Presentation on theme: "Teaching About Problem Solving"— Presentation transcript:
1Teaching About Problem Solving Welcome toModule 3Teaching AboutProblem Solving
2Getting 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?
3Getting 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
4Key MessagesTeaching about problem solving focuses on having students explore and develop problem-solving strategies and processes.
5Key MessagesWhen students are taught about problem solving, they learn to identify different kinds of problems, problem-solving strategies, and processes.T chart
6Key MessagesTeaching about problem solving will help students develop a mental model for approaching and persisting with a problem-solving task.
7Key MessagesThe 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.
8Key MessagesTeachers 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.
9Key MessagesSince 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.
10The Four-Step Problem-Solving Model Working on ItThe Four-Step Problem-Solving ModelUnderstandthe problemMake a planCarry outthe planLook back andreflect onthe solution
11The Four-Step Problem-Solving Model How am I thinking about this?As you solve the following problem, think about the processes that help you at each step of the problem-solving model.
12The 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.
13The 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.
14The Four-Step Problem-Solving Model Read “The Four-Step Problem-Solving Model” (pp ).Understandthe problemMake a planCarry outthe planLook back andreflect onthe solution
15The 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
16The Four-Step Problem-Solving Model Share...your thoughts about the model with the large group.
17Problem-Solving Strategies Working on ItProblem-Solving Strategies
18Problem-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
19Problem-Solving Strategies Two statements in the guide reflect current practice in teaching students strategies for solving problems.
20Problem-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.
21Problem-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.
22Problem-Solving Strategies In small groups, discuss ways in which teachers can help students develop problem-solving strategies. (Refer to pp – 5.34 in the guide.)Record your thoughts on chart paper.
23Problem-Solving Strategies Share...your thoughts with the large group.
24The 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
25The Teacher’s Role in Teaching About Problem Solving Use a JIGSAW strategy to explore the teacher’s role.
26The 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!
27The Teacher’s Role in Teaching About Problem Solving Expert Group 1Helping to Develop Strategies(pp – 5.34)Expert Group 2Choosing Problems (pp – 5.35)Expert Group 3Problem Posing (pp – 5.36)
28The Teacher’s Role in Teaching About Problem Solving Share...your expertise when you return to your home group.
29Working on ItObserving and Assessing Students as They Solve Problems
30Observing 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 :CognitionAffectMetacognitionFlexibility
31Observing and Assessing Students as They Solve Problems CognitionThe ability to take existing information into a new situation and know how to use it
32Observing and Assessing Students as They Solve Problems CognitionThe 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
33Observing and Assessing Students as They Solve Problems AffectA positive emotional response towards mathematics and problem solving
34Observing and Assessing Students as They Solve Problems AffectSelf-confidence as a problem solver
35Observing and Assessing Students as They Solve Problems AffectA perception of mathematics as something that can be of interest and of help in learning about the world
36Observing and Assessing Students as They Solve Problems AffectThe ability to persevere and cope with difficult problems by using learned skills
37Observing and Assessing Students as They Solve Problems AffectThe 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
38Observing and Assessing Students as They Solve Problems AffectA belief that mistakes are a way of learning more and an opportunity to deepen and enhance understanding
39Observing and Assessing Students as They Solve Problems MetacognitionThe ability to think about one’s own thinking
40Observing and Assessing Students as They Solve Problems MetacognitionThe ability to recognize when a solution makes sense and is reasonable
41Observing and Assessing Students as They Solve Problems MetacognitionThe possession of strategies for knowing what to do when one does not know what to do
42Observing and Assessing Students as They Solve Problems MetacognitionThe ability to self-monitor throughout the problem solving process
43Observing and Assessing Students as They Solve Problems FlexibilityAn understanding that plans are often modified throughout the process
44Observing and Assessing Students as They Solve Problems FlexibilityAn understanding that a solution can often be reached in more than one way
45Observing and Assessing Students as They Solve Problems FlexibilityAn openness to the ideas of others
46Observing and Assessing Students as They Solve Problems FlexibilityA willingness to try new ways or strategies
47Observing and Assessing Students as They Solve Problems FlexibilityAn understanding that diversified interpretations of problems are possible
48Observing and Assessing Students as They Solve Problems Form groups of 3 or 4. Select a problem from Appendix 5-1 (pp – 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.
49Reflecting 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?
50Reflecting 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.