1. Inquiry learning How do we plan for IBL in mathematics? Tool IF-3: Strategies for teaching problem solving

2. Overview Aim: to raise awareness of different strategies for teaching problem solving. We will: Discuss common practices; Explore research-based strategies.

3. Solving a problem Work in a group on the mathematical problem solving task 110 years on

4. 110 years on Work in a group on the mathematical problem solving task 110 years on

5. 110 years on This photograph was taken about 110 years ago. The girl on the left was about the same age as you. As she got older, she had children, grandchildren, great grandchildren and so on. Now, 110 years later, all this girl’s descendants are meeting for a family party. How many descendants would you expect there to be altogether? Use the information on the handout to help with your discussion 5

7. Teaching problem solving What might be challenging about teaching problem-solving? Why? What might work well?

8. Strategies to support problem-solving Bruner uses the metaphor of scaffolding to describe the structuring that a teacher provides (Wood, Bruner, & Ross, 1976). The teacher encourages students to do as much as they are capable of unaided and only provides the minimum of support to help them succeed. Wood (1988) categorised different levels of scaffolding, from less directive to more directive. The important idea is that scaffolding should be removed as the student begins to cope, otherwise it reinforces dependency.

9. Exploring strategies Which ideas are most difficult to implement? What could teachers actually say to students? Add your ideas to the handout.

10. Sharing strategies What were the main points that arose in discussions? Share any ideas that emerged about what teachers might say to students.

11. Finishing off Exploratory talk in the classroom means speakers build and expand on ideas in a collaborative manner through critical and constructive exchanges. (Mercer, 2000) In lesson observations try to identify examples of exploratory talk and how this was encouraged amongst students.