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ORIGINAL ARTICLE
Designing and using professional development resourcesfor inquiry-based learning
Malcolm Swan • Daniel Pead • Michiel Doorman •
Ad Mooldijk
Accepted: 11 July 2013
� FIZ Karlsruhe 2013
Abstract This paper describes an attempt to design,
analyse and refine professional development (PD) resour-
ces that encourage the implementation of inquiry-based
learning (IBL). We describe the iterative development of
the resources in England with over 100 mathematics
teachers from secondary, tertiary and adult education and
then analyse the impact these resources had on teachers’
beliefs and practices and the issues arising. This evaluation
revealed that teachers had moved away from transmission-
based orientations, encouraged by the use of less structured
tasks and sample lesson plans, but some found it difficult to
adopt IBL pedagogies. The most significant issues for
teachers may be summarised as: confusing IBL with ‘dis-
covery’ learning; developing and managing collaborative
cultures within the classroom; and planning lessons that
adapt to the emerging needs of learners.
1 Introduction
We are currently witnessing an explosion of international
interest in mathematics teacher education, fuelled partly by
the desire to make mathematics accessible to all (Adler,
et al. 2005) and also by a growing concern to reverse the
decline in students’ enthusiasm for mathematics and the
consequent drop in the numbers of students pursuing sci-
entific careers (Mullis, et al. 2008; Rocard 2007). In
response, many initiatives have appeared in order to support
teachers in moving away from traditional transmission-based
approaches towards ‘inquiry-based’, ‘student-centred’,
collaborative pedagogies, such as those currently com-
missioned by the EU. One such project is the project
PRIMAS: Promoting Inquiry-based learning in Mathe-
matics and Science (PRIMAS 2012).
In the context of this reform agenda, the design of rep-
licable professional development models is an increasingly
important focus for research. Most teacher education
research is conducted with pre-service or practicing teach-
ers with whom researchers normally work and is not ‘scaled
up’ (Adler, et al. 2005). In our work, we are engaged in a
design-research process that seeks to progressively design,
analyse and refine professional development processes and
products that may be used to help stimulate PD led by
others. In this paper we describe the design of a professional
development (PD) intervention program for mathematics
teachers, describe its impact on the beliefs and practices of
the participants and the pedagogical issues that arise.
The PD program was intended to support the investi-
gation by teachers of effective inquiry based-learning
(IBL) pedagogies. In the ideal IBL classroom, students are
active participants. They observe and formulate questions;
if problems are too complex, they simplify or model; they
make reasoned assumptions, collect and analyse data, make
representations, and make connections with what they
already know. They interpret findings, check that they are
sensible and share them with others. The teachers’ role is
not to stand back and expect students to discover every-
thing for themselves; it is rather to scaffold the processes of
inquiry through the use of carefully designed tasks and
structured lessons (Artigue & Blomhoej 2013).
M. Swan (&) � D. Pead
Centre for Research in Mathematics Education, School of
Education, University of Nottingham, Jubilee Campus,
Wollaton Road, Nottingham NG8 1BB, UK
e-mail: malcolm.swan@nottingham.ac.uk
M. Doorman � A. Mooldijk
Freudenthal Institute for Science and Mathematics Education,
Universiteit Utrecht, PO Box 85170, 3508 AD Utrecht,
The Netherlands
123
ZDM Mathematics Education
DOI 10.1007/s11858-013-0520-8
Inquiry-based learning is a complex, multifaceted con-
struct. The PD program was designed to help teachers
study and synthesise effective component teaching strate-
gies. These include: choosing substantive tasks that are
extendable, encourage decision-making, creativity and
higher order questioning (Ahmed 1987; Watson & Mason
1998); working collaboratively and developing dialogic
talk (Alexander 2008; Mercer 1995); building on students’
prior knowledge (Black & Wiliam 1998); encouraging
students to critically examine alternative approaches and
achieve consensus (Inoue 2011). It is not the purpose of
this paper, however, to evaluate IBL or attempt to answer
its critics. Suffice it to say that following an international
report (Rocard 2007), the promotion of IBL is currently a
priority area for science and mathematics education in the
European Union.
In this paper, we seek insights into two research
questions:
1. How might PD resources be designed to foster
pedagogies supporting IBL?
2. What impact might such resources have on the
practices and beliefs of teachers, and what pedagogical
issues arise as they use them?
The first question will be addressed through a discussion
of the theoretical basis for the PD (Sects. 2 and 3) and its
iterative development (Sects. 4 and 5) using a design
research paradigm. The second question will be addressed
by considering empirical evidence for the effects of the PD
during its design and subsequent take-up as part of the
PRIMAS project (Sects. 6 and 7).
2 A theoretical approach to designing PD
Our work may be characterised as one of ‘design research’.
Design-based research is a formative approach to research,
in which a product or process (or ‘tool’) is envisaged,
designed, developed and refined through cycles of enact-
ment, observation, analysis and redesign, with systematic
feedback from end-users (Barab & Squire 2004; Bereiter
2002; Cobb, et al. 2003a; DBRC 2003, p. 5; Kelly 2003;
Swan 2006a, 2011b; van den Akker, et al. 2006). Its goals
are to create innovative tools for others to use, to describe
and explain how these tools function, account for the range
of implementations that occur and develop principles and
theories that may guide future designs. In this case, the
tools are a PD process and associated resources.
The design of the PD drew on social constructivist and
socio-cultural theories of learning. From this perspective,
teachers learn just as students do; they participate in social
practices and through active engagement develop and
internalise new ways of speaking and thinking. Goal-
directed and tool-mediated activity are fundamental to this
process and these are influenced by the rules (e.g. the
curriculum goals); the communities within which teachers
play a part (within the PD events and within schools) and
the roles of participants within these communities (Enge-
strom 1999; Jaworski 2008; Vygotsky 1978; Wertsch
1991).
