programs (pulled from authors’ affiliations and

collaborations): University of Colorado’s Fiske Planetarium [6]; The Santa Barbara Museum

of Natural History’s summer camps program [7]; University College Dublin’s Quavers to

Quadratics program [8]; JILA Physics Frontier Center’s Partnerships for Informal Science

Education in the Community program [9]

1.9. Statewide/Inter-Community Programs

Some programs may have goals that naturally lend themselves to operation on a larger scale.

For example, programs whose goals include wide dissemination of field-specific content may

quickly run up against a “saturation point” if they stick to their local community. Traveling

demo shows may similarly desire to expand the pool of potential “tour stops.” In these and

other cases, it may make sense for a program to broaden their scope outside their direct

neighborhood. In these cases, programs may trade intimacy with local partners for broader

reach with non-local partners. Other types of programs may have statewide or even national

reach as well -- families or even K-12 classrooms may make day trips to science centers hours

away, a local astronomy club may participate in a state meetup in a different city, etc.

Some examples of programs with large-scale reach (pulled from authors’ affiliations and

collaborations): Colorado State University’s Little Shop of Physics program [10]; Michigan

State University’s Science Theatre program [11]; The Facility for Rare Isotope Beams’s

Physics of Atomic Nuclei program [12]; Parque de la Cultura Agropecuaria PANACA in

Colombia [13].

226 | Bennett M., Finkelstein N., Izadi D.

1.10. Institutional and National Efforts

Occasionally, informal learning efforts are undertaken at a very large scale by non-profit

organizations, grant-funded institutions, or even private companies. These efforts are often

accompanied by large-scale research efforts to understand facets of informal learning and may

take place across many different instantiations and in many different contexts. At this level, it

is important that institutions have the resources to support the varying needs of the many

locations in which they operate. Another way programs operate at the largest levels is to

centralize most activity in a location or community but produce a smaller amount of content

for participants in other locales.

Some examples of programs with national/institutional reach (not all are affiliated with

authors): STEM Ecosystems [14]; Gulf of Maine Labventure [15]; The Exploratorium [16];

EUsea, a platform that addresses the design, organization and implementation of public

engagement activities across Europe [17]; CosmoCaixa in Barcelona [18]; Deutsches Museum

in Munich [19]; Science Gallery Network, with currently eight members across four continents:

Dublin, London, Melbourne, Bengaluru, Detroit, Rotterdam, Atlanta and Berlin [20]

2. Outcomes of Informal Learning

Above, we described some of the forms that informal physics education can take in

organization and implementation. Here, we give a brief overview of some of the intended and

observed impacts that informal education can have on its various stakeholders. Note that,

although this section is informed by research on informal STEM learning (and those citations

are included here), we leave until later an in-depth look at the landscape of research on informal

physics education programs at large.

2.1. Stakeholders In Informal Learning

Crucially, we approach the question of impact from the perspective that any effort at informal

learning has more stakeholders than simply the learners who form the “audience” for informal

programs. The traditional picture of physics “outreach” is that of a group of physicists creating

informal “content” that is then “delivered” to a mostly-passive “audience.” However, we argue

that this conception of informal learning undercuts the ability of these public engagement

efforts to positively impact the physicists facilitating the informal learning and even the

institutions that support both facilitators and participants. In the same way that teaching formal

college courses can improve an instructor’s pedagogical ability, participating in public

engagement can support and provide benefits to the instructors facilitating the informal

learning. We therefore argue that in any conception of informal learning, and particularly a

consideration of outcomes, it is beneficial to consider as stakeholders not only audience

members but facilitators (students, physicists) and institutions (departments, school partners,

communities), as all of these entities indeed have a stake in the success of the program.

2.2. Impact on Participants

The majority of research on informal STEM learning outcomes has focused on the “audience,”

those members of the public who participate in the program or opportunity without running it.

Nominally, these individuals are the “target,” the persons for whom the informal learning

opportunity is created, facilitated, improved, etc. We will argue in the sections below that this

perspective is somewhat incomplete, but of course the importance of providing benefits to

participants cannot be overstated.

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Most notably, informal education can generate interest in STEM topics or in science or

physics as a field, even as it provides an opportunity for content learning. Many museums, for

example, blend hands-on, exploratory engagement with sound science principles to engage

visitors, including children who may gain a lifelong interest in STEM or physics. Another

prime example of this blend of addressing both content and affect is the ubiquitous “star party”

hosted by local astronomy clubs. Programs and events such as these can generate a foundational

drive in participants to participate in physics, and this type of broad STEM interest is one of

the most common goals of programs.

However, benefits of informal learning to participants can move beyond simply generating

interest in further STEM engagement. Participants can gain other benefits, such as: increased

sense of agency and ownership over their scientific journey; improved development of a

scientific identity; improved writing or mechanistic reasoning skills; content knowledge gains;

and even positive shifts in their interest in pursuing a STEM career [21–25].1 This last example

is of particular importance. Many academic and even governmental institutions articulate a

strategic interest in increasing participation in the STEM workforce; because it has the potential

to increase STEM career interest, including for underrepresented groups, informal physics

education likely has an outsized role to play in accomplishing these goals.

Much work has been done on pathways to STEM may be facilitated, and one resounding

message throughout many of these studies is that out-of-school STEM experiences can have a

profound impact on students’ interest in a STEM career. And, surprisingly, STEM interest has

been demonstrated to more strongly predict collegiate STEM affiliation than STEM

achievement or even high school STEM participation [25–27].

In particular, the physics education community has expressed a strong interest in the

capacity of informal activity to help participants develop a STEM identity. Recent efforts have

demonstrated the relationship between development of physics identity and likelihood of

choosing a physics career [28], as well as the importance of creating informal physics education

initiatives that attend to students’ sense of interest in physics [29]. Most recently, efforts have

been undertaken to create frameworks for understanding how informal physics programs can

influence the development of participants’ physics identity [30].

2.3. Impact on Volunteers and Facilitators

As described above, it is most common to find programs focusing on benefits to audience

participants. However, we argue that informal education programs are also naturally equipped

to provide tremendous benefits to the personnel -- departmental students and faculty,

volunteers, paid workers, etc. -- who make up the facilitators of programming efforts. Attending

to the ways in which program design and implementation can benefit these stakeholders can

dramatically shift the manner and extent of program activity.

At the most basic level, participation in an informal education program can help facilitators

gain confidence in and mastery of their abilities in their field of interest. For example, physics

students who participate in informal physics programs have demonstrated improved content

knowledge. This is perhaps not entirely surprising given the role enacting pedagogy plays in

other pedagogical environments, such as teaching assistant positions. Teaching physics, even

at an informal level in an environment not dedicated to content learning, can improve

facilitators’ physical understanding.

Similarly, facilitator participants in informal programs have been demonstrated to exhibit

positive shifts in both their pedagogical abilities and in their science communication skills [31].

Students who volunteer in these programs can improve their ability to articulate scientific

concepts to laypeople, think more critically about their pedagogical techniques, and apply a

greater variety of techniques during instruction. Of course, formal education has a long history

228 | Bennett M., Finkelstein N., Izadi D.

of borrowing techniques from informal pedagogy, so these benefits to facilitators are not

terribly surprising either -- however, it is worth mentioning them explicitly, if only so that

program designers can think about ways to incorporate design that provides opportunities for

facilitators to reap these benefits.

2.4. Impact on Institutions and Cultures

Perhaps most interestingly, participation in informal education efforts has been demonstrated

to shift volunteers’ perceptions of the importance of public engagement itself and its role as

part of the scientific enterprise. Volunteers, especially those in academic institutional settings,

may come to see participation in informal education as a means of giving back to the

community, improving the lives of others, or simply as a benefit in and of itself, rather than as

a tool for resume building or similar. We mention this finding because, in addition to

individuals, we argue that entire communities and their respective cultures stand to benefit from

participating in informal education.

As an example, consider a university physics department that houses an ongoing informal

physics education program. Student volunteers may experience the shifts described above in

terms of their science communication and pedagogy skills, as well as in how they perceive

public engagement. As those volunteers participate in their department’s activity, they bring

those shifted beliefs and attitudes with them and may influence peers or other department

members. Over time, the culture of the department itself may shift to more strongly value

pedagogy or public engagement -- in fact, research has demonstrated exactly this effect in

departments with institutionally-supported programs.

Similarly, as members of a given community participate in informal physics education,

members of that community may come to, for example, see themselves as persons interested

in science and, potentially, in science careers. These aspects of identity, essentially built by the

participants themselves, may serve as powerful counter-narratives to cultural messages about

who is “allowed” to participate in physics, and can have an empowering effect on members of

communities and, potentially, shift the disposition of the community itself [32].

These impacts, while perhaps the farthest removed from the questions that typically

accompany program design, are crucial to consider and understand. Despite the importance of

formal education, informal education is still the number one way that members of the public at

large engage with the field of physics, and with actual physicists. Attending with care to the

impacts of informal education on its various stakeholders can allow us as physicists a stronger

means of shifting cultural perception about our work and our field, for both our own benefit

and that of the cultures in which we exist.

How do we measure and assess these varying impacts? In the following sections, we will

discuss one particular program that exemplifies the kinds of stakeholder-focused design

described above, as well as some of the methods used to investigate its activity and outcomes.

3. Examples of Informal Physics Education Efforts

So far, we have discussed why participants may choose to engage in informal physics

education, why facilitators may choose to design and implement specific types of programs,

and some of the benefits that informal physics education can have on multiple groups of

stakeholders. In order to illustrate these concepts, we briefly describe one model program with

which the authors are familiar. We also briefly discuss a larger-scale effort to characterize a

wide variety of programs, leading into a broader discussion of research on informal physics

education programs.

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Our first example is a University of Colorado Boulder-based program called the

Partnerships for Informal Science Education in the Community (PISEC) [33]. We showcase

PISEC not to prop it up above other informal physics education programs, but because the

program has been designed since its inception to embody a multi-directional benefit model

based on the principles outlined above. Additionally, PISEC is a useful example for the

purposes of illustrating how these benefits can manifest in intentionally-designed programs.

3.1. Description of PISEC

The Partnerships for Informal Science Education in the Community was created as a joint effort

between the JILA NSF Physics Frontier Center and University of Colorado Boulder’s (CU

Boulder) Physics Education Research Group. The program has historically taken the form of

an afterschool program wherein CU Boulder volunteers, typically undergraduate and graduate

physics students, travel to local partner schools to engage in exploratory physics-based

activities over the course of a semester. PISEC is based on the highly successful Fifth

Dimension model, which centralizes relational aspects of learning rather than simply focusing

on content knowledge and skill acquisition [34, 35]. In this model, program facilitators are

closer to peer mentors than instructors, and students are vested with leadership, agency, and

authority at the programmatic level.

In practice, this focus on student agency often means that students are the ones deciding

which activities to undertake, evaluating when activities have been completed successfully, and

setting large-scale goals for those activities. In PISEC, afterschool program curricula are

designed to present students with a variety of activities between which students can choose as

they progress through the semester, designing their own experiments to explore physics

concepts even without explicit framing of activity as “scientific.”

As a function of this design, PISEC students typically enjoy participation in the program

much more than they enjoy science class. Assessment on the program suggests that students

frame PISEC as highly distinct from their formal classroom spaces, leading to a different

conception of their activity and, most likely, different framing about the value of that activity

as well. Student participants, who are mostly between the ages of 10 and 14 or so, also tend to

engage in activities that they dislike in class, such as writing down their thoughts and ideas.

