MODULE 3 – TEACHING ABOUT PROBLEM
SOLVING
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.
Materials: BLM 3.1, BLM 3.2, BLM 3.3, chart paper, markers
Looking Back
(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.
Getting Started
10 min
Introduction
#1 - 2
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.
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Module 3 – Teaching About Problem Solving
KEY MESSAGES
5 min
 “Becoming a better problem solver is a
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
Working on It
20 min
The Four-Step Problem-Solving Model
#10 - 16
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
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
Problem-Solving Strategies
20 min
“Strategies are not learned at a specific time or in a
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
The Teacher’s Role in Teaching About
Problem Solving
25 min
“Helping students become good problem solvers is
#24 - 28
like helping them learn how to ride a bicycle; tips
can be helpful, but it’s impossible to master the
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
Observing and Assessing Students as
They Solve Problems
Have participants review the characteristics
that impact a student’s ability to solve problems
(pp. 5.37–5.39 in the Guide).
25 min
#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
problems without relying solely on memory, procedures, and rules
Affect






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.
Reflecting and Connecting
10 min
Discussion
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
In Your Classroom
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.
For Next Time
Ask participants to read Chapter 3 – Planning the Mathematics Program.
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