The goals of the PD design were to support the collab-
orative investigation by teachers of effective IBL pedago-
gies. Conceptual and physical resources (the tools) were
found necessary to stimulate activity toward these goals.
These included novel ‘genres’ of classroom activity,
illustrated with classroom videos, and sample lesson plans.
The design was planned to work at two levels; activities for
the PD events were designed to mirror the intended
classroom experiences of students. Rules and communities
have a profound influence on the impact of PD. Teachers
must integrate IBL into the culture of the school with its
own curriculum goals, and they are expected to interact
with and justify their actions to colleagues. As for roles, the
power relations within PD are important. We do not want
to appear authoritarian, telling teachers how to teach and
limiting their creativity; neither do we want to deprive
teachers of the wisdom of well-researched models. We see
our role as PD designers, as selecting and suggesting
potentially powerful stimuli and tools (e.g. PD structures,
lesson plans) leaving it for teacher educators and teachers
to adapt, apply and evaluate in local contexts. These tools
should enable teacher educators and teachers to be chal-
lenged and to act reflectively in new ways.
Our PD is intended to allow cycles of discussions of
pedagogical issues, classroom challenges, and reflective
feedback (Even 2005; Muller, et al. 2011; Swan 2011a).
First, teachers work on collaborative classroom activities
that illustrate the pedagogical challenges of IBL. Second,
they watch other teachers using these same activities on
video. These are expected to provide a ‘challenge’ to
existing practices. Third, teachers are encouraged to adapt
and try the activities in their own classrooms, supported by
sample lesson plans. Fourth, teachers meet together to
share their classroom experiences, discuss the pedagogical
implications and reflect on the growth of new practices and
beliefs. This cyclical process is repeated at successive PD
events, as new pedagogical issues are addressed. This
process has resonances with Japanese Lesson Study (with
its pattern of investigation, planning, research lesson and
reflection (Lewis, et al. 2009; Stigler & Hiebert 1999))
though there are also major differences. Teachers are given
sample lesson plans to adapt and it is not assumed that
teachers are able to observe each other’s lessons nor that an
outside expert is available to support the extensive analysis
of all lessons. These differences we hope increase support
and scalability in a European context.
M. Swan et al.
123
3 Characterising teachers’ beliefs and practices
Ultimately, PD attempts to influence the beliefs and prac-
tices of teachers. Research has shown that teachers hold on
to their beliefs and practices tenaciously, and attempts to
dislodge or replace them through rational argument and
persuasion are usually unsuccessful (Kagan 1992; Nespor
1987). In our PD, rather than seeking to persuade teachers
to change beliefs so that they will behave differently, we
invite teachers to take risks and adopt new practices so that
they have cause to reflect on and perhaps modify their
beliefs (Fullan 1991). As Guskey (1986) noted, profes-
sional development programmes are mostly unsuccessful in
modifying beliefs, but when teachers are encouraged to
adopt a procedure and find that it improves student moti-
vation and achievement, significant changes in attitude
may be attained. The design of our PD thus attempts to
offer teachers opportunities ‘to doubt, reflect and recon-
struct’ IBL pedagogies in an unhurried, ‘safe’ environment
(Wilson & Cooney 2002). In evaluating our trials of the
materials we therefore sought to develop a framework for
describing the evolution of beliefs and practices.
Our description of the beliefs of teachers are based on
characterizations described by Ernest (Ernest 1991a,
1991b) and Askew (1997), elaborated in Table 1.
Ernest suggests that a teacher’s belief system has three
components; the teacher’s conception of the nature of
mathematics as a subject, of the nature of mathematics
teaching and of the process of learning mathematics.
Askew characterized the orientations of teachers towards
each of these components as transmission, discovery or
connectionist. These categories are ‘ideal types’ and an
individual teacher’s beliefs may combine elements of each
of them, even where these appear to conflict. These
categories were originally derived from studies of primary
teachers and we recognize that they take on different
interpretations in other settings. For example, we have
found secondary and further education teachers attended
particularly to the individual learning and collaborative
learning aspects of the ‘discovery’ and ‘connectionist’
orientations respectively. It may further be noted that both
discovery and connectionist orientations may foster IBL,
however both empirical and theoretical analyses would
suggest that connectionist orientations are more effective
(Askew, et al. 1997; Kirschner, et al. 2006).
Many researchers report inconsistencies between what
teachers say they believe about teaching and learning and
what they do in practice (Fang 1996). Beliefs may be
compromised in practice by day-to-day realities of class-
room management, student expectations, available resour-
ces and so on. One must also be suspicious of self-reporting
by teachers as they commonly claim changes that appear
exaggerated to an outsider. Often cited is the case study of
Mrs Oblier (Cohen 1990), who reported revolutionary
shifts to her practice yet, when observed closely, these
were revealed to be cosmetic. In evaluative trials of the PD
material, where opportunities for direct classroom obser-
vation was often limited, we therefore sought students’
views of teachers’ practices as well as teachers’ self-
reported practices. The evolution of the questionnaires used
is described more fully in Swan (2006b).
4 Structure and purpose of the PD units
The PD units were designed to support the investigation by
teachers of effective IBL pedagogies. The units are activ-
ity-based; and are built around the development and
Table 1 Beliefs about mathematics, teaching and learning
Mathematics is…Transmission: A given body of knowledge and standard procedures. A set of universal truths and rules that need to be conveyed to learners
Discovery: A creative subject in which the teacher should take a facilitating role, allowing learners to create their own concepts and
methods
Connectionist: An interconnected body of ideas which the teacher and the learner create together through discussion
Learning is…Transmission: An individual activity based on watching, listening and imitating until fluency is attained
Discovery: An individual activity based on practical exploration and reflection
Connectionist: An interpersonal activity in which learners are challenged and arrive at understanding through discussion
Teaching is…Transmission: Structuring a linear curriculum for the learners; giving verbal explanations and checking that these have been understood
through practice questions; correcting misunderstandings when learners fail to ‘grasp’ what is taught
Discovery: Assessing when a learner is ready to learn; providing a stimulating environment to facilitate exploration; and avoiding
misunderstandings by the careful sequencing of experiences
Connectionist: A non-linear dialogue between teacher and learners in which meanings and connections are explored verbally.
