matthew watts dr. daniel apple wade ellis jr. designing an active learning math experience
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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