Problem Solving, Problem Solving, Protocols and Practice Protocols and Practice

through the Agesthrough the Ages

Problem Solving, Problem Solving, Protocols and Practice Protocols and Practice

through the Agesthrough the Ages Wisconsin Mathematics CouncilWisconsin Mathematics Council

4141stst Annual Conference Annual Conference Friday, May 8, 2009Friday, May 8, 2009

Math Teaching Specialists:Math Teaching Specialists:

Pandora BedfordPandora Bedfordbedforpd@milwaukee.k12.wi.usbedforpd@milwaukee.k12.wi.us

Laura MalyLaura Malyguzmanlm@milwaukee.k12.wi.us guzmanlm@milwaukee.k12.wi.us

Rosann HollingerRosann Hollingerhollinrl@milwaukee.k12.wi.ushollinrl@milwaukee.k12.wi.us

www.mmp.uwm.eduwww.mmp.uwm.edu

The Milwaukee Mathematics Partnership (MMP) is supported by the National Science Foundation under Grant No. 0314898.

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

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.

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

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

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

Milwaukee Public SchoolsMathematics Framework

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

•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.

Protocol Research:

•Tuning ProtocolCoalition of Essential Schools, 1992

•Collaborative Assessment ConferenceHarvard Project Zero, 1988

•Standards in PracticeThe Education Trust, 1995

MMP ProtocolAnalyzing and Learning from

Student Work

1.Getting Started

Facilitator Volunteer to present student work Participants review the work silently

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?

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.

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

5. Debriefing: Reflect on using a protocol

How could you use this protocol in your school/district?