One of the key characteristics of PISEC design is the intentional blending of cultures and

contexts. Primary school participants do not actually know the program as “PISEC” because

the program, through partnership with schools at an institutional level, adapts to fit into existing

afterschool needs and district structures. The program has been known by students as “MESA,”

“STEM Explorers,” and other context-specific names. This “putting on” of students’ local

culture is intentional -- the goal is to ensure that PISEC explicitly does NOT feel like the

traditional “outreach” style of informal education, but as something that is being co-constructed

by students and facilitators as it happens. Similarly, at the end of each semester, PISEC students

attend a field trip to CU Boulder, where they tour scientific labs (including those labs in which

their mentors work) and engage in hands-on experiments while becoming comfortable in the

professional scientific environment. The hope is, again, that students and university mentors

will increasingly come to see themselves not as visitors to but as members of one another’s

“home” communities.

3.2. Focus on Relationships: Students and Mentors

PISEC’s focus on relationships and on community building is a central component of its design.

Because the program mentors attend the same PISEC site each week, they naturally build

relationships with the students they mentor. In many cases, students develop deep attachments

to their mentors and will, for example, inquire about their health when mentors miss a week of

230 | Bennett M., Finkelstein N., Izadi D.

the program. Students also do -- and are encouraged to -- join the program specifically to

socialize with their friends. In interviews, PISEC students who claim that they only join the

program because they enjoy socializing with friends have, nevertheless, also reported enjoying

and engaging with the program’s scientific content.

PISEC’s university mentors are also encouraged to build relationships with one another,

and the program provides opportunities for this social development as well. The schools with

which PISEC partners are far enough away from the university that the most efficient way to

travel to the sites is via carpool, giving mentors an opportunity both to socialize and to discuss

aspects of PISEC teaching and engage in peer mentoring. The program also hosts social events

throughout the semester, and maintains an online chat server for mentors to coordinate and

socialize with one another. At the start of the semester, PISEC facilitates a series of instructor

training modules to give mentors an opportunity to practice informal pedagogical techniques,

to help enculturate them into PISEC’s educational paradigm, and to give them a chance to form

initial bonds with the fellow mentors that will form their cohort for the semester.

3.3. The Sociocultural Perspective

Why does PISEC put such an emphasis on relationships and cultural aspects of learning? In

part, the emphasis is due to the program’s roots in the Fifth Dimension model,16 which itself

prioritizes social aspects of learning. But, more broadly, both the Fifth Dimension model and

PISEC itself are built from a sociocultural perspective of learning -- that is, the perspective the

actors learn about their world and their environment by interacting socially. This perspective

has roots in the learning theories of Vygotsky, Leontev, and Engestrom[36].

One of the benefits of this conception of learning is the emphasis on enculturation; because

learning is social, learners naturally cannot escape receiving messages about culture alongside

any messages about content or practice. In PISEC, this means that when students participate in

scientific activity alongside CU mentors, who are actual scientists, they are not only learning

things about the scientific world but also exploring what it means to be a scientist, as modeled

by their mentors. The ability to focus instructional time on enculturation is a tremendous

affordance of informal education, since time can be devoted to engaging in the work that

scientists actually do -- exploration, experimentation, hypothesizing, synthesis -- without

concern for test-taking, homework, and other artifacts of the formal space that do not closely

match actual scientific practice.

3.4. PISEC’s Impact on Stakeholders

To summarize: the PISEC model of informal education focuses heavily on elements of cultural

learning, affect, and student ownership. These are not the only important components of

informal education, and we again do not claim that they should necessarily be prioritized over

other goals.

3.5. Examples From the Landscape project

Over the last few years, a new research study has been developed that is focused on

characterizing the landscape of informal physics learning across the United States [37]. The

scope of this project is the wide variety of programs, events, and activities that are run and led

by the physics departments, physics faculty members, physics graduate and undergraduate

students, and department staff members. This research study also aims to connect to the

practitioners of these programs, as well as policy makers and the administratives to draw their

attention to where more support is needed. To supplement the in-depth description of PISEC

given above, we here present four quick profiles of programs studied during that investigation.

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These profiles are again not shared prescriptively, but rather as examples of the many ways

informal physics education programs embody the principles outlined above: for example, the

ways in which informal programs can implement multi-directional benefit models, treat

volunteers and participants as key stakeholders, focus content on affect in addition to content,

etc. To meet research privacy standards, all four programs use pseudonyms.

“Physics to Schools” is a physics school assembly program that visits different school

districts to present demo shows. The program introduces physics and science in general to

elementary school students. This program was initiated by an individual faculty member 20+

years ago in a hispanic serving institution. This program received an endowment money years

ago from the university and has been using the same funding source over the years to run. The

faculty and one staff from the physics department (co-leader) are in charge of building and

repairing the equipment and instruments for the demos. They also have different faculty

members from their institution giving speeches every time. The co-leaders are both in charge

of recruiting undergraduate students to help with the activities. This program provides training

for their attending volunteers, mostly about how to make social interactions with the audience

and do public speaking during the activities. Such training provides great support to the

volunteers and helps them gain confidence in their abilities to interact with the community and

mastery of their field. The co-leaders of this program are very much involved in the community,

as well. For example, their program is focused on attracting more women/girls, school districts

in underrepresented and minority geographical locations, and low-income families. They reach

the low-income schools first to prioritize them in their yearly schedule, as well. Such efforts in

reaching a broader and more diverse community has great cultural impacts and benefits for the

participants and community.

“Physics Camp” is a camp physics program led by a staff member who is the outreach

coordinator of their institution. He organizes the program and also works on other public

engagement projects. There are also a number of business support staff from the institution

who help with program logistics. Approximately 15 volunteers (including graduate students,

post-docs, faculty members) help with developing the physics content of the activities. This

program typically runs for a week during each summer for students and for another week for

teachers.

“Student Club” is a student organization run by two undergraduate student co-chairs.

When the club started over 10 years ago, public engagement was not part of the picture and

eventually the “outreach” came to the picture when the club requested funding from their

institution. They work mostly with local elementary schools, and their local planetarium. There

are a number of faculty advisors who occasionally help with the public engagement efforts and

oversee the program, but the two students mostly handle the organizational work and planning.

This program recruits 30–50 student volunteers around the year and has had positive impacts

on the institutional culture by promoting public engagement events across the department and

beyond.

“Astronomy Cafe” consists of monthly meetings at a local bar where physics and/or

astronomy public talks are given by members of the physics and astronomy department of a

large university. This program has consistent attendance of around 100 people each month. An

individual faculty member initiated the idea of the program, runs all the logistics of the program

and has been the program leader since the beginning. This program solely depends on the

donations made by its audience members and does not receive any financial support from its

institution. This program has been running for more than 6 years now. While some graduate

students and postdocs occasionally help with the question and answer and come up with other

logistics (such as live streaming the event), the faculty is doing the heavy lifting and is

responsible for all the other aspects (e.g. advertisement, reaching to the community, support

232 | Bennett M., Finkelstein N., Izadi D.

the volunteers and facilitators, recruitment and retention, collecting donations, inviting

speakers).

4. Research on Informal STEM programs

Science education researchers have developed over the course of the field’s history a vast

literature on understanding and characterizing informal science learning contexts and practices.

Audiences of informal science environments are diverse and include all ages, backgrounds,

abilities and cultures.

As mentioned before, our understanding and evaluations of how people learn physics

mostly comes from the research conducted in formal settings; however the majority of our

learning time is spent outside the classroom setting. Formal and informal learning

environments overlap, complement and influence each other but are also different in some

ways. For example, informal learning spaces are normally low stakes and no gradings are

involved, or the activities have high levels of agency for learners, as described above. Because

of the differences and overlaps, more fundamental research is needed in informal settings to

match the good work already done in formal environments.

Physicists and physics students have a long history of creating informal physics spaces

[38], and yet these spaces are not well studied from a discipline-based perspective. There have

been some efforts over the years to conduct precise documentation of the broader informal

science education activities, in the same way that we study and value discipline-based research

in formal spaces. The Mapping Out-of-School-Time Science (MOST) report to the Noyce

Foundation characterizes out-of-school STEM programs for middle- and high school-aged

youth [39]. The data for this report was collected using snowball sampling to increase the

number of subjects. In their data collection, they asked each participant to recommend

additional participants, resulting in several hundred usable survey responses. Important themes

emerging from the collected information included program structure, youth audience, program

content, program desired outcomes, and cultural relevance. The Center for Informal Learning

and Schools (CILS) did a study in 2005 to better understand how informal science institutions

can effectively inspire and reinforce science learning for school children [40]. In 2016, National

Academies published a report on chemistry informal science education efforts [41]. In the

European context, SySTEM 2020 is a project funded by the Horizon 2020 European Research

Council to document science public engagement initiatives [42–44].

In physics, a short survey was conducted by the American Physical Society’s (APS) Forum

on Outreach and Engaging the Public (FOEP) in 2015 [45]. This survey was sent to the listserv

of the 1525 FOEP members database as well as advertised in the FOEP newsletter. The survey

report provided a snapshot of some of the efforts of APS physicists, but it did not provide the

key features that an informal physics program needs to be able to perform and function.

Much of the work done in discipline-based informal physics education research has

focused on individual programs, such as the authors’ affiliated PISEC program or other singular

efforts at universities. In many cases, research efforts are undertaken in an ad-hoc manner,

rather than built directly into the core design of the program. Because the PISEC program

began as a collaboration between a laboratory and the University of Colorado Boulder’s

Physics Education Research Group, research and assessment has been an intentional

component of program activity since 2008. Research in PISEC has historically used the

importance of its various stakeholders as a beacon for deciding how to conduct research; early

efforts showed benefits to primary-school students’ and volunteers’ content knowledge. PISEC

research has also focused on improvement to volunteers’ science communication skills and

Chapter 13 | 233

attitudes and beliefs about public engagement, as well as learners’ objectives and goals

engaging in informal physics education and mechanistic reasoning.

Again, we highlight our work with PISEC not to vaunt the accomplishments of our

program, but because we want to emphasize the power of an informal physics education model

that combines research and practice from the very beginning. Part of the reason the authors

have been able to engage in this high level of PISEC-oriented research is because key

stakeholders, like the school districts in which PISEC operates, have had joint ownership over

the program and know that the program’s success through research translates to its success in

implementation. By applying a design-based implementation research (DBIR) framework to

research efforts, research findings can be utilized to improve program aspects, such as

volunteer preparation or curriculum design for students.

One particular example of this feedback loop for PISEC is the spat of recent studies on

volunteer pedagogy. Physics pedagogy in informal spaces has not been studied in-depth, but

since 2016 the authors have been engaging in a systematic effort to characterize and define the

techniques volunteer instructors use in environments like PISEC, resulting in a model of

pedagogical modes somewhat analogous to the “epistemic frames” model commonly referred

to in studies of formal classroom spaces. This model has been put to use in improving PISEC

training for volunteers -- training in the modes as pedagogical tools has helped volunteers

engage more freely and fluidly in the PISEC environment, rather than return to the familiar

techniques they are used to in classrooms, but which are likely less effective in an informal

environment.

The most recent large-scale, systematic research study in physics is the landscape project

mentioned in Section III [5, 46–50]. The goal of that study is two-fold: to understand the size

and scope of the existing informal physics programs and how they function, and to map the

existing landscape of public engagement and outreach activities that physicists and physics

students lead, run or facilitate. This study looks at the variety of existing theory frameworks to

identify and understand the key components of individual programs that influence their

functionality. The landscape project’s authors have chosen to focus on the public engagement

types from Aurbach’s framework that are relevant to educational settings, mainly Alternative/

Lifelong/ Informal Learning, Community-Engaged/Service Learning, and P-14 Education and

Educational Outreach [51–52].

In the landscape project, the authors developed a multi-step and iterative process of

obtaining complementary types of data about existing informal physics activities from the

program leaders: personal and local contacts and word of mouth at conferences, internet

research, survey design and validation, and interview development and collection. The

landscape study is limiting the search to “in-person” activities, such as public talk and lectures,

after-school programs, open houses, demonstration presentations, summer camps, science

festivals and planetarium shows. Media-related works, websites, books published, television-

related activity, movies, or games are not included in the current study.

