Authentic Contexts in Early College Mathematics Lauretta Garrett, Mathematics Maria Calhoun...
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Transcript of Authentic Contexts in Early College Mathematics Lauretta Garrett, Mathematics Maria Calhoun...
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)
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)
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
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?
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