Authentic Contexts in Early College Mathematics Lauretta Garrett, MathematicsMaria Calhoun Charlton, Mechanical EngineeringLi Huang, Psychology and Sociology

TM

Authentic . . . What?

What does “authentic” mean? “Real or genuine: not copied or false”

“True and accurate”“Made to be or look just like an original”

(www.merriam-webster.com)

Authentic TasksAuthentic tasks – “situated in meaningful contexts that reflect the way tasks might be found and approached in real life” (Harris & Marx, 2009, para. 1)

Authentic AssessmentAuthentic assessment – can be used with authentic tasks (Rhodes & Finley, 2013)

assesses what we really value (Rhodes & Finley, 2013,

Arter & Spandel, 1992)

Authentic Learning Authentic learning – “learning by doing” involving “real-world, complex problems” (Lombardi, 2007, p. 2)“It was the primary mode of learning for apprentices” (Lombardi, 2007, p. 2)

http://www.life2point0.com/2007/06/the-joy-of-wall.html

Why is this Hard?

Tasks may need extended time

If it’s a new way of learning It must be carefully sequenced and scaffolded

It’s hard to make everything personally meaningful to everybody

May not be an easy solution to the problem being examined

Hard to fit into the way school is run and done

(Harris & Marx, 2009)

Authentic Contexts: A Setting for Authentic Learning“opening the classroom to the complexity of the real world”

“countering the effect of oversimplification”

“bringing reality from outside of [the school] back into classrooms”

(Strobel, Wang, Weber, & Dyehouse, 2013, p. 143)

Authentic Contexts Provide Students with . . .

Material for complex realistic problems

Mathematical connections to their everyday lives

Applications of mathematics in their future careers

Authentic Contexts Help Teachers . . .

Bring in authenticity within a clear framework

Foster authentic learning through authentic settings that Involve complex problem solvingClarify “the way [real world] tasks [are] found and approached” (Harris & Marx, 2009)

Authentic contexts: External Dimensions

Context authenticity – the context actually uses data collected in a professional field

Task authenticity – the students are doing something people might really do in their profession

Impact authenticity – students’ products are actually used outside of the classroom

(Strobel et al., 2013, p. 144)

Authentic Contexts: Personal Dimensions

Personal authenticity – projects involve something “close to students’ own [lives]”

Value authenticity – projects answer genuine personal questions or satisfy genuine community needs

(Strobel et al., 2013, p. 144)

Reflection and Sharing

Take a minute to reflect on where you see this in your practice already.

The Dimensions in Teaching Strategies Engaging students in issues of social justiceWanting to know why things are the way they are motivates learning (Gutstein, 2013)Context authenticityPersonal authenticityValue authenticity/Impact authenticity

Using technology to facilitate data analysisContext authenticity

The Dimensions in Teaching Strategies

Problem based learning:Complex problems similar to those professionals might tackle (Strobel et al., 2013)Context authenticity Task authenticity

Analogies: Connect abstract concepts to something meaningful to students (The University of Kansas, 2014) Context authenticityPersonal authenticity

Our Experiences

Pre-calculus Algebra

Psychological Statistics

Probability and Statistics for Manufacturing

Pre-Calculus Algebra: Analogy – a simple way to increase authenticityObjective: Students will understand and

be able to describe the nature of a functional relationship using different settings and different representations. Assignment: Students were asked to

describe real-life examples exhibiting the qualities of a functional relationship Personal authenticity – they chose

topics of interest to them

Jonelle’s Example “When in a relationship it should be 2 people and not extra people. That would be called cheating. . . . A boy is not supposed to date 2 girls at a time.”

Jonelle’s Example

Pre-Calculus Algebra: Geogebra Project(www.geogebra.org)

Objective: Improve familiarity with the properties of functions by connecting with a topic of interest

Preparation: Training in statistical features of Geogebra, including polynomial regression

Assignment (Worth 20 points)Find or invent data about a topic of interest that

demonstrates the properties of a functional relationshipEnter that data into the spreadsheet in GeogebraFind polynomial function that, within that limited

domain, most closely models the dataPresent their information and respond to questions

Sylvia’s Work

Thomas’s Work

“. . . Because of my strong allergies that I have to pollen”Used “”The Weather Channel’ & ‘Allergy Alert’ android app”“I am extremely allergic to pollen and wanted to see the data in mathematical form, instead of on an android app.”

Pre-Calculus TopicsPersonally connected Data Exhibiting a Functional Relationship can help students understand The Meaning of Function Properties of FunctionsTypes of FunctionsLinearQuadraticPolynomialExponential Logarithmic

Project based-learning

Authentic, motivational, and enjoyable tool for learners .

Students take charge of their own learning

create their own knowledge Do rigorous and relevant work (Roessingh & Chambers, 2011).