Misunderstandings are made explicit and worked on
PD resources for IBL
123
analysis of real lessons. Each unit includes a PD session
guide for a facilitator (who may be a teacher) and handouts
for participants, as well as sample classroom activities and
lesson plans. The video sequences show teachers trying
these materials with their own classes for the first time.
Their status is not to exemplify ‘best practice’ but rather to
illustrate the issues that arise as teachers attempt to modify
their own practice. They invite participants to share in a
learning process.
Moving towards an inquiry-based learning (IBL)
approach raises many pedagogical issues for teachers: How
can I encourage my students to ask and pursue their own
questions? How can I help students to follow up these
questions in profitable ways? How can I teach students to
work cooperatively and to learn from each other? The PD
is structured in a way that systematically tackles such
questions in seven units (Table 2). These units are freely
available online (Swan & Pead 2008, 2011) and are
intended to provide a cumulative experience, and the
gradual integration of the pedagogical challenges are
illustrated by lesson plans.
We illustrate the activity sequence with one unit, Asking
Questions that Promote Reasoning.
1. Make existing beliefs and practices explicit. Teach-
ers are asked to identify the different types of questions
they ask, the different functions served, the frequency
they use them, and the most common mistakes they
make when asking questions.
2. Consider ‘contrasting practices’. Teachers are asked
to reflect on the types of questions that are most likely
to encourage student inquiry, and are offered princi-
ples, drawn from research, for effective questioning
(Watson & Mason 1998). Participants are shown a
video of a teacher attempting to put such principles
into practice, are invited to identify occasions where
the teacher employs each principle and then consider
the effects of such questioning.
3. Develop a lesson plan. Teachers are offered a situation
and are asked to prepare an introduction, ground rules
for interaction (e.g. ‘think, pair, share’), intervention
strategies, and specific questions that may be asked at
different points in the lesson. To support this, they are
offered a lesson plan showing a possible structure for a
1-h lesson. An outline of this is shown in Table 3. The
full lesson plan is more detailed, offering sample
questions teachers might ask at various stages of the
lesson and typical student responses.
4. Teach a lesson. Teachers use their collaborative lesson
plan incorporating the questioning strategies they have
considered. They are encouraged to audio record some
of the questions they use to share in the post-lesson
discussion.
5. Analyse the lesson. After teaching the lesson, partic-
ipants meet again to share experiences of questioning
and reflect further at how students may be made more
aware of the value being placed on reasoning. Further
strategies for making reasoning more ‘visible’ are
discussed.
The important role of the teachers in the development of
these units must be mentioned. During early drafts of the
units, groups of teachers were invited to use them. Each
group met for 1 h to reflect on existing practice and discuss
the pedagogical focus of the unit. Teachers then taught
their own adaptations of the sample lesson plan, paying
particular attention to its pedagogical focus. Finally they
met up again to discuss what they had learned. This process
was videotaped and analysed. The issues raised by teach-
ers, their enacted lessons and their reflections were then
incorporated into the revised, now video-enhanced PD
resources. Thus the teachers’ own interpretations of the
pedagogical ideas were systematically built into the
resources.
5 The historical development of the PD units
The PD units evolved slowly over several years and have
now been adapted for different contexts. When opportunity
and funding has allowed, empirical data have been col-
lected to evaluate the impact of the PD and lesson plans on
teachers and students. In this section we describe some data
gathered from three early cycles of the design. These
involved a study with 44 teachers of low-attaining
16–19 year old students, a study with 24 teachers of adult
numeracy classes and a study with 30 secondary school
teachers (Table 4). Later in the paper, we report on more
qualitative data from later trials of the material as they have
been used more widely. At each stage of development, the
content of the PD was adapted to incorporate issues raised
by teachers.
The PD programs during the trials in Table 4 each
consisted of an initial two-day residential workshop, fol-
lowed by a number of 1-day follow-up meetings. In
between, teachers were invited to use the lesson plans in
their own classrooms.
The first version of the PD resources was constructed in
a limited domain: the use of collaborative learning activi-
ties in the teaching of algebra to low-attaining students
aged 16–19. A series of algebra lesson plans were devel-
oped with eight teachers over 1 year. These teachers were
filmed using and discussing the lessons and this was
incorporated into the PD. The lessons included specific
‘genres’ of classroom activities that were designed to
engage students’ concept development: classifying
M. Swan et al.
123
mathematical objects, interpreting multiple representa-
tions, evaluating mathematical statements, creating and
solving students’ own problems, and generalizing existing
problem situations. In the second year the resource was
used within a four-day course for 44 teachers spread over
6 months. In between meetings, teachers tried a variety of
classroom tasks within each genre. The results of this
empirical study are summarized below (Swan 2006a,
2007). The resulting resources were published and copies
were sent to all Further Education Colleges in England by
the Learning and Skills Development Agency, a govern-
ment body (Swan & Green 2002).
