1 Welcome to Teaching About Problem Solving Module 3.

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Welcome to

Teaching About Problem Solving

Module 3

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Getting Started

Module 3 continues the focus on problem solving. Module 2 covered the importance of problem solving and teaching through problem solving. Module 3 deals with teaching about problem solving

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Getting Started

“Becoming a better problem solver is a gradual building process that requires taking on challenging and sometimes frustrating problems.”

- Baroody, Fostering Children’s Mathematical Power, Erlbaum, 1998, p. 2-11

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Key Messages

Teaching about problem solving focuses on having students explore and develop problem-solving strategies and processes.

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Key Messages

When students are taught about problem solving, they learn to identify different kinds of problems, problem-solving strategies, and processes.

T chart

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Key Messages

Teaching about problem solving will help students develop a mental model for approaching and persisting with a problem-solving task.

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Key Messages

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.

Snowflakes have many lines of symmetry! I know this because when I make them, I cut on folds through

the centre.

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Key Messages

Teachers become role models for problem solving by being flexible, modeling a variety of strategies, and encouraging students to use strategies that make sense to them.

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Key Messages

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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Working on It

The Four-Step Problem-Solving

Model Understand the problem

Make a plan

Carry outthe plan

Look back and reflect on the solution

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The Four-Step Problem-Solving Model

As you solve the following problem, think about the processes that help you at each step of the problem-solving model.

How am I

thinking about this?

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Your teacher is organizing a barbeque. Picnic tables need to be ordered so that people will have a place to sit while they are eating. Each picnic table will seat 6 people. Your teacher has sent out invitations that ask for a reply stating the number of people attending from each family. All the replies have been returned and 99 people are planning to attend. How many picnic tables does your teacher need to order?

Record your solution on BLM 3.1.

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Reflect on the processes (actions, thinking strategies, communication) that helped you at each step of the problem-solving model.

Record your thoughts on BLM 3.2.

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Read “The Four-Step Problem-Solving Model” (pp. 5.25 - 5.27).

Understand the problem

Make a plan

Carry outthe plan

Look back and reflect on the solution

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“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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your thoughts about the model with the large group.

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Working on It

Problem-Solving Strategies

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“Strategies are not learned at a specific time or in a single lesson. Children will use them when they are ready. We structure situations that promote their use, but realize that the child has to decide to use them.”

- Trafton & Theissen, Learning Through Problems, Heineman, 1999, p. 44

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Two statements in the guide reflect current practice in teaching students strategies for solving problems.

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Statement One: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.

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Statement Two: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.

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In small groups, discuss ways in which teachers can help students develop problem-solving strategies. (Refer to pp. 5.33 – 5.34 in the guide.)Record your thoughts on chart paper.

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your thoughts with the large group.

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The Teacher’s Role in Teaching About Problem Solving

“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 process without actually trying it.”

- Baroody, Fostering Children’s Mathematical Power, Erlbaum, 1998, p. 2-11

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The Teacher’s Role in Teaching

About Problem Solving

Use a JIGSAW strategy to explore the teacher’s role.

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Form home groups of six. Pair yourselves. Each pair chooses a different topic, and joins pairs from other groups to study the topic.

Let’s find the expert group that’s studying our topic!

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Expert Group 1Helping to Develop Strategies (pp. 5.33 – 5.34)

Expert Group 2Choosing Problems (pp. 5.34 – 5.35)

Expert Group 3 Problem Posing (pp. 5.35 – 5.36)

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your expertise when you return to your home group.

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Working on It

Observing and Assessing Students as They Solve Problems

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There are characteristics that have an impact on a student’s ability to solve genuine problems. These characteristics involve :

Cognition Affect Metacognition Flexibility

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The ability to take existing information into a new situation and know how to use it

Cognition

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The adaptive expertise to use sense-making and reasoning to solve a problem in a way that does not rely solely on memory, procedures, and rules

Cognition

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A positive emotional response towards mathematics and problem solving

Affect

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Self-confidence as a problem solver

Affect

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A perception of mathematics as something that can be of interest and of help in learning about the world

Affect

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The ability to persevere and cope with difficult problems by using learned skills

Affect

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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

Affect

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A belief that mistakes are a way of learning more and an opportunity to deepen and enhance understanding

Affect

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The ability to think about one’s own thinking

Metacognition

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The ability to recognize when a solution makes sense and is reasonable

Metacognition

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The possession of strategies for knowing what to do when one does not know what to do

Metacognition

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The ability to self-monitor throughout the problem solving process

Metacognition

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An understanding that plans are often modified throughout the process

Flexibility

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An understanding that a solution can often be reached in more than one way

Flexibility

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An openness to the ideas of others

Flexibility

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A willingness to try new ways or strategies

Flexibility

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An understanding that diversified interpretations of problems are possible

Flexibility

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Form groups of 3 or 4.

Select a problem from Appendix 5-1 (pp. 5.40 – 5.46).

Think about what a teacher might observe that would indicate whether students are being successful in solving the problem. Record your thoughts on BLM 3.3.

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Reflecting and Connecting

Identify a change that you would like to make in how you teach your students about problem solving. How will you implement the change?

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Reflecting and Connecting

Select a problem from Appendix 5-1 to try with your students.

Be prepared to share some of your discoveries, observations, and thoughts at our next session.

1 Welcome to Teaching About Problem Solving Module 3.

Documents

following problem

importance of problem

solution slide

better problem solver

primary goal of problem

good problem solvers

mental model

key messages teaching