The landscape study turns to the business literature as an appropriate lens for

understanding the nature of some informal physics programs performances. A variety of

Organizational Theory frameworks (including Nonprofit organizations) exist in the literature

and each of them utilizes their own metrics to evaluate the performance and functionality of

different organizations. This study contextualized the overarching themes of organizational

frameworks into six main themes/building blocks: Personnel are the people involved in the

functionality of the program, Program is the content, format, goals and logistics of the events

and activities, Resources are the physical and financial aspects of the program, Institution is

the larger organization that the program is affiliated with, Audience is the group of participants

that are engaging with the program content, and Assessment is the set of tools by which a

234 | Bennett M., Finkelstein N., Izadi D.

program evaluates its outcomes. These six themes are used to understand and assess each

program’s performance.

The landscape project has tried to be inclusive of all programs and activities that fit in its

scope, but there have been some limitations. First, the research study is not fully conducted and

has been only able to collect full or partial data (survey data, or survey and interview both) for

72 contacts from 63 programs in twelve different states across the nation. Second, not all the

data has been fully analyzed to represent all the collected data.

Among the programs that the landscape study has looked at so far [45], the main positions

of the Personnel in their home institutions vary from Tenure Track faculty to non-tenure faculty

members, staff, graduate and undergraduate students, with the staff being the highest

representative of the program leaders and the student volunteers being the majority of the

involved personnel in counts. The programs have been mostly student groups or organizations.

The rest of the programs have been projects of individual faculty members, and/or

department/college programs led by faculty and staff, and/or museums and planetarium efforts.

The Program category characterizes the main events and activities that take place when

the personnel are interacting with the audience around some type of physics content. The

physics and astronomy content covered in programs’ activities and events is diverse and

includes a variety of physics and astronomy subtopics (i.e. Classical Mechanics, Electricity and

Magnetism, General Astronomy, Stars, Planets and Telescopes and more)

The format and frequency of the programs were also classified into the following four

categories of responses from the program leaders:

1. Presentation format: Programs that intend to communicate information about one

or multiple particular physics topics in an oral format. These include public

lectures, observation/planetarium and demo shows.

2. Afterschool/Club format: such groups of programs provide activities and illustrate

physics concepts for K-12 students outside of school-time and are held at various

places including schools, community centers and/or university campus locations.

3. Festival format: Science or physics festivals, open houses, or “physics days” that

typically last a full day or several days.

4. Camp format: Programs that provide educational and recreational activities for

specific age groups during a limited period.

5. Connections to Practice

With a perspective on informal physics education that prioritizes benefit to multiple

stakeholders and focuses on the impacts of culture and community, what kind of programs and

efforts is it possible to create? And, what ways of assessing and evaluating these programming

efforts can be employed based on the foundations of research described above? Here we

synthesize the above sections and offer some principles of practice that can be used to

implement the broad ideas described in this chapter. We also use this opportunity to cast

forward about the future of informal physics education.

5.1. Informal Education Can Span Multiple Contexts -- And Those Contexts Should Be

Considered

As described above, we take the position that informal education is more nearly defined by the

parameters of design and activity -- the focus on agency and enjoyment, the importance of

learner agency, the ability to improve STEM participation outcomes -- than by the trappings of

format such as location or timing. Although likely not a tremendous surprise given the wide

Chapter 13 | 235

variety of successful programs, we do emphasize that this principle means that informal ed

efforts can thrive in a wide variety of contexts. Therefore, we strongly encourage those

interested in creating informal physics programs to think of ways that the program can be

designed beyond the traditional and familiar models of demo shows and public talks.

In particular, we encourage would-be program creators to consider reaching out to and

collaborating with members of the community contexts in which they want to work to

determine a set of common goals and ideas for format and implementation -- in the example of

PISEC, the program has been designed from the ground up with consideration for and direct

input from the local schools with which the program partners. While program designers may

be physics content experts, education experts, even highly skilled public engagement experts,

community members are the experts in the needs and desires of their communities -- programs

being implemented within a specific context, or “targeting” specific groups of people, are

therefore more likely to succeed if those community members are co-leaders in designing and

implementing the program.

As an example of an informal education effort that spans multiple contexts and involves

community members at the top level, we describe a PISEC effort to implement programming

with high school students.

In 2017, the PISEC director was approached by a local high school teacher familiar with

the program with the request to collaborate on an offering for that teacher’s 9th grade physics

students. The typical PISEC format of an afterschool program was not viable for these students,

so the teacher and the PISEC director worked together to design a series of project modules

that could be implemented during the standard school day while still meeting PISEC’s program

goals of giving students full control over their learning and enculturating them into the

scientific community. Rather than small activity prompts facilitated weekly over the semester,

students were given large-scale prompts that encouraged them to take on the role of principal

investigator, designing an experiment or engineering some implement to answer a certain

question or meet a need.

These projects spanned the entire semester and, crucially, were implemented both within

class time and outside of it, via teleconferencing software. PISEC mentors carpooled to high

school classes a few times during the semester to serve as “consultants” for students as they

planned, designed, and worked through their projects. Throughout the semester, students and

mentors also engaged occasionally in simultaneous teleconferencing in order to check in on the

students’ progress on their projects and present a chance for students to ask mentors for

guidance as well as ask them about their experiences as scientists. Students and mentors also

were provided with a shared online space where they could collaborate on written documents,

share files, etc. At the end of the semester, once student projects were completed, students

visited the University of Colorado in order to present their work in a poster symposium that

included students from other high schools as well as CU scientists, simulating presentation in

a conference environment.

One of the goals of this format, designed through collaboration between the program and

the high school partner, was to give high school students hands-on experience with the types

of skills -- planning, project design, experimentation, presentation and dissemination -- that

professional scientists use in their daily work in addition to their scientific skills. Formats like

this span the bridge between formal and informal spaces, drawing on techniques common to

both environs in order to provide students with something that is more than simply the sum of

their formal and informal experiences. Further, this format was created from the ground up to

meet the needs and interest of the high schoolers with which it was implemented; as a result,

response to the program has been very positive among those students, many of whom come

from underrepresented groups.

236 | Bennett M., Finkelstein N., Izadi D.

While we do not argue that there is NO difference between formal and informal education,

we bring up this example to demonstrate how attentiveness to context can help produce

memorable and meaningful experiences that can attend to the goals of both informal and formal

ed spaces.

5.2. Working Towards a Systemic Informal Physics Education Effort, and the Importance of

Research

Much of what we have discussed in this chapter hinges upon a model for informal physics

education that prioritizes partnership between programs and their communities. While we

believe that working from a mindset of partnership helps programs design meaningful content

for their audiences, we also argue that increased collaboration and partnership between

programs is useful and likely needed as informal physics education and, in particular, research

on informal physics education mature alongside their formal counterparts. As discussed above,

the landscape of informal physics education programs is not at present as well-described as

might be useful for the field. Part of the benefit of such research is that it lays the groundwork

for connecting programs and informal physics efforts that might otherwise be laboring

completely separately. Increased centralization and systemization of informal physics

education will lead to increased collaboration, more efficient development and implementation,

and, hopefully, improved outcomes for programs as well.

In many cases, those workers involved in informal physics education are not necessarily

physicists themselves, instead being trained in science education, science communication, or

simply interested individuals. Departmentally-focused public engagement activity is usually

relegated to one or a few professors or student groups as a “pet project” or as required efforts

supplementing more “important” grant activity (i.e., research). These individuals may be and

often are enthusiastic, creative, and driven, but may lack the discipline-based curriculum and

pedagogical expertise of those engaged fully in physics education research. Additionally,

without connection to the broader community of discipline-based practitioners, the risk of

duplicating efforts and redundancy is high.

Some institutional field-level support structures exist, such as the IOP and the APS in

Europe and the U.S. respectively, to provide would-be practitioners with basic physics

education resources. Communities such as the Center for Advancement of Informal STEM

Education (CAISE) also exist, populated largely by those with training in general science

education. What is missing is the confluence of these two traits: discipline-based informal

physics education resources provided at the institutional level. We argue that such an effort is

necessary for the future health of informal physics education activity and that informal physics

programs should look for ways to connect with and potentially partner with other programs in

their locale, even just at their own institution.

One such effort in the U.S. is the recent creation of the “Informal Physics Education

Research Network” (IPER) by a group of physics education researchers including the authors,

which at the time of writing provides a mailing list to connect interested parties across the globe

to one another and organizes meetups at conferences. IPER strives to create a foundation for

both practitioners and researchers in informal physics education to communicate, share ideas,

support one another, etc. Currently run on a volunteer basis, the network is in the process of

reorganizing itself as the Joint Network for Informal Physics Education and Research (JNIPER)

so as to provide a more institutionally-supported community for practitioners and researchers.

Chapter 13 | 237

6. Conclusions

When one considers the “core activities” of a physics department, one typically considers

research first and foremost, with teaching second and service, including “outreach,” a distant

third if considered at all. Informal education efforts are typically considered as “pet projects”

for faculty members, relegated to student groups, or implemented as mandatory components of

research grants. As mentioned, many of the individuals engaged in informal physics education

efforts are not even necessarily trained or practicing physicists themselves. The outcome is that

informal education has typically been treated as an “extracurricular” activity in departments.

However, we argue that public engagement is -- and should be treated as -- a core

departmental activity, as a result of the fact that these efforts are the primary way in which non-

physicists interact with and learn about the people who make up the physics community.

Informal physics efforts have the potential not only to shape how audience members view our

field, they also have the potential to shape how audience members view themselves and,

crucially, how they view themselves in relationship to the field. Many physics departments

articulate improved diversity and representation as important goals, but how many of those

departments systemically support the initiatives that are best equipped to accomplish this goal?

As described above, research shows the tremendous benefits to facilitators, audience

participants, and departments even with the low overall level of support afforded to informal

education efforts. While practitioners have historically played a primary role in the design,

creation and implementation of the informal physics programs, a lack of institutional support

means that, historically, programs are designed according to practitioners’ instincts and their

own personal experiences, rather than systemic research based practices. Often, the

practitioners running these programs do not receive research support in how to design and

initiate a program or ongoing support in leading their program to a place of sustainable

functioning . Especially evident during the COVID pandemic [48], the formation of

constructive collaboration between the researchers and the practitioners in the field would

create the opportunity for practitioners to implement research-based practices to create

thriving, effective programs. To that end, the researchers leading the aforementioned landscape

project team have started a project that focuses on deep understanding of the main components

that would impact on the performance of informal programs from a research point of view.

The team has also engaged in preliminary research-practice partnerships, which have been

highly effective elsewhere [53], with some programs that are willing to adjust program design

based on research feedback. The team is also developing a model which will be used by the

researchers and practitioners for evaluation of the existing programs as well as designing new

programs. In addition, efforts to understand informal education and public engagement can

impact the way we think about classroom teaching and, potentially, workforce development as

well. Many companies, including those engaged in physics-related activity, are interested in

improving their own demographics. Indeed, the importance of a “diverse STEM workforce”

has been noted even at the governmental level. Collaboration between departmental informal

ed efforts and industry partners could lead to improved recruitment outcomes for both

members, especially when buttressed by large-scale organizational support for informal

education.

Ultimately, our hope is that readers of this chapter have come to an understanding of not

only the formats of informal physics education typically employed in the field, but also the

frameworks, paradigms, and objectives that shape those methods. Readers are encouraged not

to see this chapter as concrete instructions on how informal physics education must be done,

but rather as a look at what informal physics education is now and could be in the future.

238 | Bennett M., Finkelstein N., Izadi D.

