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1 Welcome to Teaching About Problem Solving Module 3

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2 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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3 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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4 Key Messages Teaching about problem solving focuses on having students explore and develop problem-solving strategies and processes.

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5 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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6 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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7 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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8 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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9 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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10 Working on It The Four-Step Problem-Solving Model Understand the problem Make a plan Carry out the plan Look back and reflect on the solution

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11 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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12 The Four-Step Problem-Solving Model 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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13 The Four-Step Problem-Solving Model 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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14 The Four-Step Problem-Solving Model Read “The Four-Step Problem- Solving Model” (pp. 5.25 - 5.27). Understand the problem Make a plan Carry out the plan Look back and reflect on the solution

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15 The Four-Step Problem-Solving Model “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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16 The Four-Step Problem-Solving Model your thoughts about the model with the large group.

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17 Working on It Problem-Solving Strategies

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18 Problem-Solving Strategies “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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19 Problem-Solving Strategies Two statements in the guide reflect current practice in teaching students strategies for solving problems.

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20 Problem-Solving Strategies 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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21 Problem-Solving Strategies 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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22 Problem-Solving Strategies 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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23 Problem-Solving Strategies your thoughts with the large group.

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24 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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25 The Teacher’s Role in Teaching About Problem Solving Use a JIGSAW strategy to explore the teacher’s role.

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26 The Teacher’s Role in Teaching About Problem Solving 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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27 The Teacher’s Role in Teaching About Problem Solving 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)

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28 The Teacher’s Role in Teaching About Problem Solving your expertise when you return to your home group.

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29 Working on It Observing and Assessing Students as They Solve Problems

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30 Observing and Assessing Students as They Solve Problems 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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31 Observing and Assessing Students as They Solve Problems The ability to take existing information into a new situation and know how to use it Cognition

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32 Observing and Assessing Students as They Solve Problems 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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33 Observing and Assessing Students as They Solve Problems A positive emotional response towards mathematics and problem solving Affect

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34 Observing and Assessing Students as They Solve Problems Self-confidence as a problem solver Affect

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35 Observing and Assessing Students as They Solve Problems A perception of mathematics as something that can be of interest and of help in learning about the world Affect

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36 Observing and Assessing Students as They Solve Problems The ability to persevere and cope with difficult problems by using learned skills Affect

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37 Observing and Assessing Students as They Solve Problems 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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38 Observing and Assessing Students as They Solve Problems A belief that mistakes are a way of learning more and an opportunity to deepen and enhance understanding Affect

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39 Observing and Assessing Students as They Solve Problems The ability to think about one’s own thinking Metacognition

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40 Observing and Assessing Students as They Solve Problems The ability to recognize when a solution makes sense and is reasonable Metacognition

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41 Observing and Assessing Students as They Solve Problems The possession of strategies for knowing what to do when one does not know what to do Metacognition

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42 Observing and Assessing Students as They Solve Problems The ability to self-monitor throughout the problem solving process Metacognition

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43 Observing and Assessing Students as They Solve Problems An understanding that plans are often modified throughout the process Flexibility

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44 Observing and Assessing Students as They Solve Problems An understanding that a solution can often be reached in more than one way Flexibility

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45 Observing and Assessing Students as They Solve Problems An openness to the ideas of others Flexibility

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46 Observing and Assessing Students as They Solve Problems A willingness to try new ways or strategies Flexibility

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47 Observing and Assessing Students as They Solve Problems An understanding that diversified interpretations of problems are possible Flexibility

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48 Observing and Assessing Students as They Solve Problems 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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49 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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50 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.

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