Subsequently, government funding (from the then DfES
Standards Unit) permitted us to develop a second version
of the PD resource and make this freely available to all
post-16 providers in England (Swan 2005). This was
Table 2 The PD units for PRIMAS
These are downloadable from: http://www.primas-project.eu
1. Student-led inquiry. In this unit, teachers are presented with phenomena and are then invited to pose and pursue their own questions. They
thus experience what it feels like to think like a mathematician or scientist and are then invited to try a similar activity with their own
students and reflect on the outcomes
2. Tackling unstructured problems. This unit invites teachers to consider the decisions that we make for students when we present them with
structured problems. It invites comparison of structured and unstructured versions of problems and considers the demands and challenges
unstructured problems present in the classroom. Teachers are invited to try out unstructured versions of textbook problems in their own
classrooms and report back on their experiences
3. Learning concepts through IBL. This unit considers how the processes of inquiry-based learning may be integrated into the teaching of
content. Often, these two aspects of learning are kept separate: we teach content as a collection of facts and skills to be imitated and
mastered, and/or we teach process skills through investigations that do not develop important content knowledge. The integration of
content and process raises many pedagogical challenges. The processes under consideration here are: observing and visualizing, classifying
and creating definitions, making representations and translating between them, finding connections and relationships, estimating,
measuring and quantifying, evaluating, experimenting and controlling variables
4. Asking questions that promote reasoning. This unit contains a selection of stimuli designed to help teachers to reflect on: characteristics of
their questioning that encourage students to reflect, think and reason; ways in which teachers might encourage students to provide
extended, thoughtful answers, without being afraid of making mistakes; the value of showing students what reasoning means by ‘thinking
aloud’ as problems are worked on in collaborative classroom environments. As before, teachers systematically try to develop their own
classroom questioning and report back on what happens
5. Students working collaboratively. This unit is designed to offer teachers the opportunity to reflect on the characteristics of student–student
discussion that benefit learning; to recognize and face their own concerns about introducing collaborative discussion; to explore researched
techniques for promoting effective student–student discussion; and to consider their own role in managing student–student discussion.
They plan and carry out discussion-based lessons and report back on what happened
6. Building on what students already know. This unit considers the different ways teachers can use formative assessment techniques to make
effective use of students’ prior knowledge. It focuses on the following questions: How can problems be used to assess performance? How
can this assessment be used to promote learning? What kinds of feedback are most helpful for students and which are unhelpful? How can
students become more engaged in the assessment process?
7. Self and peer assessment. This unit encourages discussion of the following issues: How can we help students to become more aware of IBL
processes, and their importance in problem solving? How we can encourage students to take more responsibility for their own learning of
IBL processes? How can students be encouraged to critically assess and improve each other’s work?
Table 3 A generic lesson plan for a 1-h lesson
Teacher introduces lesson (5 min) Students are given an unfamiliar task, for which they have not been explicitly prepared. The teacher
engages interest in the problem, introducing the context and encouraging students to formulate
questions
Individual thinking time (5 min) Students are encouraged to work independently and develop initial questions/ideas for approaching
the task
Students work collaboratively (20 min) Students work in groups of two or three on the task. Teacher monitors work and seeks ideas that
might be shared with whole class later. Teacher interacts with students that are stuck offering
strategic guidance rather than technical help
Whole class shares approaches being
used (10 min)
Teacher selects students to present their approaches to whole class. Teacher introduces fresh ideas
that have not been considered. (‘‘Here are ideas I observed in another class’’). Students discuss the
possible approaches—strengths and weaknesses
Students continue to work collaboratively
on task (10 min)
Students have second attempt using ideas that have been shared
Whole class reports on their reasoning.
(10 min)
As students report on reasoning used, teacher draws attention to significant ideas, makes connections
and generalisations to other work. Teacher may conclude by modelling reasoning for class
PD resources for IBL
123
developed over 2 years, and expanded the content from
algebra to relate to other content. Over 50 lesson plans
were written and piloted with 90 teachers. Again videos
were made and incorporated into the PD materials.
Unfortunately, however, no systematic study of the effects
of this PD was made. During regular inspections of post-16
education institutions, however, Ofsted1 came across these
resources in use and they noted their use in their report:
These materials encouraged teachers to be more
reflective and offered strategies to encourage students
to think more independently. They encouraged dis-
cussion and active learning lessons. While some
colleges were just dipping into the resources, a few
had used the full package to transform teaching and
learning across an entire mathematics team.
(Ofsted 2006 paras 32, 33).
Then a third UK government agency (the Department
for Education and Skills), embarked on a further program
(Maths4Life) to improve the teaching of adult literacy and
numeracy. We were offered funding to develop PD
resources for this and used this as an opportunity to further
develop the resources. This time, a formal evaluation was
conducted (Swain & Swan 2007, 2009; Swan & Swain
2010) and some of the results from this are shown below.
Up to this point, the emphasis in the PD resources had
been concerned with the pedagogical skills necessary for
teaching mathematical concepts. A further project, funded
by an independent charity, Bowland Maths, allowed us to
further extend this work to consider the development of
mathematical processes with lower secondary classrooms.
These processes included those involved in mathematical
modelling: simplifying and representing, analysing and
solving, interpreting and evaluating, communicating and
reflecting. This was the first version of the resources that
incorporated the IBL units in Table 2 (Swan & Pead 2008).
This was evaluated with funding from one local district in
England (Somerset). The results are summarized below
(previously unpublished). Currently, the PD materials are
being adapted for secondary classrooms around Europe as
part of the PRIMAS project (Swan & Pead 2011). This
adaptation involves removing specific cultural content
(such as references to the English National Curriculum)
and including some emphasis on science learning. We are
currently redeveloping the resources to support the devel-
opment of the mathematical practices (or processes) in the
common core state standards in the US (Swan, et al. 2012).
Evaluation of the use and impact of these is still in its early
stages.
6 The impact of the trials of the PD units on teachers
Teachers were asked to rate their own beliefs by assigning
weightings to each of nine descriptive categories (Table 1).
These were cross-validated with more qualitative descrip-
tions which showed remarkable consistency, when checked
by independent researchers. The results concerning chan-
ges in beliefs of the teachers in England during the pilot
studies (averaging over Mathematics, Learning and
Teaching) are given in Table 5.
The FE teachers and the secondary teachers both began
with predominantly transmission views. Both groups were
focused on getting students through the examinations. The
adult numeracy teachers, on the other hand, had lower
expectations, and worked with much smaller classes that
included students with severe learning difficulties. These
teachers had a different profile, and the discovery orien-
tation was more evident in this group.
