Module 3 continues to focus on Chapter 5 – Problem Solving . In Module 2, participants learned about the importance of problem solving and teaching through problem solving. In Module 3, they explore teaching about problem solving.
: BLM 3.1, BLM 3.2, BLM 3.3, chart paper, markers
(based on Module 2)
Have participants explain how they revised a closed problem to make it richer and more open-ended. Ask them to share their experiences of using the revised problem with their students.
Explain to participants that the focus of this module is on teaching about problem solving, and that they will examine how teachers can help students understand and develop effective problem-solving strategies and processes.
#1 - 2
10 min
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Module 3 – Teaching About Problem Solving
 “Becoming a better problem solver is a
5 min gradual building process that requires taking
#3 - 9 on challenging and sometimes frustrating problems.”
– Baroody, Fostering Children’s Mathematical Power
, Erlbaum, 1998, p. 2
–11
 Teaching about problem solving focuses on having students explore and develop problem-solving strategies and processes.

When students are taught about problem solving, they learn to identify different kinds of problems, problem-solving strategies, and processes.

Teaching about problem solving will help students develop a mental model for approaching and persisting with a problem-solving task.
 The primary goal of problem solving is making sense of mathematics, rather than mastering the steps of a problem-solving model or a set of problem-solving strategies.

Teachers become role models for problem solving by being flexible, modeling a variety of strategies, and encouraging students to exercise innovation by using strategies that make sense to them.
 Since attitudes and beliefs about problem solving have a major impact on student learning, the most important influence that a teacher can have on students is to help them develop attitudes and beliefs that confirm their capability as good problem solvers.
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Module 3 – Teaching About Problem Solving
20 min
Discuss Polya’s four-step model (PowerPoint slide
#10):

Understand the problem

Make a plan

Carry out the plan

Look back and reflect on the solution
#10 - 16
Have participants work in groups of three or four to solve the Picnic Table
Problem on BLM 3.1. After groups have solved the problem, ask participants to reflect on the processes (actions, thinking strategies, communication) that helped them at each step of the problem-solving model. Participants can record their thoughts on BLM 3.2.
Lead a discussion with the large groups by asking participants to share the processes they used at each step of the problem-solving model.
Ask participants to read 'The Four-Step Problem-Solving Model' (pp. 5.25
–5.27 in the Guide). Have participants respond to the following quote:
”Polya’s model can also be misleading if taken at face value. Except for simple problems, it is rarely possible to take the steps in sequence. Students who believe they can proceed one step at a time may find themselves as confused as if they had no model.”
– Reys, Lindquist, Lambdid, Smith, & Suydam,
Helping Children Learn
Mathematics , Wiley, 2001, p. 95
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Module 3 – Teaching About Problem Solving
“Strategies are not learned at a specific time or in a
20 min single lesson. Children will use them when they are
#17 - 23 ready. We structure situations that promote their use, but realize that the child has to decide to use them.”
– Trafton & Theissen, Learning Through Problems , Heinemann, 1999, p. 44
Two statements in the Guide reflect current practice in teaching students strategies to solve problems. These statements indicate a shift away from traditional practices in some classrooms.

Problem-solving strategies are best explored by primary students incidentally
– within the context of solving daily problems – rather than through direct instruction about the problems themselves.

Students are often taught to use key words as a strategy for solving word problems. A better strategy would be to have students discuss the known information, the unknown information, and the asked-for information.
Arrange participants in groups of three or four. Ask them to discuss ways in which teachers can help students develop problem-solving strategies.
(Participants can refer to pp. 5.33
–5.34 of the Guide.) Have participants record their ideas on chart paper. Ask groups to present their ideas to the whole group.
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Module 3 – Teaching About Problem Solving
25 min
“Helping students become good problem solvers is like helping them learn how to ride a bicycle; tips can be helpful, but it’s impossible to master the
#24 - 28 process without actually trying it.”
– Baroody, Fostering Children’s Mathematical Power , Erlbaum,1998, pp. 2 –11
Use a jigsaw strategy (see Module 1, p. 4) to explore the teacher’s role in teaching about problem solving. Have participants form home groups of six. Ask home-group members to find a partner in their home group. Each pair selects one of the following topics, and joins the corresponding expert group.
Expert groups will study the following aspects of the teacher’s role:
Expert Group 1 –

Helping to Develop Strategies (pp. 5.33
–5.34)
Expert Group 2 –

Choosing Problems (pp. 5.34
–5.35)
Expert Group 3
–

Problem Posing (pp. 5.35
–5.36)
After working in their expert groups, participants return to their home groups to share what they have learned.
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Module 3 – Teaching About Problem Solving
25 min
Have participants review the characteristics tha t impact a student’s ability to solve problems
(pp. 5.37
–5.39 in the Guide).
#29 - 48
Cognition

The ability to know how to use existing information in a new situation

The adaptive expertise to use sense-making and reasoning to solve
Affect problems without relying solely on memory, procedures, and rules

A positive emotional response towards mathematics and problem solving

Self-confidence as a problem solver

A perception of mathematics as something that can be of interest and of help in learning about the world

The ability to pursue and cope with difficult problems by using learned skills

The ability to take risks and know that the mathematics class is a safe environment in which students’ ideas are valued and their mathematical thinking, ideas, and/or strategies are neither ridiculed nor criticized

A belief that mistakes are a way of learning more and an opportunity to deepen and enhance understanding
Metacognition
 The ability to think about one’s own thinking

The ability to recognize reasonable and sensible solutions

Knowledge of a variety of strategies, as needed, to solve difficult problems

The ability to self-monitor throughout the problem-solving process
Flexibility

An understanding that plans are often modified throughout the process

An understanding that a solution can often be reached in more than one way

An openness to the ideas of others

A willingness to try new strategies

An understanding that diversified interpretations of problems are possible
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Module 3 – Teaching About Problem Solving
Arrange participants in groups of three or four. Instruct them to select a problem from Appendix 5-1 (pp. 5.40
–5.46 of the Guide) and to discuss what the teacher might observe if students are either being successful or else are struggling with the problem. On BLM 3.3, participants can classify their ideas according to the four categories of characteristics that impact on students' problem-solving abilities.
Ask participants to share their thoughts with the large group.
10 min
Ask participants to consider ways to improve how they might teach their students about problem solving. Provide an opportunity for them to share their thoughts with a partner.
#49 - 50
Ask participants to select a problem from Appendix 5-1 to try with their students.
Have them observe whether their students use problem-solving strategies similar to those suggested in the Guide.
Ask participants to read Chapter 3 – Planning the Mathematics Program.
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