Project-based Learning: 5 Criteria Projects are central to the curriculum

Activity connects to conceptual knowledge

Investigation must involve knowledge construction

Investigation must answer a question

Learner centered and largely student driven.

Authentic - simulates real-life challenges.

(Thomas, 2000)

Psychological Statistics: Project based learning

Objective: Help students understand the nature of Statistics and its role in their future work

Assignments: Progressive data collection and analysis assignmentsContext authenticityThinking criticallyAnalyzing and evaluating informationWorking cooperativelyCommunicating effectively

Project 1: Understanding Psychological Research

Pick a specific topic covered in the course (e.g., the effects of prenatal alcohol exposure on child cognitive development.) Search PsycINFO, ERIC Clearing House,

Medline, etc. Find out what research has been done on

this topic recently. Write a brief summary on what has been

done in this area; include the abstracts in an appendix.

Project 2 : Understanding graphic representations

Gather cigarette and alcohol ads from popular magazines.

Turn these ads into health warnings by superimposing important health statistics.

Use graphic images of newborns affected by alcohol or tobacco. Make a booklet of ads, or a poster including information from many ads.

Project 3 : Connecting knowledge to real life

Identify an issue covered in the media.

See how it is covered differently by different papers, magazines, or TV programs.

Keep a diary of its coverage similar to the one used in the first exercise.

Summarize themes in the coverage.

Project 4: Interpreting the results in psychological research

Review and evaluate a recent research article on a course topic.

Review the research design and the statistical analyses.

Suggest how the study might be improved and what additional research is needed.

Psychological statistics: Fostering Successful Projects

Clear GuidanceInstructor gives specific guidance clear statementslearning goalslearning impact

Student effort and knowledge construction Individually AND cooperatively

They feel more empowered when they choose established statistical strategies supported by guidance from instructor.

Probability and Statistics for Manufacturing: Project based learningObjective: Students will be able to formulate and test hypotheses, and draw conclusions about their findings

Assignments: Topics determined by students (TDS)Topics determined by manufacturing case studies (TDCS)

Student Determined Topics

Social Media

College Life

Games Engineering STEM Education

Spring 2013

8 1 -- 0 2

Fall 2013 2 6 1 2 --

Spring 2014

2 3 1 3 1

TOTALS 12 9 2 5 3

Probability and Statistics for Manufacturing: Observations

Topic selectionProjects where students are asked to create their

own research topics with no restrictionsEngineering students generally never choose to

observe something that is of a technical natureThey overwhelmingly prefer to create surveys

than to observe some phenomena and collect numerical data

Projects from manufacturing case studiesStudents approach as “homework problem”

rather than a “technical problem”Looking for the correct answer

Probability and Statistics for Manufacturing:Observations

It is often difficult for groups to form a consensus on a topic for a project

Challenging for all group members to have authentic experience if all do not connect to topic

Groups that do form consensus tend to outperform those who don’t, regardless of topic selection

MATH CONCEPT Function

CONTEXThas allergies

AUTHENTIC LEARNING

connects all three

DATA Pollen levels

MATH CONCEPT Function

Your Assignment Use Authenticity Frameworks to plan instruction

Select a topic in a course you teach and draft a task/lesson

How might you build on what we did?

How will you bring in authenticity?

How might you use technology?

Discussion

Share your ideas

ReferencesGutstein, E. (2013). Mathematics education in a

time of crisis: For what purpose? Association of Mathematics Teacher Educators Seventeenth Annual Conference. Orlando, Florida.

Harris, C., & Marx, R. (2009). Authentic tasks. Retrieved March 14, 2014, 2014, from http://www.education.com/reference/article/authentic-tasks/

Lombardi, M. M. (2007). Authentic learning for the 21st century: An overview: Educause.

Merriam-Webster. (Ed.) (2014) Merriam-Webster.

Rhodes, T. L., & Finley, A. (2013). Using the VALUE rubrics for improvement of learning and authentic assessment. Washington, DC: Association of American Colleges and Universities.

References Roessingh, H., Chambers, W. (2011). Project-Based

Learning and Pedagogy in Teacher Preparation: Staking out the Theoretical Mid-Ground, International Journal of Teaching and Learning in Higher Education, 23 , 60-71.

Strobel, J., Wang, J., Weber, N. R., & Dyehouse, M. (2013). The role of authenticity in design-based learning environments: The case of engineering education. Computers & Education, 64, 143-152.

Thomas, J. (2000). A review of research on project-based learning, Prepared for the AutoDesk Foundation. Http://www.bie.org/research/study/review_of_project_based_lerning_2000.

University of Kansas. Creating authentic mathematics learning contexts. Retrieved January 28, 2014, from www.specialconnections.ku.edu/?q=instruction/mathematics/teacher_tools/creating_authentic_mathematics_learning_contexts