Generally speaking, in the post-questionnaire in all three
studies, teachers reported a shift away from transmission
orientations (see Table 4). Initially the percentages of
Table 4 Three formative trials of the PD development
Further education (FE) teacher study Adult numeracy teacher study. Secondary teacher study
Teachers
involved
44 teachers from 44 post-16 colleges (35
provided data)
24 teachers from 12 organizations
(17 provided data)
30 teachers from 17 schools (21 provided
data)
PD structures 4 days over 6 months (2 ? 2 9 1 days) 5 days over 9 months
(2 ? 3 9 1 days)
6 days over 10 months.
(2 ? 4 9 1 days)
Mathematical
focus
Algebraic concepts Mathematical concepts Mathematical concepts and processes
PD content
addressed
(Table 2)
3, 4, 5. 2, 3, 4, 5, 6. 1, 2, 3, 4, 5, 6, 7.
Data collection Teacher and student questionnaires.
Limited lesson observation. Interviews
Teacher questionnaires. Extensive
lesson observation. Interviews
Teacher and student questionnaires.
Limited lesson observation. Interviews
1 Ofsted, the Office for Standards in Education, is an independent
national inspection service that reports directly to Parliament in the
UK.
M. Swan et al.
123
teachers expressing overall preferences for Transmission,
Discovery, Connectionist were respectively 44:22:23. After
the PD these ratios were 16: 21:53.
In Table 5 we have aggregated each of the 71 teachers’
reported orientations and allocated them to the most pre-
dominant one.
The trajectories of these changes are particularly inter-
esting. Some of the transmission teachers claimed little
change in their beliefs. These beliefs had been long-held
and were associated with a need to be ‘‘in control’’ and a
belief that students could not cope with IBL pedagogies:
Students are more confident with an imitation
approach. Only stronger students can cope with non-
linear dialogue.
(FE teacher).
Others blamed examination pressures for an unwilling-
ness to change:
I feel that these (lessons) are very good for learning
breakthroughs, but I don’t think they are going to get
the bulk of my students through their exams. I think
you need a ‘crammed’ approach. This is the big issue
for me. I’d be quite happy to use these materials
every lesson, the time went ‘like that’ and it’s great to
see people not yawning and actually enjoying them-
selves. You don’t have discipline problems. But, I
feel that for an exam, I’ve got to feel that I am giving
them the knowledge that they need to pass that exam
and I feel that I can do that through the traditional
approaches and a bit of bullying.
(FE teacher)
Some teachers moved from ‘transmission’ towards
‘discovery learning’ orientations. These teachers clearly
recognized the shortcomings of transmission methods and
that ‘telling’ was not an effective way of helping learners to
develop concepts and processes. In reaction to this, it
appeared that they moved to a position in which they
seemed uncertain of their own role in the classroom,
beyond that of ‘facilitator’:
It is allowing them to make discoveries for them-
selves rather than you writing it up on the board […]
It is their discovering, not mine; it is nothing to do
with me really. I have just to keep an eye on it.
(Adult numeracy teacher).
Three-quarters of the teachers that began with a dis-
covery orientation moved towards a connectionist orien-
tation. These teachers appear to have adopted a more
interventionist role, and were prepared to challenge and
discuss concepts and approaches with groups of students in
a collaborative manner.
These and other qualitative data suggested to us that
many teachers may follow a transmission to discovery to
connectionist trajectory as they at first withdraw support
from students and then recognise the need to redefine their
own role in the classroom. If, as some researchers assert
(Askew, et al. 1997; Kirschner, et al. 2006), discovery
approaches are less effective than transmission-based ones,
this may have the consequence that teachers at first become
less effective, before they become more effective as they
develop along this trajectory.
6.1 The impact on practices
We further examined both teachers’ and students’ percep-
tions about the changes that had occurred in teachers’
practices. Both open and closed response questionnaires
were used. These were given by the researchers to teachers
during the PD sessions and by the teachers to students
in the classrooms. The rationale and design of these
questionnaires is given in Swan (2006b). On pre- and post-
questionnaires, teachers were asked to describe how
frequently they now displayed 25 classroom behaviours on
a 5-point scale: 1 = almost never to 5 = almost always.
The results (Table 6) are ranked in order of the overall
changes in means. Teachers described their own practices
as mostly ‘teacher-centred’ at the outset of the PD and
reported that these had changed towards more ‘student-
centred’ practices by the end. This is reflected in the table
Table 5 Trajectories of changes in predominant beliefs (%)
From To
Transmission (%) Discovery (%) Connectionist (%) No overall orientation (%) Total (%)
Transmission 15.1 11.0 11.0 6.8 43.8
Discovery 0.0 2.7 16.4 2.7 21.9
Connectionist 0.0 5.5 17.8 0.0 23.3
No overall orientation 1.4 1.4 8.2 0.0 11.0
Totals 16.4 20.5 53.4 9.6 100.0
PD resources for IBL
123
by the S statements increasing in frequency, while the T
statements decreased in frequency (these labels did not
appear on the questionnaire). Teachers reported more col-
laboration and discussion (including the discussion of
mistakes) giving more choice about the questions to tackle,
fewer graded exercises, students were encouraged to be
more creative, lessons were more responsive to student
needs and less predictable.
As we have said, self-reporting is unreliable, so to
confirm teachers’ accounts, we asked students to describe
their teachers’ behaviours. In the FE project, this was only
done on one occasion as the course was short and at the
Table 6 Changes in teachers’ practices (self-reported)
Further
education
n = 35
Adult numeracy
n = 17
School teachers
n = 21
All teachers
n = 73
Pre-
mean
Post-
mean
Pre-
mean
Post-
mean
Pre-
mean
Post-
mean
Pre-
mean
Post-
mean
Change
Post-
pre
16 S Learners work collaboratively in pairs or small
groups
2.5 3.6 3.4 4.3 2.9 3.5 2.8 3.7 0.9
15 S Learners learn through discussing their ideas 2.6 3.5 3.7 4.3 3.1 3.7 3.0 3.7 0.7
5 S Learners choose which questions they tackle. 1.9 2.6 2.4 2.9 2.1 2.9 2.1 2.8 0.6
12 S I am surprised by the ideas that come up in a
lesson
2.0 2.6 3.0 3.5 2.3 2.9 2.3 2.9 0.5
28 S I jump between topics as the need arises 2.5 2.8 3.0 3.8 2.4 3.0 2.6 3.1 0.5
27 S I encourage learners to make & discuss mistakes. 2.7 3.2 3.7 4.2 3.1 3.6 3.0 3.5 0.5
17 S Learners invent their own methods 1.9 2.4 2.6 3.2 1.8 2.4 2.0 2.6 0.5
7 S Learners compare different methods for doing
questions.