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240

Chapter 14

Science Education in the Post-Truth Era

N. G. HOLMES Laboratory of Atomic and Solid State Physics, Cornell University,

142 Sciences Drive, Ithaca, NY 14853 USA

Anna MCLEAN PHILLIPS Laboratory of Atomic and Solid State Physics, Cornell University,

142 Sciences Drive, Ithaca, NY 14853 USA

and

Tufts University, Department of Physics and Astronomy,

574 Boston Avenue, Medford, MA 02155 USA

David HAMMER Tufts University, Department of Education, 12 Upper Campus Road,

Department of Physics and Astronomy, 574 Boston Avenue, Medford, MA 02155 USA

Abstract. We argue there is an urgent need for science education to respond to the societal

phenomenon of "post-truth," to do much more in supporting students to understand how

science constructs and reconstructs “truth.” This is not to abandon canonical content but to

prioritize essential objectives. Students should develop a sense of how science arrives at and

refines ideas; the messy complexity of the process; what sort of questions it can address; how

it evolves and interacts with culture and community; how it can result in reliable knowledge

and how it can go wrong. We draw examples from introductory physics laboratories.

1. Introduction

The editors invited us to reflect on what physics education research might have to say about

“the post-truth era.” We are happy for the opportunity, because we do see a connection to

physics education, although the phenomena of concern go beyond physics.

1.1. The Idea of Post-Truth

At the start of 2017, the new press-secretary Sean Spicer claimed, “This was the largest

audience to ever witness an inauguration, period.” He said that despite plain, compelling

photographic evidence that the attendance was much smaller than at President Obama’s

inauguration in 2009. This is what people mean by “post- truth”: an apparent disregard of

evidence.

If there is a post-truth era, though, it started long before 2017. Stephen Colbert was talking

about “truthiness” in 2005, in reference to disregard of evidence concerning the Iraq war. In

that case, the public did not have direct access to evidence; we had to consider secondary

reports of it and, if it mattered to us, make judgments about their reliability. As we the authors

write this chapter, the matter of President Biden’s election is still in the news, with ongoing

challenges to its validity.

“Post-truth” was the Oxford Dictionary’s Word of the Year for 2016, defined as “relating

to or denoting circumstances in which objective facts are less influential in shaping public

opinion than appeals to emotion and personal belief” [1]. We cannot rely on that definition,

Chapter 14 | 241

however, for our purposes here, because it begs a question that is pivotal to any reflection on

science and science education: What are “objective facts”?

To his credit, in a way, the press secretary felt the need to rebut the counter-evidence to his

claim, arguing that the use of “floor coverings” on the mall made the photographs misleading.

President Trump’s counselor, Kellyanne Conway, famously defended her colleague by saying

he “gave alternative facts.” But what motivated those facts? The claim was similar to previous

claims about Iraq (that it was responsible for the attack on the World Trade Center, that it had

weapons of mass destruction), and it is similar now to claims about the election: There are

efforts to refute evidence for widely accepted conclusions, but there is no evidence to support

the “alternative facts.” Still, many people seem to believe them.

Perhaps the name “post-truth” is misleading. Is it plausible that people do not care about

what is true? There must be conviction driving people who, for example, put themselves at

significant risk storming the Capitol Building. Maybe the problem isn’t so much caring about

the truth as it is in deciding what truth is. Rather than ask “why don’t people care about truth,”

we might ask, “How do people arrive at their truths?” What are the means they have available,

from their communities and from their schooling, for forming, considering, assessing, and

refining their beliefs about the world? Clearly people have many ways [2]: from tradition (it’s

what our people have always thought); from affiliation (it’s what my people think); from

commitments of values, authority, deduction, or what just seems obvious.

1.2. The Denial of Science

Scientists and science educators have written about the problem in terms of politicians’ and the

public’s “denial of scientific evidence” and “rejection or ignorance of scientific expertise,” as

Kienhues et al put it, “the heart of post-truthism” [3, p. 144]. There have been many examples

over the years, such as with respect to climate change or, most strikingly this past year, COVID-

19. Again, and like Kienhues and her colleagues, we argue there is more to consider. Again the

term science denial may be a misnomer: The public and the honest science-denying politicians

(some may not be honest!) may not understand what science is or how it constructs truth. Most

of what they experienced of science in schools asked and graded them for accepting the

authority of their teachers and texts [4, 5]. Perhaps it is not science they are denying, per se,

but “science” as they know it, the practices they learned in school of senseless memorization

and submission to authority.

The case of COVID-19 is most striking, and fresh in our minds, so we’ll focus on it. Again,

the claims in the news have offered the public only secondary reports of evidence–about the

disease, its origins, what measures are needed to stop it spreading, how it might be treated.

People have had to make judgments about what to believe. Often that has entailed navigating

conflicts between what they hear science says and the beliefs they have constructed by other

means, what their communities think and trusted leaders say, and/or what makes sense to them

by their intuition and experience.

Most challenging, the “facts” have kept changing. In February 2020, the public was told

not to buy masks, that masks were essential for health care workers but not important for the

general public. A month or two later the advice was different: Science said the evidence was

very much in favor of masks for the public. For most of the year, there was strong emphasis on

washing hands and sterilizing surfaces, even suggestions to sequester mail and groceries, based

on studies of how long the virus survived on surfaces. More recent evidence suggests the risk

of transmission by contact with surfaces is low. And so on: Science keeps changing its mind.

For those familiar with science and how it constructs knowledge, all of that is to be

expected: What seems to be true shifts over time, with evidence, with theoretical progress and

new calculations. The construction of truth in science takes time and is always to some degree

242 | Holmes N. G., Phillips A., Hammer D.

uncertain. Depending on the question, the data available, and the approaches to research, that

uncertainty can be larger or smaller—very often, the “conclusions” at any moment can only be

tentative. In the early months of COVID-19, epidemiological data (what happened on the

Diamond Princess cruise ship, for example) were, by their nature, difficult to analyze. They

were the data that were available, and scientists did the best they could. Students of science

learn about “the test of time,” a shorthand for years of theoretical and experimental

argumentation, but in a public health emergency it becomes important to act before the data

undergo “the test of time.”

Naturally, too, scientists remain human, and humans are “fraught with all kinds of

imperfection and deficiency,” as Ibn al-Haytham put it 1000 years ago [6]. The construction of

knowledge is not infallible—science, after all, promoted the idea that there are different races

of people [see 7, for example], with different levels of ability, and scientists held that idea for

many years before rejecting it. The idea failed the test of time, but it has obviously had lasting,

terrible consequences for humanity. It is for this reason we do not advocate for education to

support blanket deference to science, but for education that will enable people to make better

judgments about when and how to consider what science has to say [3, 8].

Today there are vaccines and the news reports that they are effective and safe. For those

familiar with randomized controlled trials and statistical power, these findings are far more

reliable than the results from epidemiology—to be clear, this is not at all to disparage

epidemiology; it is to recognize that testing the safety of a vaccine is amenable to controlled

study, which greatly helps to reduce uncertainties. (Of course, those familiar with the particular

subject matter have still more basis for accepting the findings.) For others, the reports of

vaccines’ effectiveness and safety could easily seem like the latest best guesses, maybe to

change like other advice over the year.

None of that is about physics per se, but in what follows, we argue that physics education

can and should contribute to helping students experience and better understand how science

seeks and assesses truth—some kinds of truth, that is, such as about the climate or COVID-19.

The ways that truth-seeking happens are messy and changing; new ideas in science often imply

new methodologies. That makes it difficult to define; Einstein thought determinism was

necessary for science. For our purposes here, we take science to be a pursuit of knowledge

about the natural world that is typically based on uncertain evidence and on reasoning that

includes assumptions, approximations, and simplifications. Something comes to be true in

science because the community finds it to fit with other ideas and with observations.

Perhaps most important, anyone can be wrong, including scientists; that, in fact is much

of what science has to offer, epistemic practices that expect even obvious ideas can be wrong.

We will argue that the best response for science education to the post-truth era–and an urgent

need–is to place much more emphasis on learners’ experiencing the messiness and

contingencies involved in doing science themselves. They should experience how apparently

obvious “facts” can turn out to be false, as well as how doing science can sometimes lead to

reliable conclusions, “facts” worth accepting as true. Thus, we hope physics education can help

address the phenomena of “post-truth” both as they concern science directly, such as in

COVID-19 and climate change, and as they concern more general matters of evidence and

argumentation, such as election results.

1.3. The Structure of this Chapter

We begin with a brief discussion of “How truth is constructed in physics,” highlighting the

messiness and ambiguities and uncertainties that physics curricula, in their focus on the

canonical content, tend to set aside. We reflect on the role of community, including judicious

reference to others’ expertise as well as the importance of the community’s hearing and

Chapter 14 | 243

considering multiple perspectives, and on how the history of physics is filled with examples of

radical, initially unthinkable ideas eventually folding into the canon. The next section, “Doing

physics in physics class,” describes and presents some examples of classroom activities shifted

to focus on the goal of students learning how truth is sought through inquiry.

In the closing sections of the article, we step back out again to consider the urgent needs

for physics education to transform, in response to the phenomena described as “post-truth” and

“science denial.” We reflect on how physics education sits within and can manifest larger

societal dynamics, often to the effect of limiting who participates and how. Finally, we reflect

on some of the challenges for teachers and propose elements of a reformed agenda for teacher

preparation.

2. How is Truth Sought and Assesed in Physics?

The history of physics is filled with accounts of how ideas that once seemed true—that objects

return to rest if they are not caused to move, that space and time are independent, that the cause-

and-effect laws of physics are local and deterministic—turned out to be false or limited in

validity. There are, of course, debates among philosophers over the nature of scientific

progress. Kuhn wrote of “scientific revolutions” [9], arguing that the shifts of views are so

dramatic as to make them “incommensurable,” challenging Popper’s account of “falsifiability”

[10]. But it is clear that being wrong, and being confused or uncertain, are staples of experience

in physics.

2.1. Checking How Ideas Might Be Wrong

Practices of research in physics revolve around considerations and procedures for checks of

how an idea or fact or measurement might be wrong or uncertain. Moreover, these checks are

part of the motivation and joy physicists experience to discover a gap or inconsistency. As we

write this chapter, there are many physicists gleeful over a discrepancy from theory in a recent

measurement of the magnetic moment of a muon, which might mean the current theory, the

“standard model,” needs revision. These checks are part of the pleasure for individuals, as well,

to discover a confusion they can work to resolve and for the experience of the pleasure in that

challenge [11].

The moral for physicists is that what seems to be true is always, in principle, to some

degree uncertain. Nothing is ever absolutely certain, but over time the uncertainty can become

so small the community starts to ignore it. Ideas and findings come to be accepted as true if

they pass the test of having survived challenges of counter-arguments and counter-evidence.

By some accounts, the time to be most sure of a theory is when the community has established

when it fails—that is when one can see the boundaries of its domain of validity [12].

The moral is explicitly recognized in the community and culture of physics: things that

seem true can be false, so do what you can to check for that possibility. It may not be so

explicitly recognized that the practices of checking keep evolving themselves or deciding what

assumptions and previous ideas need revision is a complex, messy process. One might think,

and physicists often say, that the bottom line is what experiments show, that physics is an

empirical science, but evidence from the history of science challenges that simple story.

Consider two examples. The first is from the late 1920s, in measurements of β decay. In

this process, a neutron decays into a proton and an electron, which fly apart at high speed. The

problem was that the sum of the energies of those two particles fell short of the theoretical

prediction; the process also seemed to violate conservation of momentum and of angular

momentum. In 1930 Enrico Fermi posed the idea of a neutrino as a tiny, neutral, and, as far as

he knew, undetectable particle that is emitted during the interaction. This idea was initially

244 | Holmes N. G., Phillips A., Hammer D.

rejected; science needs experimental verification. But over time, it came to be taken seriously

based on its theoretical, explanatory power: Allowing an undetectable “ghost” particle was

preferable to allowing an exception to well-established conservation laws. Eventually,

physicists found ways to detect neutrinos and they are now firmly established in the canon.

Fermi’s initial idea was correct but included one key mistake: just because the neutrino was

undetectable by experiments at the time did not mean it was fundamentally undetectable [13].

