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

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What makes a great learning experience in mathematics? Thought Provoking Challenging Relevant Effective Learner Centered

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Overview Background on Learning Process Components of Activity Design Example of Completed Activity

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Theory of Performance

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Levels of Learner Knowledge Level 1: Information Level 2: Conceptual Understanding Level 3: Application Level 4: Working Expertise Level 5: Research

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Learning Process Methodology Stage 1 - Preparing to Learn 1. Why 2. Orientation 3. Prerequisites 4. Learning Objectives 5. Performance Criteria 6. Vocabulary 7. Information

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Learning Process Methodology (LPM) Stage 2 – Performing a Learning Activity 8. Plan 9. Models 10. Thinking Critically 11. Transfer/Application 12. Problem Solving

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Learning Process Methodology (LPM) Stage 3 – Assessing and Building New Knowledge 13. Self-assessment 14. Research

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Assessment Assessment – How can the level of quality of a performance be improved in the future? SII Method Description of Strengths Areas for Improvement Insights of the Assessor

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Activity Design 1-2 class meetings 1-2 sections in a textbook Sample Topic: Analyzing a Function

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

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Objectives What students should know by the end No more than 3 Allows for validation of learning later on LPM Step 4

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Performance Criteria Describes area and level Sets expectations of quality Simple, Realistic, and Measureable Criteria for Assessment LPM Step 5

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Discovery Activity Find an interesting context relevant to the learner Incite creativity and discovery Identity as a Mathematician Context as a Learner/Professional

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What do you already know? Identify Pre-Requisites Build off previous knowledge LPM Step 3

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The Language of Mathematics Terminology and Notation used Instructor can provide list or Students can be asked to find them Identity as a Mathematician LPM step 6

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Resources & Information Reading Internet Sites LPM Step 7

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Methodology Generalized Procedure alongside Worked Example Other example requires student input Focus shifts from product to process LPM Step 7

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Addressing Common Errors Common mistakes with examples and reasoning Trains learner to validate their own work.

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Are you ready? What they should be able to do to be ready for class Checklist or Scale Documentation of Questions LPM Step 8

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Plan Directions for the activity May Include: Team Assignments Sharing of Pre-Activity Analysis of Models Critical Thinking LPM Step 8

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Models Exemplar Performances Used for Critical Thinking LPM Step 9

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Critical Thinking Questions The Heart of the LPM (Step 10) Raises Level of Learning 6-10 Questions 2-3 Directed 3-6 Convergent 1 Divergent

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Demonstrate Your Understanding Student’s Apply their knowledge Elevate level of learning Familiar Context Less Familiar Context Unfamiliar Context LPM Step 11

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Hardest Problem Students come up with the hardest problem they can Try to solve it or Challenge another team LPM Step 11

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Troubleshooting Solutions What Went Wrong? Why? Identify and Correct the Errors LPM Step 13

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Making it Matter Academic or “Real-Life” Problems Context as a Professional and member of society LPM Step 12

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Learning to Learn Mathematics Target Areas of Mathematical Learning to Reflect on Identity as a Mathematician, Self- Learner LPM Step 13 Assessment (Focus on Math)

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Assessment Use Performance Criteria for Self- Assessment LPM Step 13 Assessment (Focus on Learning Process)

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Facilitation F2F 1-2 Classes Before: Purpose - Are You Ready During: Review, Plan - Hardest After: MIM – Assessment

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Unique Features of the Math Learning Experience Discovery Activity What Do You Already Know? Language of Mathematics Avoiding Common Errors Hardest Problem What did you learn about Learning Mathematics?

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

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