2.2 2.9 3.1 3.7 2.7 2.7 2.5 3.0 0.5
6 S I encourage learners to work more slowly 1.9 2.3 2.4 3.2 1.7 2.2 2.0 2.5 0.5
11 S I draw links between topics and move back and
forth between topics
3.0 3.4 4.1 3.9 2.5 3.1 3.1 3.4 0.3
23 S I teach each learner differently according to
individual needs.
2.3 2.8 3.5 3.6 2.6 2.6 2.7 2.9 0.3
22 S I find out which parts learners already understand
and don’t teach those
2.2 2.6 2.4 2.4 2.8 3.0 2.4 2.7 0.2
3 T Learners use only the methods 1 teach them 3.0 3.0 2.3 1.9 3.2 2.9 2.9 2.7 –0.2
2 T Learners work on their own, consulting a
neighbour from time to time.
3.5 3.1 2.7 2.9 3.0 2.7 3.2 2.9 –0.3
21 T I only go through one method for doing each
question
3.3 2.8 1.7 1.5 2.2 2.2 2.6 2.4 –0.3
25 T I tend to teach each topic separately. 3.2 2.9 2.7 2.2 3.2 3.0 3.1 2.8 –0.3
8 T I teach each topic from the beginning, assuming
they know nothing.
3.2 2.8 2.2 1.5 2.4 2.2 2.7 2.3 –0.4
10 T I try to cover everything in a topic 3.8 3.2 2.3 1.6 3.1 3.2 3.2 2.8 –0.4
14 T I tend to follow the textbook or worksheets
closely
3.3 2.7 1.9 1.4 2.4 2.2 2.7 2.3 –0.4
9 T I teach the whole class at once. 3.9 3.4 3.1 2.8 3.8 3.3 3.7 3.2 –0.5
1 T Learners learn through doing exercises 3.7 3.2 2.9 2.6 3.4 2.8 3.4 2.9 –0.5
13 T I avoid learners making mistakes by explaining
things carefully first.
3.2 2.7 2.6 2.1 2.7 2.2 2.9 2.4 –0.5
26 T I know exactly what maths the lesson will contain. 3.9 3.5 3.2 2.5 3.6 3.0 3.7 3.1 –0.5
19 T I tell learners which questions to tackle 4.1 3.5 2.6 2.4 3.6 2.9 3.6 3.0 –0.6
4 T Learners start with easy questions and work up to
harder questions
4.0 3.3 3.8 3.1 3.7 3.2 3.9 3.2 –0.6
Means of frequencies of self-reported practices before and after the PD, ordered by changes. 1 = almost never; 5 = almost always. First column
indicates order of items on questionnaire (standard deviations are omitted from the table for clarity, for all statements 0.7 \ SD \ 1.2)
M. Swan et al.
123
beginning students were unable to comment on teachers’
practices. We also found it difficult for the adult education
teachers to administer questionnaires to students of very
limited attainment. The results from the secondary schools
are reported below in Table 7. The student statements were
derived from the teacher statements by excluding those that
refer to a teacher’s motivation for behaving in particular
ways and strategic issues such as curriculum design and
coverage. It was felt that students would be unable to
respond to these. Noyes (2012) also used these items in a
large survey with over 2,900 11-year-old students in state-
funded comprehensive schools in the Midlands of England
and the means from this data are presented for comparison.
The rank order of teaching behaviours reported in the
pre-questionnaires for the Noyes data and the secondary
schools is almost identical. The most predominant style,
according to students, appears to be worksheet or textbook-
led; the teacher selects the questions, demonstrates the
method, expects students to practice this intensively,
working mostly on their own.
Comparing the pre- and post-questionnaire data, there is
evidence that the incidence of pair and group work, dis-
cussion and making connections between topics have all
increased, and teachers are beginning to discuss multiple
ways of doing questions. Comparing with the Noyes data,
in these schools, there is perhaps less emphasis on fol-
lowing textbooks and imitating procedures than in other
schools. A factor analysis was conducted on these state-
ments and this showed that they do not form a uni-
dimensional scale. The S statements taken alone, however,
are acceptably consistent (Cronbach alpha = 0.722) and
the pre-post changes using this measure are statistically
significant (Table 8).
7 Issues arising for teachers
In the above projects, and as the PD resources have been
disseminated more widely across the EU as part of the
PRIMAS project, we have had many opportunities to
observe and interview teachers. In this section we draw
together and exemplify some of the major findings that
have emerged in the United Kingdom and in the Nether-
lands. In order to preserve the relationship between the
findings and the contexts involved (adult education, school
education; UK, Netherlands), we present these issues study
by study rather than in a thematic manner. We then syn-
thesise the common issues that have emerged.
The principles underlying IBL are complex and teachers’
appropriation of them is often gradual, and at first, partial. In
the UK-study involving adult numeracy teachers (Swain &
Swan 2009), for example, 49 semi-structured teacher inter-
views and 110 classroom observations were carried out, and
each teacher was observed between 3 and 6 times. These
findings showed that some teachers had initially adopted
superficial understandings of IBL pedagogies, seeing IBL as
merely adding ‘fun’ or ‘enrichment’ to an otherwise dull
curriculum. Others, as noted above, confused IBL with
‘discovery learning’ and did not support students sufficiently
in their learning. This study also attempted to identify
aspects of IBL pedagogy that appear to be more accessible
for teachers and those that appear more problematic. By the
end of the PD, a majority of the adult education teachers
were observed effectively and consistently using unstruc-
tured, collaborative tasks, organising co-operative group
work and using more probing questions to assess and pro-
mote reasoning. Teachers, however, found it much more
difficult to develop connections and build on students’ prior
knowledge. These aspects require sound content knowledge
and an ability to flexibly adapt teaching to students’ needs
‘in the moment’. They also found it particularly difficult to
focus on teaching process skills for problem solving.