The second example is of another theoretical proposal. In the late 60’s, astronomer Vera

Rubin found that the rotational speed of galaxies could not be explained by the measurements

of mass distribution and well-established models of gravitation. If most of the mass in galaxies

were concentrated in the stars of the galaxy, as was assumed through most of the 20th century,

one would expect the stars near the edge of the galaxy to orbit more slowly than ones near the

middle. Rubin observed that the rotational velocity of stars near the edge remains

approximately constant. Perhaps, she suggested, there is dark matter, unseen mass distributed

throughout galaxies, as had been proposed as early as the 1930’s. Some of the initial reaction

was to question the quality of her observations (questioning that was no doubt tinged with

sexism [14]). However, Rubin’s findings and the idea of dark matter became mainstream faster

than Fermi’s did for neutrinos; the community seems to have been more willing to prioritize

theoretical coherence without empirical evidence. To this day, nobody has directly detected

dark matter, yet one would be hard pressed to find a physicist that doubts it exists. (Whether or

not physicists will one day be able to detect it, however, is a lively debate.)

Of course, there are many other ways that the epistemological values of physics—the

values for what gets to count as evidence—have evolved. Over the 20th century, quantum

mechanics brought dramatic change in physicists’ expectations of a valid, complete the-

oretical account of phenomena. Einstein was famously unhappy about it, claiming that “God

does not play dice,” developing careful arguments that quantum mechanics must be incomplete

[15], even writing in private correspondence that “if all this is true then it means the end of

physics.” [16].

Some of that evolution has differentiated subfields. High energy physics, for example,

relies on the “5 σ” criteria for a measurement to count as a “discovery.” The measurement must

be in the very tail of the predicted normal distribution, equivalent to a p-value of 3 x 10−7, far

beyond what is used in most other scientific fields (such as the social sciences with the p < .05

threshold). This threshold is made possible and necessary by the fact that they are working with

a tremendous amount of noisy data: The particle collisions in the LHC generate an astonishing

peta-byte of data per second [17]. Condensed matter physics, in contrast, needs to pay more

attention to systematic effects than to statistical noise and so there is not a corresponding sigma-

level threshold for accepting a measurement. The condensed matter physicists still have to

contend with and seek to minimize those systematics, but, overall, their criteria for

measurements are much more about apparent trends in the data. Von Klitzing’s analysis of the

integer quantum hall effect, for example, though containing extensive accounting of

uncertainties and systematics, the voltage “clearly levels off” when the conductivity and

resistivity “are zero” [18].

To summarize so far, we have highlighted how the approaches in physics for con- structing,

assessing, and revising what the community takes as true can be messy, vary and evolve, and

are connected deeply by theoretical and experimental understandings. Throughout, though,

what remains stable about doing physics is that it involves deliberately looking for reasons to

disbelieve an idea or identify possible inconsistencies and gaps. Many ideas do not survive;

that is part of doing physics: the positing and rejection of ideas. As well, the practices and

values support questioning any idea, including long-held views, as new possibilities for

challenging them arise.

Chapter 14 | 245

2.2. The Limited Roles of Authority and Tradition

In these ways, the practices of constructing and assessing what is true in physics, and in other

sciences, places much less value on authority or tradition than other means of seeking and

assessing truth in society. That ideas have been in place for centuries or millennia, or that they

are advocated by established figures, are reasons to give them consideration, but they are not—

at least not explicitly—sufficient reasons for their acceptance in science. This is in contrast

with other approaches to deciding what is true in society and it is in contrast with how science

is often depicted, perceived, and taught. Part of our motivation for writing this chapter is that

traditional pedagogy—the physics community is driven by tradition in pedagogy—tacitly

encourages students to accept truth by authority, very much in contrast to the practices of

physics [19]. We have more to say about pedagogy below.

The perception of physics as authority-driven is certainly not what physicists aspire to and

it is in conflict with disciplinary values of pushing boundaries and seeking inconsistencies in

theory. Although Fermi’s theory of neutrinos did not fit with the understandings of particles at

the time, the community was eventually compelled by the evidence to shift from the previously

established “truths.” The practices and values of physics support questioning any person; the

cultural aesthetics of physics and science do not respect deference to authority. It would sound

odd to say “Fermi said” or “Rubin said” as the way to support the existence of neutrinos or

dark matter.

One might, however, say “Fermi found” or “Rubin showed,” respecting the scientists’

expertise but pointing toward their having gone through some process of derivation or

empirical study. And their standing in the field would become part of that support. To rely on

others’ expertise is certainly within the values and practices of physics; not as blind trust or

obedience, but out of a general understanding of the nature of that expertise and how it works.

In evaluating a scientific claim, result, or methodology, a physicist (or scientist generally)

makes a decision about when to think deeply through the ideas themselves and when to respect

and rely on the expertise of others. If the approach seems inconsistent with epistemological

values, one might choose to take more care, perhaps studying the arguments more closely,

perhaps checking with others in the field.

That’s within the explicit values of the discipline. There is a similar explicit respect for

tradition; one does not reject a long-held idea the moment there is counter-evidence, physicists

will certainly work to find explanations that remain consistent with previously established

“truths.” Consider, for example, the response to physicists who claimed to have measured

neutrino velocities faster than the speed of light. Their findings were met with intense

skepticism and close examination of their work revealed small but essential flaws.

2.3. The Persistence of Biases

We have been describing the values of the discipline, more precisely the epistemic values, but

it is essential to acknowledge that they are not all that drive how truth is constructed. There is

abundant evidence that physics has not been successful in managing social biases, which affect

who participates and rises to prominence in the field. By the explicit epistemic values, the fact

that Vera Rubin was a woman should not have had an effect on the perceived value of her

work—but it did.

There are numerous examples of how implicit (or explicit) biases have led to voices being

excluded from physics; from the female “calculators” (particularly women of color) at NASA

being disregarded for their contributions to the space race to Marie Curie and others being

denied faculty positions. Many would argue the issues of sexism and racism in physics are

much more subtle today than in the past. However, biases in everything from citations [e.g.,

246 | Holmes N. G., Phillips A., Hammer D.

20], grant funding [e.g., 21], hiring decisions [e.g., 22], reference letters [e.g., 23], teaching

evaluations [e.g., 24–28], or grades [e.g., 29–36] impact whose voices, and thus whose results

and claims and evidence, are heard, celebrated, and re-voiced. This further leads to a negative

feedback cycle where women and people of color do not see themselves in the authority figures

being celebrated and are further alienated from the field [37, 38]. These issues directly impact

the progress of physics and what and whose truths emerge on to the field.

Ultimately, physicists are humans and what really happens in the community of physics

does not always match its aspirations. There are social dynamics as in the rest of society. An

individual’s sense of truth is not simply an individual sense. Truth is motivated by the beliefs

and values of the individual’s community (or communities). To fit into the community, to be

respected and valued by them, one must generally take to be true what they take to be true. The

trust in the community also translates into trust in the community’s beliefs. Our trust in science

led us to get vaccinated and wear masks, but we were all surrounded by colleagues, friends,

and family who were also vaccinated mask-wearers; we were influenced by surrounding

cultural values. The same goes for the cultural values of physics and the physic classroom.

While aspects of these social dynamics may be problematic, the humanity of physics is an

important part of its identity and culture. Only by making it more explicit (throughout physics

and physics education) can we strive for change.

Our core claim in this chapter is that the messy, complex, and evolving set of practices and

values in how physicists seek, assess, and revise “truth” should reflect in what students

experience. Not only are these practices and values essential features of the discipline, as we

and many others have long argued [39–41], they are also of urgent priority for society’s

grappling with post-truth. In the next section, we discuss and give examples of how physics

class might change to support students’ learning about how science pursues truth.

There are challenges of course, in providing students such experiences and in coordinating

with goals of their learning the canon (which we do not propose to abandon). One challenge,

clearly, is that the time scales of historical progress in professional physics are years and

decades, not the days and months that are available in school. Other challenges include views

about schools and assessment long accepted as “truth” that we argue need to change.

3. “Doing Physics” in Physics Class

It is, we and others argue, an urgent objective for science education to prepare students to be

sophisticated consumers and critics of claims and arguments they hear in the world, scientific

or otherwise [42]. Our purpose here is to consider how physics classes might contribute to that

objective by giving students their own experiences of doing physics and engaging in their own

pursuits of knowledge about phenomena.

To summarize the previous section, physicists are professional learners, so learning

physics should mean learning how to learn. That includes developing the discipline to revise

what you believe based on evidence and reasoning; learning to expect that you’ll be wrong.

Learning in physics (by physicists and by physics students) forces humility, as ideas that seem

like they have to be true often end up needing revision.

This has to be at least part of why physics has a reputation for being more difficult than

humanities and social sciences (which also work on “truth”): it happens so much more often

that you find out you’re wrong. The practices of the discipline, and the nature of the knowledge

it produces, allow learners to see contradictions in theoretical calculations or unexpected results

from empirical investigation. If you expect the period of a pendulum does not vary with

amplitude, for an example we’ll discuss, and you take careful measurements, you’ll have to

contend with data that doesn’t agree.

Chapter 14 | 247

In the social sciences, by contrast, it’s not so easy, or perhaps we should say forced, to find

out you must be wrong about something. To be sure, that is a challenge for us right now in this

chapter: Many readers have the strong intuitive sense that students must come away from

physics class with correct understanding and we are arguing for a different urgency, that

students come away with a rich sense of how “correctness” comes to be. While we do not

propose abandoning canonical objectives, we are contesting their priority. But we do not have

“objective” means of forcing the point. In matters of educational objectives and assessment, it

is harder to know when you’re wrong. (That has to be part of why progress in education is more

difficult than progress in STEM fields.)

The salience of being wrong is precisely why, we argue, physics class provides a wonderful

opportunity for cultivating epistemic virtues, including humility, open-mindedness, and

attention to multiple lines of reasoning. To take advantage of that opportunity, however, means

shifting from that overriding focus on correctness, which so often has students accepting ideas

by authority (if only for the purpose of a good grade) rather than as a result of having done

physics for themselves.

It will help to have some examples of how that shift might happen. For this chapter we

focus on what students experience in labs.

3.1. Two Examples of Labs

For many decades, physics teachers have assigned students to replicate Galileo’s findings about

pendula, in particular that the period is independent of the mass and amplitude. He was right

about mass and wrong about amplitude, the age-old moral is that even Galileo could be wrong;

science is about evidence and reasoning, not authority.

We have used this as our first lab in our introductory courses, guiding students to make

their measurements precise. The tools have changed over the years, but one old, simple

approach is to time swings by hand with a stopwatch, let the pendulum swing 5–10 times, and

divide the total time by the number of swings. That’s good enough for students to get their

measurement uncertainties small enough to see the not-quite-as-small deviations from the

result they had expected to confirm [see 43, for sample data].

Students using this method typically find evidence there is some small dependence on

amplitude [43]. That’s not what Galileo said and that’s not what the equation says (𝑇 = 2𝜋√𝐿

𝑔

) for those who have seen it in their textbook or searched for it on the web. When faced with

this contradiction, many students stall, re-estimate the size of the uncertainties in their

measurements, or write it all off to the catch-all “human error.” Some even manipulate their

data to obtain the desired outcome [44].

Why? Their expectation (their framing of the situation [45, 46]) is that the lab should verify

the known result; known by the authority of the instructor, the textbook, Galileo. Authority is

often the principle way they have learned to arrive at truth in their schooling, especially in

science courses [47, 48]. It’s not irrational, that approach to arrival at truth. It certainly makes

sense in school to trust the authority, particularly when that same authority (or its agent) will

be scoring your tests and assigning your grades. And as we discussed above, it often makes

sense in science: Should a single, two-hour experiment be enough to “disprove” apparently

established findings in the field?

