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Problem Solving, Protocols and Practice through the Ages Wisconsin Mathematics Council Wisconsin Mathematics Council 41 st Annual Conference 41 st Annual Conference Friday, May 8, 2009 Friday, May 8, 2009 Math Teaching Specialists: Pandora Bedford bedforpd@milwaukee.k12.wi.us Laura Maly guzmanlm@milwaukee.k12.wi.us Rosann Hollinger hollinrl@milwaukee.k12.wi.us www.mmp.uwm.edu The Milwaukee Mathematics Partnership (MMP) is supported by the National Science Foundation under Grant No. 0314898.

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In this Session, we will: become acquainted with the Think Aloud as a problem solving strategy. examine and experience a protocol for collaboratively looking at student work. MMP Protocol Analyzing and Learning from Student Work

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Think Aloud A Problem Solving Strategy for Mathematics The Think Aloud strategy helps children develop independent thinking during problem solving situations through the use of questioning.

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Effective questioning will help students to: Visualize the situation Develop important mathematical concepts Clarify vocabulary Develop points of entry Focus on what is needed for an answer

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Setting the Stage – Task Clarification Read the problem Visualize the situation Restate the problem Connect to real-life situations Clarification of Concept and Context; Making Connections Clarify vocabulary specific to the math content Clarify vocabulary related to the context of the problem Connect the mathematical ideas to previous work

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Working on the Problem Discuss various approaches for entry into the problem Redefine the question in the problem Solve the problem independently or with a partner Explain your work or your partner’s work Thinking about the Solution Relate connections between the answer and the problem Share student work samples; discuss the mathematics, the approach to the problem and the student reasoning

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Milwaukee Public Schools Mathematics Framework

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Objective: Mathematical Processes Students will effectively use mathematical knowledge, skills and strategies related to reasoning, communication, connections, representation and problem solving. Descriptors, such as but not limited to Use reasoning and logic to perceive patterns, formulate questions, identify relationships, pose problems, make and test conjectures, and evaluate and justify strategies. Continue

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Effectively use the vocabulary of mathematics and communicate mathematical ideas and logical arguments in a variety of ways e.g. using words, numbers, symbols, charts, tables, diagrams, graphs, and models. Connect mathematics to the real world, as well as within mathematics. Create and use representations to organize, record, and communicate mathematical ideas. Solve and analyze routine and non-routine problems.

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Protocol Research: Tuning Protocol Coalition of Essential Schools, 1992 Collaborative Assessment Conference Harvard Project Zero, 1988 Standards in Practice The Education Trust, 1995

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MMP Protocol Analyzing and Learning from Student Work 1.Getting Started Facilitator Volunteer to present student work Participants review the work silently

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2.Discussing the Work Round 1. Describing: What do you see? Round 2. Interpreting: What do the students understand? Round 3. Questions: What questions does this work raise?

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3.Hearing from the Presenting Teacher Comment on students’ work, respond to questions raised Insights from surprising or unexpected comment Repeat Steps 1–3 with another presenting teacher.

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What are some thoughts which may have surfaced using the Protocol that you have about your own teaching or about children’s learning? 4. Implications for Teaching

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5. Debriefing: Reflect on using a protocol How could you use this protocol in your school/district?

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