The issues arising from the secondary school study were
distilled from both oral and written responses made during
structured debriefing sessions with the 30 teachers. A
variety of issues emerged, which we list below. Teachers
consistently expressed surprise at increased levels of stu-
dent engagement and creativity when engaging in IBL
activity. They reported that the lesson plans were shifting
the emphasis from ‘answer-getting’ to analysing and rea-
soning, particularly when students were encouraged to
assess the work of others (in units 6 and 7). A few claimed
that this revealed misconceptions of which the teachers
themselves had been unaware. Some began to recognise the
need to reduce their expectations of what they might
‘cover’ in a lesson. Rather than completing lists of ques-
tions, they were exploring fewer, richer tasks in multiple
ways. They began to recognise the power of giving for-
mative feedback; rather than ‘correcting’ answers, asking
follow-up questions to cause further reflection.
These teachers also reported many anxieties and strug-
gles. Their main fears concerned the introduction of col-
laborative learning. They commented that discussions
reduced the ‘pace’ of lessons and made it more difficult to
‘cover’ the required curriculum content. Several reported
that their students did not want to discuss or explore
mathematics. Many students had difficulty turn-taking,
listening and elaborating each other’s reasoning, and talked
in ‘disputational’ rather than ‘exploratory’ ways (Mercer
1995). This led to concerns about maintaining classroom
control. Teachers were also concerned with accountability
issues and frequently referred to the ephemeral nature of
discussions and the lack of individual written outputs.
‘‘What hard evidence will I have of learning?’’2 The Cronbach alpha for the T statements was 0.63.
PD resources for IBL
123
In the Netherlands, the PD materials were taken up and
used as part of the PRIMAS project. Twenty teachers from
two secondary schools joined a PD program based on the
resources, from different disciplines. In one school the
teachers chose to join the program (they were allowed to
choose from a school-selected offer of PD-activities). The
teachers from the other school were asked to join by their
school authority as part of their obligatory professional
development. The teachers varied in level of experience.
Teachers were paired, so that they were able to support
each other in planning and observing lessons. They were
asked to report on lessons through structured feedback
forms (including topic, plans, experiences and new
insights). Initially, teachers were sceptical of letting the
students pose their own questions and follow their own
lines of inquiry, but they nevertheless agreed to try. They
met with mixed success. The examples below are drawn
from this work.
A mathematics teacher created a worksheet for
experimenting and explaining parallax in a ninth
grade class. The teacher hoped that the students could
find explanations within small groups. The questions
on the worksheet were open and the students did not
get any guidance during the process of searching
proofs or explanations. The teacher ran from group to
group to solve small questions or misunderstandings.
She reported that: ‘‘these kind of activities might be
suitable for better students, but not for whole class
group work’’.
(Researcher notes)
When asked to report about their experiences with new
pedagogies the teachers also reported that some students
felt uncomfortable with the new approaches. Without
careful guidance and scaffolding of their inquiry process
they became lost and unclear about the purpose of their
activity. This example illustrates again the danger of
equating IBL with ‘discovery’ approaches. One cannot
expect minimal guidance to result in learning ‘unless stu-
dents have sufficiently high prior knowledge to provide
internal guidance’ (Kirschner, et al. 2006). Our lesson
plans, however, do not advocate minimal guidance
throughout the lesson, but rather strategic support at times
of need. Teachers that used these plans met with greater
success:
Table 7 Changes in teachers’ practices (student-reported)
The teacher: Student reports
n = 330
Means
(Noyes)
Pre-
mean
SD Post-
mean
SD Change
Post–
pre
9 S Asks us to work in pairs or small groups 2.6 1.0 3.1 1.0 0.5 2.7
6 S Shows us how topics link together (like algebra and shape) 3.2 1.0 3.4 1.1 0.2 3.2
8 S Expects us to learn through discussing our ideas 3.1 0.9 3.3 1.0 0.2 3.5
4 S Lets us choose which questions we do 1.8 1.0 2.0 1.0 0.2 1.8
14 S Encourages us to make and discuss mistakes 3.5 1.2 3.6 1.1 0.1 3.4
10 S Lets us invent and use our own methods 2.6 1.1 2.7 1.2 0.1 2.6
5 S Asks us to compare different methods for doing questions 2.9 1.0 3.0 1.0 0.1 3.1
1 T Asks us to work through practice exercises 3.6 1.1 3.6 1.0 0.0 3.7
3 T Shows us which method to use, then asks us to use it 3.9 1.0 3.8 1.0 –0.1 4.2
2 T Expects us to work mostly on our own, asking a neighbour from time to 3.6 1.0 3.5 1.0 –0.1 3.8
7 T Expects us to follow the textbook or worksheet closely 3.8 1.0 3.6 1.0 –0.2 4.2
11 T Tells us which questions to do 4.4 0.8 4.2 0.9 –0.2 4.5
12 T Shows us just one way of doing each question 3.0 1.1 2.7 1.1 –0.3 3.2
13 T Teaches each topic separately from other topics 4.0 0.9 3.7 1.1 –0.3 Not used
Means of frequencies of student-reported practices before and after the PD programme, ordered by changes. A five-point scale indicating
perceived frequency of use is used: 1 = almost never; 5 = almost always. The first column indicates the order of items on questionnaire
Table 8 Changes in the ‘Student-centred’ mean rating
Pre-PD Post-PD Change in
meanMean SD Mean SD
‘Student-centred’ mean
rating
2.84 0.65 3.05 0.59 ?0.22**
** p \ 0.01, paired samples t test (n = 329)
M. Swan et al.
123
A physics teacher took an existing, highly structured,
‘‘cookbook’’, practical assignment from his own
curriculum and created a less guided version. The
original task led students step-by-step to deduce a
conclusion about the formula for converging lenses.