In the investigation, we are after students’ learning to do science for themselves, to see

their methods produce a discrepancy from Galileo’s claim. It is appropriate for them to take the

authority seriously, as physicists respect the authority of their colleagues in other disciplines,

but they should take their own findings seriously as well. We are after their working to grapple

with the discrepancy, to examine their methods, compare their findings to other groups’, to

248 | Holmes N. G., Phillips A., Hammer D.

wonder if there’s something so many of them could be doing wrong. Part of learning physics

is learning that findings like Galileo’s should be replicable; anyone ought to be able to make a

pendulum and see what happens.

Here is another example, used by the first author to follow the pendulum lab. Students by

this point have studied two possible models for objects moving freely through air: a gravity-

only model and a gravity+drag model [49, 50]. The lab activity begins with students predicting

the acceleration of an object on the way up and on the way down according to the two models.

The gravity-only model predicts the acceleration to be 9.8 m/s2 in both directions, while the

gravity+drag model predicts the acceleration to be less than 9.8 m/s2 on the way up and greater

than 9.8 m/s2 on the way down. The lab is designed, again, for students to encounter a

contradiction and this one is striking: When they measure the acceleration of a beach ball, they

find it to be less than 9.8 m/s2 in both directions.

In our observations of students in this lab, many grapple productively with this

contradiction; that it follows the pendulum lab helps them frame the lab as something other

than a game in confirmation. They check calculations, retake data, systematically consider the

forces on the object, or begin to invent a mysterious constant upwards force on the ball [50].

Almost as many groups, however, engage less productively: For some, it seems, the pendulum

lab was not sufficient to disrupt a confirmation framing; others apparently focus mainly on

getting done with the lab as quickly as possible [49].

It is rare for a group to settle on an explanation for the discrepancy by the end of two-hour

lab period, but that is not our goal. We see their struggles themselves as scientifically

productive. They are opportunities for problematizing [11, 51, 52], a core part of doing physics,

identifying and articulating inconsistencies in one’s knowledge or understanding. Successful

groups in this lab are those that arrive at identifying and articulating a problem: There seems

to be some other force acting upward on the ball, but they do not know what it is. Some groups

might come up with buoyancy as a conjecture, but that is not the instructional goal of the lab

(although when the topic of buoyancy comes up later in lecture, later in the semester, data

students have from the lab can certainly contribute).

3.2. A Focus on Students’ Learning About Empirical Investigation

The instructional goals of these labs are that students learn how to learn about the physical

world and to experience doing physics for themselves–that is, to experience some of the

disciplinary practices of working toward “truth.” It is something they can do, for themselves;

it involves uncertainty, simplifications, iteration, and continual refinement. Many students have

difficulty with this reframing, particularly as it is one with which they are not familiar, which

we take as evidence of the need for labs like these.

To be clear, the instructional purpose is not simply to focus on scientific skills and practices

[53]. Too often, a focus on skills (e.g. the control of variables strategy, hypothesis formation,

algorithms for error analysis) can lead to a sense of science as comprised of a trivialized set of

procedures [54–57] that one must implement to obtain objective truth [19]. The notion of

developing a sense of the practice of science must include all the messiness and subjectivity

and uncertainty that is inherent in the practice of science. Students must have the opportunity

to enact their agency to critique claims and construct their own [48, 55, 56, 58]. That is to say,

the epistemology of science must be explicitly attended to such that the process is not overly

simplified to a set of routine procedures.

While this seems like a lofty goal, physics activities at the middle school [59], high school

[60–62], and college levels [43, 58, 63–70] have found ways to do this successfully. In these

examples, students are not necessarily exploring novel questions whose answers are unknown

in the scientific community and therefore could lead to publishable results, although this is a

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direction many college-level biology lab courses have been taking through Course-Based

Undergraduate Research Experiences or CUREs [71]. In fact, recent work has proposed that

the pursuit of an authentic (i.e., novel, publishable) research question is not a requisite for the

learning benefits from CUREs [72, 73] or even undergraduate research [74]. Instead, the

important feature seems to be that students engage in an experiment where the outcome of the

investigation is not predefined–where the students do not know (and better yet do not believe

the instructor knows) what answer the experiment should produce [69].

This reframing presents a tension for the possibilities of developing core concepts and

ideas alongside scientific practices and epistemology. This tension has been excellently

articulated by others elsewhere [e.g., 19, 75], identifying the potential shortcomings of

curricular reforms that maintain a focus on canonical knowledge alongside a focus on scientific

practice.

For us, and the teaching assistants (TAs) we prepare for this different sort of work, it is

essential to recognize that the pendulum experiment is not about teaching students about

pendula and the free-flight experiment is not about teaching students about buoyancy. Rather,

they are about cultivating students’ understandings of empirical investigation, and that

objective would be at odds with goals to verify or demonstrate particular phenomena. If the

labs are to provide students experience of what it means to learn as nascent physicists, then

there must be room in them for students to devise their own procedures, to grapple with

uncertainties and ambiguity, even to find and explore their own conjectures and questions–we

speak of welcoming and cultivating students’ “epistemic agency” [76].

3.3. The Importance and Challenges of Engaging with Multiple Perspectives

It is a wonderful feature of physics, that everyone has experience of it. That includes widely

shared experiences of motion and forces, of sound and light, of magnets. It also includes

particular experiences not everyone shares, a variety among students of different sports, jobs,

tools, musical instruments.

It’s not enough to make room for these experiences: The instructors–ourselves, our TAs–

need to respect and engage with what students do and think and to teach them to do the same

with each other. This is, again, how doing physics works to seek, assess, and revise what to

accept as true, by attending, interpreting, and responding to arguments and counterarguments,

evidence and reasoning. A great deal of work has focused on the importance of argumentation

in science [77]; labs are wonderful spaces for it to happen. Novel, unfamiliar perspectives are

valuable.

This, of course, is part of the challenge of participating in these labs, for students as for

instructors, to hear and make sense of someone else’s thinking, especially if it is novel,

especially if they express it in unfamiliar terms. As it has been for physicists, it can be

challenging for instructors and students to manage implicit biases cued by others’ race, gender,

accent, or appearance — part of learning the discipline is learning to manage those biases.

Cultivating practices of doing science means supporting students in these efforts.

Too often an individual’s personal cultural values are pitted against the cultural values of

the discipline, pushing students out of physics and thwarting any sense of trust in the culture

and activities. There are tensions, no doubt, but the overlap in values is much larger than we

typically give credit [78].

4. Final Remarks

We began this chapter suggesting that “post-truth” may not be precisely a matter of people not

caring about truth; to the contrary, people seem confident, attached, and deeply caring about

250 | Holmes N. G., Phillips A., Hammer D.

the truth as they see it. The problem, we posit, is in how they arrive at and maintain those

commitments. And, we suggest, the essence of “science denial” is that people do not know

what science is.

Findings from Physics Education Research have shown repeatedly that traditional

pedagogy promotes counterproductive epistemologies [79–82] assess students’ learning

physics as information to memorize, provided by authority, that need not connect deeply with

their experience of the physical world. To succeed in school, most learn to set their sense aside;

the focus is more on students’ obedience than it is on their developing the discipline of mind

physics has the potential to teach. It should come as no surprise that later, when they are out of

school and don’t need to care about collecting points or being obedient, many come back to

trusting their own sense of the world, sticking with their own means of deciding what is true.

For those who stay obedient, accepting what science says as true, it must be jarring when

science says one thing and then later changes its mind.

We have argued for a shift in priorities in physics education toward giving students

experience in doing physics for themselves. We focused on what can happen in introductory

laboratories, largely because we suspect labs are the easiest places to start. They are typically

only loosely connected to the lecture portions of classes, and there is strong evidence that

traditionally designed labs fail in the goal of reinforcing lecture content [83]. It is, however, also

possible and important for the shift in priorities to reflect in lecture portions of courses. There has

been a great deal of work there as well, toward reform of lectures and discussion sections [11,

84], although relatively little so far to prioritize students’ epistemological progress [85].

Scoping out still further, the arguments we have presented here apply to other sciences as

well. Most of what happens in introductory physics is amenable to controlled experimentation,

but for the epidemiology of the pandemic, climate change and other matters of societal

importance, scientific investigation takes place mainly through observations. Other

introductory courses would be better positioned to give students experience problematizing,

constructing, and refining knowledge with data collected from events in no one’s control, such

as in evolutionary biology or astronomy. While different scientific fields and subfields have

their own “epistemological culture” [86] that determine what types of experimental and

observational data are valued and are used in constructing knowledge, working with ambiguity

and limited data are common activities across the sciences. So too is working towards a

collective understanding through robust debate [87]. Exposure to the diverse ways in which

scientific subfields construct knowledge and settle on truth by muddling through that ambiguity

in multiple educational contexts will serve to further students’ ability to scientific information

in their everyday lives.

We have suggested that a shift in priorities, such as we have illustrated can happen in labs,

could contribute to addressing the problems of science denial and post-truth. Experience doing

science might help students develop a sense of what goes into the construction of knowledge

in science, of what science can do and what it cannot, of why some findings about some ideas

might be worth believing, even if they are inconvenient or go against common sense. It is an

important area for further work in Physics Education Research to study how epistemological

progress in introductory physics might affect later experience [88, 89].

Reflecting on ourselves personally, we believe that having a sense of how evidence

supports results has helped us understand what has taken place over these past two years. It

helped us understand why the views kept changing over how COVID-19 is transmitted, as well

as why the findings are very unlikely to change over the safety of the vaccines and their efficacy

for known variants. It helped us as consumers of advice over whether and when to wear masks,

get vaccinated, wash our hands, eat at restaurants, although none of us is specifically trained in

bioscience. In fact, one of us hesitated: None of the vaccines had been tested on pregnant

women and so there was a dearth of evidence for its effectiveness or potential side effects. This

Chapter 14 | 251

level of uncertainty was sufficient to necessitate a pause, to seek information from respected

authorities, consider the impacts of other vaccines on pregnancy, dig into the biological

mechanism, and ultimately make a decision to get vaccinated. As well, having a sense of how

science works and what it does helped us think of these questions as matters of science rather

than of politics. Of course, at other times, it helped us consider the limits of what science can

offer.

We wonder if studying science might have broader benefits for post-truth, in particular in

what one learns about knowing. It is salient in physics: Ideas that seem to be true, even obvious,

even necessary, even believed for centuries by millions of people, may ultimately prove to need

revision. It seemed obvious the Earth isn’t moving, that objects will stop moving if you stop

pushing them, and so on and so on. Doing science well involves humility; students and

scientists get used to the phenomenon of being wrong. Perhaps there is a potential for this to

help with thinking beyond what is specifically science: Arguments about structural and

systemic racism are, in part, arguments to challenge old, automatic, “obvious” thinking.

Still, there is evidence that having learned humility at the lab bench doesn’t necessarily

transfer to humility about one’s views in politics or pedagogy. Physics educators have been

arguing for shifts in priority toward students doing science for more than 100 years [90, 91].

But traditional pedagogy remains in place, supported by what seems obvious: that it is essential

students learn the canon of established knowledge, as evidenced by their solving problems

correctly; that explaining causes learning; that educators should assess students’ progress

“objectively,” such as by standardized exams; that students feeling confused is a problem to

avoid during instruction, and to punish on an exam.

Acknowledgement

This work was supported in part by the U.S. National Science Foundation, Grants DUE

2000739 and 2000394.

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255

Biographical Sketches

Alberto Stefanel has been a researcher at the University of Udine since 2009, following a

twenty-year career as high school mathematics & physics teacher. From December 2015 to

2021, he was the Director of the Centro Interdipartimentale di Ricerca Didattica

(InterDepartmental Center for Educational Research) at the University of Udine. His research

activity is documented in more than 300 works on the following topics: teaching and learning

modern physics in high school; cognitive studies on the role of informal learning environments

and hands-on/minds-on activities in activating learning process of primary school pupils on

thermal states and processes, electromagnetism, mechanical phenomena, sound, energy; role

of ICT in Physics education; studies on teacher preparation and training on educational

innovation; role of web environments for physics learning both in university teaching and in

teacher training.

