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

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

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

Theory of Performance

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

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

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

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

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

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

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

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

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

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

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

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

Resources & Information Reading Internet Sites LPM Step 7

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

Addressing Common Errors Common 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 Scale Documentation of Questions LPM Step 8

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

Models Exemplar Performances Used for Critical Thinking LPM Step 9

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

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

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

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

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

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)

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

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

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?

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