Matthew Watts Dr. Daniel Apple Wade Ellis Jr. Designing an Active Learning Math Experience.

Matthew WattsDr. Daniel Apple

Wade Ellis Jr.

Designing an Active Learning Math Experience

What makes a great learning experience in mathematics?

Thought ProvokingChallengingRelevantEffectiveLearner Centered

OverviewBackground on Learning Process

Components of Activity DesignExample of Completed Activity

Theory of Performance

Levels of Learner KnowledgeLevel 1: InformationLevel 2: Conceptual Understanding

Level 3: ApplicationLevel 4: Working ExpertiseLevel 5: Research

Learning Process Methodology Stage 1 - Preparing to Learn

1. Why2. Orientation3. Prerequisites4. Learning Objectives5. Performance Criteria6. Vocabulary7. Information

Learning Process Methodology (LPM)Stage 2 – Performing a Learning Activity

8. Plan9. Models10.Thinking Critically11.Transfer/Application12.Problem Solving

Learning Process Methodology (LPM)Stage 3 – Assessing and Building New Knowledge

13. Self-assessment14. Research

AssessmentAssessment – How can the level of quality of a performance be improved in the future?

SII MethodDescription of StrengthsAreas for ImprovementInsights of the Assessor

Activity Design1-2 class meetings1-2 sections in a textbookSample Topic: Analyzing a Function

PurposeWhat is to be learned?Why is it important?How does it relate?LPM Steps 1 & 2

ObjectivesWhat students should know by the end

No more than 3Allows for validation of learning later on

LPM Step 4

Performance CriteriaDescribes area and levelSets expectations of qualitySimple, Realistic, and Measureable

Criteria for AssessmentLPM Step 5

Discovery ActivityFind an interesting context relevant to the learner

Incite creativity and discoveryIdentity as a MathematicianContext as a Learner/Professional

What do you already know?Identify Pre-RequisitesBuild off previous knowledgeLPM Step 3

The Language of MathematicsTerminology and Notation usedInstructor can provide list orStudents can be asked to find them

Identity as a MathematicianLPM step 6

Resources & InformationReadingInternet SitesLPM Step 7

MethodologyGeneralized Procedure alongside Worked Example

Other example requires student input

Focus shifts from product to process

LPM Step 7

Addressing Common ErrorsCommon mistakes with examples and reasoning

Trains learner to validate their own work.

Are you ready?What they should be able to do to be ready for class

Checklist or ScaleDocumentation of QuestionsLPM Step 8

PlanDirections for the activityMay Include:

Team AssignmentsSharing of Pre-ActivityAnalysis of ModelsCritical Thinking

LPM Step 8

ModelsExemplar PerformancesUsed for Critical ThinkingLPM Step 9

Critical Thinking QuestionsThe Heart of the LPM (Step 10)Raises Level of Learning6-10 Questions

2-3 Directed3-6 Convergent1 Divergent

Demonstrate Your Understanding

Student’s Apply their knowledge

Elevate level of learningFamiliar ContextLess Familiar ContextUnfamiliar Context

LPM Step 11

Hardest ProblemStudents come up with the hardest problem they can

Try to solve it orChallenge another teamLPM Step 11

Troubleshooting SolutionsWhat Went Wrong? Why?Identify and Correct the ErrorsLPM Step 13

Making it MatterAcademic or “Real-Life” Problems

Context as a Professional and member of society

LPM Step 12

Learning to Learn MathematicsTarget Areas of Mathematical Learning to Reflect on

Identity as a Mathematician, Self-Learner

LPM Step 13Assessment (Focus on Math)

AssessmentUse Performance Criteria for Self-Assessment

LPM Step 13Assessment (Focus on Learning Process)

FacilitationF2F

1-2 ClassesBefore: Purpose - Are You Ready

During: Review, Plan - Hardest

After: MIM – Assessment

Unique Features of the Math Learning ExperienceDiscovery ActivityWhat Do You Already Know?Language of MathematicsAvoiding Common ErrorsHardest ProblemWhat did you learn about Learning Mathematics?

Matthew WattsDr. Daniel Apple

Wade Ellis Jr.

Designing an Active Learning Math Experience