Anna McLean Phillips began her career in science education as a secondary school teacher.

She later completed her PhD in Physics Education Research at Tufts University. Her

dissertation focused on problematizing, the process of refining areas of uncertainties into clear

questions and problems, in professional physics and K-16 classrooms. She then completed a

post-doctoral research position with the Physics Education Research Lab at Cornell University,

studying students’ engagement and problematizing in undergraduate instructional laboratories.

She returned to Tufts as a post-doctoral researcher and instructor, where she has begun work

studying how students engage in the practices of physics within computational physics

courses.

Dagmara Sokołowska (PhD) is an adjunct at the Faculty of Physics, Astronomy and Applied

Computer Science, Jagiellonian University. She is involved in physics/science education

research in Inquiry-based Learning and Practitioner Inquiry at all levels of schooling - from

primary to higher education. She participated in the following EU projects on education:

Fibonacci, SECURE, SAILS (7th FP); 3DIPhE, STAMPEd, RISE (ERASMUS+);

Akademickie Centrum Kreatywności, Wiking, Feniks (EU Structural Funds). She has been a

member of GIREP vzw (International Research Group on Physics Teaching) Board since 2014.

She is the author of the National Contest in Science for K1-K8 (Swietlik, eng. Firefly) in Poland.

David Hammer has been a professor in Physics Education research (PER) for 30 years. He

started in Education at Tufts in 1992, moved in 1998 to join Joe Redish in Physics at the

University of Maryland, with a joint appointment in Curriculum & Instruction, and then in

2010 returned to Tufts where he is now Professor of Education with a secondary appointment

in Physics & Astronomy. For much of his time since 2010 he served as chair of the Department

of Education. At the end of 2018, he began as director of the Tufts Institute for Research on

Learning and Instruction, following a gift from the McDonnell Family Foundation.

David R. Sokoloff is Professor of Physics, Emeritus at the University of Oregon. He earned

his BA at Queens College of the City University of New York and his PhD in AMO Physics at

the Massachusetts Institute of Technology. For over three decades, he has studied students'

conceptual understandings, and developed active learning approaches (with NSF and FIPSE

support). These include Interactive Lecture Demonstrations (ILDs) and RealTime Physics:

Active Learning Laboratories (RTP), both co-authored by Priscilla Laws and Ronald Thornton.

256 |

His work has been published in the American Journal of Physics, the European Journal of

Physics, Physical Review—Physics Education Research and The Physics Teacher. He has

conducted numerous international and national workshops for secondary and university faculty.

Since 2004, he has been part of the UNESCO Active Learning in Optics and Photonics (ALOP)

team, presenting workshops in more than 30 countries in Africa, Asia and Latin America. He

was awarded the 2010 APS Excellence in Physics Education Award (with Priscilla Laws and

Ronald Thornton), the 2011 SPIE Educator Award (with the ALOP team), the AAPT Millikan

Medal (2007) and Oersted Medal (2020), and the 2020 GIREP Medal. He has been a Fulbright

Specialist in Argentina (2011) and Japan (2018), a member of IUPAP Commission 14, and was

elected to AAPT’s Presidential Chain (2009-2012).

Dena Izadi is a senior research associate in the physics education research lab at Michigan

State University. She holds a PhD in experimental biophysics. Izadi’s work is focused on using

qualitative methods in characterizing the landscape of physics public engagement across the

United States. Her primary research interests are creating evidence-based assessment tools and

designing and conducting qualitative research practices for equitable and accessible education.

Izadi is also passionate about creating hybrid spaces for blending physics with other disciplines,

including art and design, to make physics more inviting to non-physicists and the general

public.

Eilish McLoughlin is an Associate Professor at the School of Physical Sciences, she holds a

PhD in Surface Physics from Dublin City University and is a fellow of the Institute of Physics.

She was co-founder of the Research Centre for the Advancement of STEM Teaching and

Learning (CASTeL) at Dublin City University and served as Director from 2008-2021. Her

interests focus on physics and science education research at all levels of education. She has led

and collaborated in a wide range of research projects at European, national, and local level that

examine the development of teacher education, curriculum and assessment strategies that adopt

integrated STEM and active learning approaches. She was awarded the Institute of Physics

Lise Meitner Medal for widening public engagement and education in physics in 2019. She

was also honored in 2019 by Science Foundation Ireland for her Outstanding Contribution to

STEM Communication. She has served as Chair/co-Chair of IOP Ireland Education group since

2006, as member of IUPAP C14 Commission for Physics Education 2014-2021 and as

Executive Secretary of GIREP since 2020.

Elizabeth J. Angstmann, Associate Professor, has been first year director in the School of

Physics at the University of New South Wales, Australia, since 2011. She is responsible for the

education of thousands of students each year. Prior to this, she obtained her PhD in theoretical

atomic physics but decided to focus her career on education and obtained a master’s degree in

teaching. Her educational background and experience as a high school teacher underpin her

use of sound pedagogical bases in her courses. She has an interest in the appropriate use of

technology in education and active learning methods. Elizabeth has focused on expanding

physics education at the University of New South Wales, introducing both new subjects and

degrees. In 2018, she launched an online graduate certificate in physics for science teachers.

This exemplifies her passion for assisting schoolteachers to provide the best possible physics

experience for their students. Elizabeth is the current Chair of Physics Education Group of the

Australian Institute of Physics. Her work has been recognized through an Australian Award for

University Teaching citation in 2018 and the prestigious Australian Institute of Physics

Education Medal in 2020.

Biographical Sketches | 257

Eugenia Etkina is a Distinguished Professor at Rutgers, the State University of New Jersey.

She holds a PhD in physics education from Moscow State Pedagogical University and is a

Recipient of the 2014 Millikan Medal of the American Association of Physics Teachers,

awarded to educators who have made significant contributions to physics teaching. Professor

Etkina designed and coordinated one of the largest physics teacher preparation programs in the

United States. She runs professional development for high school and university physics

instructors (over 150 workshops since 2000) and contributes to reforms in undergraduate

physics courses. Her research is on students learning physics and physics teacher knowledge,

in which she has over 100 peer-refereed articles. In 1993, she developed a system, now called

the Investigative Science Learning Environment (ISLE) approach, in which students learn

physics using processes that mirror scientific practice. The ISLE approach can be used in a

physics course of any level (from middle school to graduate coursework). It serves as the basis

for the textbook “College Physics: Explore and Apply” and supporting Active Learning Guide

and Instructor Guide that are used in many universities and high schools all over the world.

Ileana María Greca is a Full Professor of Specific Didactics at the Universidad de Burgos

(Spain), with a PhD in physics teaching (2000), from the Federal University of Rio Grande do

Sul (Brazil). Her main research interests are improving science teaching using psychological,

epistemological and didactic frameworks and introducing modern physics topics for secondary

and high school students. She has recently focused on the epistemological aspects of

simulations; integrated STEM/STEAM approaches for comprehensive student competency

development and science teachers’ professional development. She has participated in more than

30 competitive research projects (regional, national, and European) as the principal researcher

in 13 of them; and has more than 90 articles published in national and international journals

indexed in JCR, SCOPUS, and SCIELO; more than 23 book chapters and 3 books.

Irene Arriassecq has a PhD in Science Teaching from the University of Burgos, Spain; M. Sc.

in Epistemology and Methodology of Science from the National University of Mar del Plata,

Argentina and Professor in Mathematics and Physics from the National University of the

Center of the Province of Bs. As., Argentina (UNICEN). She is a CONICET Independent

Researcher. Full Professor in the area of Epistemology and History of Science in the

Department of Teacher Training of the Faculty of Exact Sciences at UNICEN, in undergraduate

and postgraduate degrees. She has also given courses, workshops, seminars and conferences at

various national and foreign universities. She is currently the Director of the Center for

Education in Sciences with Technologies (ECienTec) belonging to UNICEN and associated

with the Scientific Research Commission of the Province of Buenos Aires. At ECienTec, she

chairs the line “Teaching contemporary physics topics in secondary school: contributions from

and to the nature of science”. She is the author of a book, book chapters and research articles

in various reference journals in the area of Science Teaching. In the Association of Physics

Teachers of Argentina, she is the Local Secretary for the city of Tandil and a member of the

Board of Directors.

Jaume Ametller is a Serra Húnter Associate Professor of Science Education at the University

of Girona. He studied Physics at the Autonomous University of Barcelona where he later

completed an MA and a PhD in science education. He has been a full-time researcher and a

lecturer of science education at the University of Leeds and a post-doctoral fellow at the

University of Hokkaido. He is interested in the design of teaching sequences and materials for

physics education, the role of communication and dialogue in the construction of knowledge,

and how theory informs our understanding of how people learn, particularly in contexts with

digital networked tools.

258 |

Jenaro Guisasola received his BS in Physics and an MS in Theoretical Physics, both from the

University of Barcelona, as well as a PhD in Applied Physics from the University of the Basque

Country. He is Assistant Professor of Physics at the University of Basque Country Applied

Physics Department. Since 2008, he has also taught Physics Education on the Initial Training

of Secondary Science Teachers MA course. His research interest follows two interwoven paths:

(1) How Design Based Research can promote instructional models and enhance learning in

science curriculum topics. Supported by several grants from Spanish and European projects,

this research has given rise to new knowledge about the design of materials and teaching

strategies. (2) The use of history and philosophy of science as tools to help organize teaching

and learning in science curricula. The agenda includes understanding of the development of

scientific knowledge to apply it to science classrooms. He has given numerous invited talks on

his research at national and international meetings and conferences. He leads Physics Education

Research at University (PERU) for the GIREP thematic group. He is member-elect of the

Spanish Royal Physics Society Committee of Physics Education.

Knut Neumann is Director of the Department of Physics Education at the IPN – Leibniz

Institute for Science and Mathematics Education and Professor of Physics Education at the

Christian-Albrechts- University of Kiel. His research interests include how to assess student

competence and the development of student competence in science at various levels of

education, how to support students in developing such competence and how to provide teachers

with the professional competence, in particular the pedagogical content knowledge (PCK), to

best support students in developing competence in science. Dr. Neumann studied mathematics

and physics for the teaching profession at the University of Düsseldorf and holds a PhD from

the University of Education at Heidelberg.

Kristina Zuza is a lecturer in the Applied Physics department of the University of the Basque

Country (UPV/EHU). She graduated in Physics (specializing in Astrophysics) from the

University of La Laguna (Canary Islands, Spain) and she got her PhD in Physics Education

from the University of the Basque Country. She developed her dissertation about Teaching and

Learning Electromagnetic Induction within the A level Research Group (Basque Government)

DoPER (DOnostia Physics Eduction Research) led by Jenaro Guisasola where she works to

this day. Her research has different interest points. She studies students' difficulties

understanding physics laws and concepts and the design, implementation and evaluation of

Teaching Learning Sequences at university level. On the other hand, she is interested in the

relationship between the general theories on education and discipline-based research needs.

She has co-supervised two PhD theses. She is involved in national and European projects and

she has several publications in journals like Physical Review-Physics Education Research,

American Journal of Physics, European Journal of Physics, Revista Brasileira de Ensino de

Fisica, International Journal of Science Education and Enseñanza de las Ciencias.

Lane Seeley earned his Ph.D. in experimental condensed matter physics at the University of

Washington. His doctoral work focused on testing microscopic and mesoscopic models for

phase changes in the nucleation of ice from liquid water. Since joining the faculty at Seattle

Pacific University in 2001, he has worked closely with colleagues to build a close-knit physics

department that is primarily focused on student learning. Lane has worked with departmental

colleagues on several grant-funded projects aimed at supporting K-12 physics and physical

science teachers. He has played an active role in the development of web based diagnostic tools

for physical science teachers. Most recently, Lane has been a lead researcher on the SPU Energy

Project, a research effort aimed at studying and supporting energy learning among K-12

Biographical Sketches | 259

teachers. Lane's current research interests include building bridges between the energy we learn

about and the energy we care about, studying growth in learner's ability and disposition to use

a rigorous energy model creatively and flexibly, understanding some of the real and perceived

obstacles to student-centered science instruction. Lane is currently serving as a co-PI on an

NSF funded Energy and Equity project which aims to address barriers to inclusion and equity

at the core of our discipline. We are searching for ways to re-frame and re-prioritize energy

learning so that it is more accessible and culturally relevant for all students and particularly for

students who do not see their ideas and priorities reflected in our disciplinary cannon.

