1. Teaching About Problem Solving
Welcome to
Module 3
Teaching About
Problem Solving

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 ?

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

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

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

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

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.

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.

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.

10. The Four-Step Problem-Solving Model
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

11. The 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.

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.

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.

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

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

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

17. Problem-Solving Strategies
Working on It
Problem-Solving Strategies

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

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

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.

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.

22. Problem-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.

23. Problem-Solving Strategies
Share...
your thoughts with the large group.

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

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

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!

27. The Teacher’s Role in Teaching About Problem Solving
Expert Group 1
Helping to Develop Strategies
(pp – 5.34)
Expert Group 2
Choosing Problems (pp – 5.35)
Expert Group 3
Problem Posing (pp – 5.36)

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

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

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

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

32. Observing and Assessing Students as They Solve Problems
Cognition
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

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

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

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

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

37. Observing and Assessing Students as They Solve Problems
Affect
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

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

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

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

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

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

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

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

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

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

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

48. Observing 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.

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?

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.