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Concept development and Problem Solving

This document outlines effective formative assessment strategies for concept development and problem solving in mathematics education, led by educators Amy Lundy, Stephanie Finn, and Kami Wyse. It emphasizes the importance of pre-assessments for understanding student misconceptions, paired student collaboration based on performance, and providing constructive feedback. Lessons are designed to engage all students in analyzing mathematical concepts through collaborative work, promoting critical thinking, and exploring multiple representations. Techniques for grouping students according to their strategies and mistakes are discussed to better tailor instruction.

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Concept development and Problem Solving

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  1. Formative Assessment Lessons Concept development and Problem Solving

  2. Stephanie Finn, Paulding County • Amy Lundy, Jones County • Kami Wyse, Hall County

  3. Formative Assessment Lessons Concept Development Problem Solving

  4. Commonalities • 2/3 of the way through the unit. • Pre-assessment/Post assessment • Teachers give feedback to pre-assessment • Students are paired based on pre-assessment performance • Not graded • Accessible to ALL students • Make effective use of Standards for Mathematical Practice

  5. Concept Development • Concept Development lessons are intended to assess and develop a students’ understanding of fundamental concepts through activities that engage them in classifying and defining, representing concepts in multiple ways, testing and challenging misconceptions and exploring structure.

  6. Genres of Concept Development Lessons • Classifying mathematical objects • Interpreting multiple representations • Evaluating mathematical statements • Exploring the structure of problems

  7. Structure of Concept Development Lessons--Student • Students complete an assessment task individually • Whole class introduction • Collaborative work on a substantial activity • Students share their thinking • Students revisit the assessment task

  8. Structure of Concept Development--Teacher • Planning the lesson • Framing the task • Analyze the pre-assessment and offer feedback • Students will be grouped based on COMMON misconceptions • Whole group introduction

  9. Structure of Concept Development--Teacher • Facilitate the task, asking questions • Facilitate the sharing of work • Whole group discussion • Give feedback questions • Post-Assessment • Analyze post-assessment

  10. Mistakes and Misconceptions • Why do students make mistakes in mathematics? • What different types of mistakes are there? What causes these mistakes? • How do you respond to each different type of mistake? Why?

  11. Grouping based on… • Mistakes and misconceptions made on the pre-assessment • Look for common misconceptions • This helps students get what they need from the task

  12. Problem Solving • Problem Solving FALs are intended to assess and develop students’ capacity to select and deploy their mathematical knowledge in non-routine contexts and typically involve students in comparing and critiquing alternative approaches to solving a problem.

  13. Structure of Problem Solving Lessons--Students • Complete an assessment task individually • “Having Kittens” Activity • Whole class introduction • Reflect on feedback question individually • Collaborative work with a student whose approach is different • The collaborative pair will work to create a third solution that is even better • Checking posters • Sharing of work • Review sample work • Revisit the assessment task

  14. Structure of Problem Solving--Teachers • Planning & Preparation Framing the task • Analyze the pre-assessment and give feedback • Whole class introduction • Analyze student work • Allow students to reflect on feedback questions and improve their own work

  15. Structure of Problem Solving--Teachers • Facilitate collaborative work • Students are paired based on different approaches to the assessment task • Facilitate the sharing of work • Whole group discussion • Sharing sample work • Give the post-assessment • Analyze post-assessment responses

  16. Grouping • Students are to be grouped based on different approaches to reaching a solution

  17. Practical Advice • Allow students time to understand and engage with the problem • Offer strategic rather than technical hints • Encourage students to consider alternate methods and approaches • Encourage explanation • Model thinking and powerful methods

  18. Differences • Intended to assess and develop understanding of fundamental concepts • Feedback given after task but before post-assessment • Students are grouped based on common misconceptions from pre-assessment. • Intended to assess and develop capacity to select and deploy mathematical knowledge in non-routine context • Feedback given as part of task • Students are grouped based on different strategies. Concept Development Problem Solving

  19. Ability Levels and FAL’s

  20. Personal Experiences

  21. Personal Experiences Amy Lundy’s Benchmark Scores– Powerful Data Results

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