Laurie McNeil is the Bernard Gray Distinguished Professor in the Department of Physics and

Astronomy at the University of North Carolina at Chapel Hill. She earned an AB degree in

Chemistry and Physics from Radcliffe College, Harvard University, and a PhD in Physics from

the University of Illinois at Urbana-Champaign. After two years as an IBM Postdoctoral

Fellow at MIT she joined the faculty at UNC-CH in 1984. She serves as a Deputy Editor at

the Journal of Applied Physics. Prof. McNeil is a materials physicist who uses optical

spectroscopy to investigate the properties of semiconductors and insulators. She is a Fellow of

the American Physical Society and has worked throughout her career to enhance the

representation and success of women in physics. She served as co-chair of the Joint Task Force

on Undergraduate Physics Programs, a group convened by the American Association of

Physics Teachers and the American Physical Society that produced the report, Phys21:

Preparing Physics Students for 21st Century Careers.

Manjula Sharma completed her early studies at the University of the South Pacific followed

by a PhD in physical optics and MEd research methods at The University of Sydney. She is a

Professor of Science Education at The University of Sydney, Director of the STEM Teacher

Enrichment Academy and Heads the Sydney University Physics Education Research (SUPER)

group. She is serving as Vice Chair of IUPAP Commission C14 on Physics Education.

Nationally, she has led several substantive government-funded projects such as the Science and

Mathematics network of Australian University Educators, SaMnet; and Advancing Science and

Engineering through Laboratory Learning, ASELL Schools. Professor Sharma co-founded the

premier Australian Conference on Science and Mathematics Education (ACSME) and the

International Journal of Innovation in Science and Mathematics Education (IJISME). She has

over 100 peer-reviewed publications and has supervised influential PhD students. The findings

from her work are being translated into practice and informing decisions. As a change agent,

she invests in professional learning and building capacity in science and mathematics education

across sectors - universities and schools. Her work is recognized internationally through

research partnerships, service on expert/advisory panels, editorial boards and conference

committees. Her awards include the 2012 Australian Institute for Physics Education Medal,

2013 OLT National Teaching Fellowship and she is a Principal Fellow of the Higher Education

Academy, UK.

Marisa Michelini is a full time Professor of Physics Education in the Department of DMIF at

the University of Udine, where she has been Rector Delegate from 1994 for different areas and

now for GEO University Consortium, head since 2014. She is responsible of the Physics

Education Research Unit (URDF) that she founded in 1992. She is head of the IDIFO project

series of PLS on Innovation in Physics Education involving 20 Italian universities from 2006,

and ran 6 biannual national Masters for teacher education, 8 full immersion summer schools

for talented students and 6 full immersion teacher education schools at national level.

Internationally, she has been President of the International Research Group on Physics

Education (GIREP) since 2012, board member of the PED Section of the European Physical

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Society (EPS) since 2016, board member of Multimedia Physics Teaching Learning (MPTL)

since 2014, consultant for CERN- Education since 2019. Her research activity is focused on

electrical transport properties of thin films (1985-2000) and physics education research carried

out continuously throughout her career on the following lines of research: A) innovative

physics education paths on modern physics and prototypes for lab experiments; B) research

and development on multimedia; C) initial and professional development of teachers on

classical and modern physics, and guidance; D) models of collaboration between school and

university: E) informal education: development of an exhibition of 650 hands-on experiments;

F) problem solving test (PSO method); G) computer based interactive environments for

learning and BYOD; H) learning progression and building of formal thinking in science

education base. Internationally, she was the principal investigator on two EU Projects and

responsible of the Italian Unit for 5 other EU Projects, 32 national projects and 15 Regional

projects in physics education research. She received two main Awards: a) 1989 Italian Physical

Society Award for the Exhibit Games Experiments Ideas; b) 2018 IUPAP-ICPE international

award for the research in physics education. Her research activity is documented by 620 peer

review selected publications in books or journals.

Melanie Keller started her journey in empirical educational research after obtaining her

diploma in astrophysics in 2007. This began by researching secondary school physics teachers’

enthusiasm in a cross-national study as part of her PhD, which she finished in 2011. Afterwards,

she toured several German and Austrian universities and now works as a PostDoc at IPN –

Leibniz Institute for Science and Mathematics Education in Kiel, Germany. In her research,

she focuses on the role of emotions in teaching and learning and the communication of science.

Mieke De Cock studied physics at KU Leuven (Belgium) where she also obtained her PhD in

Theoretical Physics. After her PhD, she worked for a few years as a medical physicist at the

Radiotherapy Department in the University Hospital Brussels. In 2007, Mieke returned to KU

Leuven where she is now a full professor in the Department of Physics and Astronomy. She is

responsible for the Teacher Education Program in Science and Technology and leads the APER

(Astronomy and Physics Education Research) group. Her research has a strong focus on

conceptual understanding in Physics and Astronomy and on the mathematics-physics interplay,

both at secondary and university level.

Michael Bennett is the Director of Education and Workforce Development at the Q-SEnSE

NSF Quantum Leap Challenge Institute. Currently, he directs education efforts across the

distributed Q-SEnSE institutions to create a comprehensive workforce development landscape

that will produce a diverse and skilled quantum workforce. Prior to Q-SEnSE, Dr. Bennett

served as the JILA NSF Physics Frontier Center Director of Public Engagement and a Research

Associate at the University of Colorado Boulder, leading the University's flagship informal

physics education program and studying aspects of instructor pedagogy in informal spaces. He

is a member of the American Physical Society and the American Association of Physics

Teachers and is involved in both communities.

Mojca Čepič trained as a physics teacher. After graduating, she worked as a high school

physics teacher for a few years. She did her PhD in theoretical studies on soft matter, on liquid

crystals, focusing on the theory of polar smectics. She proposed the phenomenological model

of antiferroelectric liquid crystals, which led to predicting the structure of one of the liquid

crystalline phases. The structure was confirmed a few years after her prediction when the

resonant X-ray scattering method was developed, which is sensitive not only to the position

but also to the orientation of the molecules. She is still active in theoretical research into soft

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matter. After completing her PhD, she worked as an Assistant Professor of Physics at the

University of Ljubljana, Faculty of Education, Department of Physics and Technology. Since

her audience consisted of prospective physics teachers, she also became active in research on

physics education. She mainly focused on introducing contemporary physics to different levels

of education, from superconductivity to liquid crystals and polymers. In addition, she also drew

inspiration from everyday phenomena and observations. She developed models to enable

controlled studies of circumstances in which phenomena occur such as a double or spreading

shadow, an artificial solar eclipse, or underwater rays. She is currently editor-in-chief of the

European Journal of Physics, that publishes articles on university physics education.

Natasha G. Holmes is the Ann S. Bowers assistant professor in the Department of Physics at

Cornell University with the Laboratory of Atomic and Solid-State Physics. She received her

undergraduate degree in physics from the University of Guelph and her master’s and PhD in

physics at the University of British Columbia. She completed her postdoctoral work at Stanford

University with Carl Wieman. Her research focuses on studying the educational impacts of

hands-on physics laboratory experiences, exploring student learning and skills development,

their attitudes and perceptions of experimental physics, and issues of equity. Her group aims to

develop a rigorous evidence base for understanding and improving physics lab instruction.

Nathan Lima has a PhD in Physics Education. He is an associate professor at the Physics

Department and the Graduate Program on Physics Education of Federal University of Rio

Grande do Sul (Brazil), where he researches History, Philosophy and Science Teaching

(HP&ST). His main interests have recently focused on the history of Quantum Theory and

implications for Physics Education. He is also an assistant editor at the HPS&ST Newsletter

and associate editor at Caderno Brasileiro de Ensino de Física, a Brazilian journal on Physics

Education.

Noah Finkelstein is a Professor and Vice Chair in the department of Physics at the University

of Colorado, Boulder. He conducts research into physics education, specifically studying the

conditions that support students’ identities, engagement and outcomes in physics –

developing context models. In parallel, he conducts research on how

educational transformations get taken up, spread, and sustained. He is a PI in the Physics

Education Research (PER) group and was founding co-director of CU’s Center for STEM

Learning. He co-directs the national Network of STEM Education Centers, is building the

STEM DBER-Alliance, and coalitions advancing undergraduate education transformation. He

is involved in education policy serving on many national boards, sits on a National Academies’

STEM education roundtable, is a Trustee of the Higher Learning Commission, is a Fellow of

the American Physical Society, and a Presidential Teaching Scholar and the inaugural

Timmerhaus Teaching Ambassador for the University of Colorado system.

Paula R.L. Heron is a Professor of Physics at the University of Washington. She holds a PhD

in physics from the University of Western Ontario. Dr. Heron’s research focuses on the

development of conceptual understanding and reasoning skills. She has given numerous

invited talks at international meetings and in university science departments. Dr. Heron is co-

Founder and co-Chair of the biannual “Foundations and Frontiers in Physics Education

Research” conference series, the premier venue for physics education researchers in North

America. She has held leadership roles in the American Physical Society (APS), the American

Association of Physics Teachers (AAPT), and the European Physics Education Research Group

(GIREP). She served on the National Research Council committee on the status and outlook

for undergraduate physics education and co-chaired an APS/AAPT joint task force that

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produced the report Phys21: Preparing Physics Students for 21st Century Careers. She also

serves as Associate Editor of Physical Review – PER. She is a Fellow of the APS and a co-

recipient of the APS Education award with colleagues Peter Shaffer and Lillian McDermott.

Dr. Heron is a co-author on the upcoming 2nd Edition of Tutorials in Introductory Physics, a

set of that has widely used and influential instructional materials.

Ricardo Karam is an associate professor at the Department of Science Education of the

University of Copenhagen and the leader of its research group on Didactics of Physics. He

holds a PhD in Physics Education from the University of São Paulo (Brazil) and was a

postdoctoral fellow of the Humboldt foundation at the universities of Hamburg, Dresden and

Helsinki. His research interests include the educational implications of the relationship

between physics and mathematics and the pedagogic value of the history of physics for the

teaching/learning of physics concepts.

Stamatis Vokos, an APS Fellow, investigates cognitive and affective aspects of teaching and

learning in physics, supporting systemic change efforts at the local, national, and international

levels. He has served on multiple committees of APS and AAPT and has chaired the National

Task Force on Teacher Education in Physics. He is currently professor of physics at California

Polytechnic State University in San Luis Obispo, where he also directs the STEM Teacher and

Researcher program. As part of the Physics Education Group at the University of Washington

from 1994 to 2002, Vokos contributed to the research and curriculum development efforts of

the Group, and played a leadership role in its local, regional, and statewide teacher education

efforts. At Seattle Pacific University from 2002 until 2016, he was instrumental in the

recruitment one of the most prolific groups of physics education researchers in the United

States. In the last two dozen years, he has collaborated with scores of senior and junior

researchers, having done some of his most treasured work over the years with his co-authors

on this chapter, Eugenia Etkina and Lane Seeley.

Stefan Sorge is a postdoctoral researcher at the Department of Physics Education at the IPN –

Leibniz-Institute for Science and Mathematics Education in Kiel, Germany. After graduating

from Martin-Luther University Halle-Wittenberg with the first state examination for

mathematics and physics teachers in 2014, he went to the IPN to pursue a PhD in physics

education. His research focus is on the development of pre-service and in-service physics

teachers’ professional competence.

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