The teacher revised his pedagogical approach, fol-
lowing the lesson plan from the video. At first the
students were asked to think what they could inves-
tigate with the material they had been given. Students
made suggestions concerning the relationship
between the distance between the object and the lens
and the size of the image obtained. After five minutes
the teacher discussed students’ suggestions, priori-
tised possible questions to investigate, invited stu-
dents to choose a research question and then continue
with their investigation. The teacher monitored
groups and restricted feedback to those relating to
process. During the final discussion students’ findings
were presented. While no student had discovered the
formula, they had become more aware of the rela-
tionships with lenses when compared to the tradi-
tional cookbook approach. The teacher was happy
with the increased motivation of the students, their
creativity in trying to find a formula, and wanted to
change practical assignments more often into this
approach.
(Researcher notes)
From an analysis of the feedback from teachers, we
found that when the teacher used the lesson plans provided
to scaffold the students’ inquiry processes, or modelled
their own planning on these examples, the lessons were
consistently reported as more successful. Sixteen of the 18
feedback forms supported this pattern. In summary, the
Dutch teachers removed the structure from textbook
activities for experimenting with IBL-related pedagogies.
The success of their reported experiences was related to the
care with which they prepared lesson plans to structure
student activity. It is important to note here that we are not
talking about simply replacing the structured guidance
embedded within textbook tasks with similar structured
guidance given by the teacher. The structure within the
lesson plans refers not so much to cognitive features, but
rather to structuring the order and type of interaction that
students engage in. Thus a structured plan may include
periods for individual work, pair work, group discussion,
reporting back, evaluation and so on. It also attempts to
anticipate student difficulties and organise planned
responses that lead to students further engaging in reflec-
tion and discussion. The provision of adaptable sample
lesson plans that incorporate such features appear to be
valuable resources for developing new pedagogies for
inquiry-based learning.
We are currently undertaking further design research
into the use of lesson planning to address the issues that
have emerged from this paper. Only one example will be
given. As we have noted, many teachers found it difficult to
anticipate student approaches to open, unstructured tasks.
In consequence, they struggled to respond appropriately
and strategically to student learning needs as they arose in
lessons. In response to this, we are now studying the effect
of sample lesson plans that include the use of assessment
tasks that students complete, individually, before lessons,
together with a list of difficulties that students typically
experience with these tasks and sample strategic questions
that might move students’ thinking forward. In the PD,
teachers are invited to assess their own students’ work on
the assessment tasks, identify issues that are pertinent and
use the sample questions as models for their own ques-
tioning. These questions may then be written into the
teachers’ own lesson plans. These approaches are being
trialled in current PD materials supporting the introduction
of mathematical practices in the US (Swan, et al. 2012).
8 Concluding comments
At the start of this paper we set ourselves two research
questions. We first set out to study how PD resources may
be designed to foster pedagogies that support IBL. Our
discussion illustrates something of the complexity and
difficulty in designing and researching such resources in an
authentic context. The PD exhibited many features that are
reported to be ‘effective’: it was sustained, related to local
contexts (Cobb, et al. 2003b), involved teachers in active
and collective participation (Garet, et al. 1999), focused on
teachers’ knowledge of content, pedagogy and principles
(Hammerness, et al. 2005) and offered support for trans-
lating new ideas into everyday practice (Lee & Wiliam
2005). The ‘tools’ that were devised stimulated reflection
and discussion on key pedagogical issues and the diffi-
culties noted have provided ideas that will be incorporated
into subsequent designs. The design process is continually
evolving. Teachers are involved in the design, particularly
in providing examples of their practice, for other teachers
to scrutinise.
The second question set out to study the potential impact
of such resources and the pedagogical issues that arise for
teachers. The teachers claimed changes to their beliefs and
practices, and that students also confirmed changes to
teachers’ practices, but to a lesser degree. This may be due
to a combination of the teacher unconsciously adopting a
‘melange’ of old and new practices (Cohen 1990), and the
delay between a teacher first adopting and reporting a new
practice and students’ noticing it being used in a sustained,
embedded manner.
PD resources for IBL
123
Teachers frequently reported to us that their under-
standing of the new pedagogies developed slowly, and that
they continued to struggle with embedding and sustaining
them. The most significant broad issues for teachers may be
summarised as: confusing IBL with ‘discovery’ learning,
fostering the development of processes, developing and
managing collaborative cultures within the classroom and
planning lessons that adapt to the emerging needs of
learners.
We recognise many limitations of the work reported.
While we have paid some attention to the culture within the
PD events themselves, we have paid little to the various
school-based cultures in which teachers work. In future
designs we will need to give greater attention to this. In
particular, we are beginning to recognise the importance of
designing resources that teachers can use with colleagues
and senior managers to help inform and evolve these local
cultures.
Finally we note that, with the international effort being
poured into PD that promotes inquiry-based learning there
is an urgent need for design research to provide more
efficient products and processes for PD. We hope that the
products and processes described here and available on the
websites will be a modest, but valuable contribution to this
work.
Acknowledgments This paper is based on work carried out within
the following funded projects: Bowland Maths funded by the Bow-
land Charitable Trust (UK); ‘Learning Mathematics through Discus-
sion and Reflection’ funded by the Learning and Skills Development
Agency (UK); ‘Improving Learning in Mathematics’ funded by the
Standards Unit, Department for Education and Skills (UK); ‘Math-
s4Life’ funded by National Research and Development Centre for
adult literacy and numeracy (UK), and the PRIMAS project funded by
the European Union Seventh Framework Program under grant
agreement n� 244380.
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