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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 [email protected]@milwaukee.k12.wi.us
Laura MalyLaura [email protected] [email protected]
Rosann HollingerRosann [email protected]@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
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