How do we plan for IBL in mathematics? Inquiry learning How do we plan for IBL in mathematics? Tool IF-3: Advice for teaching problem solving This activity addresses the well recognised difficulty that teachers have with teaching problem solving in mathematics. The teachers discuss what they find difficult about teaching problem solving and what works for them, before exploring some research-based approaches. © 2016 mascil project (G.A. no. 320693). Lead partner University of Nottingham; CC-NC-SA 4.0 license granted. The project mascil has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013).

Overview Aim: To raise awareness of different strategies for teaching problem solving. We will: Discuss our current practice; Explore research-based strategies. This tool aims to address some of the main difficulties that the group have with teaching problem solving in mathematics. The teachers discuss what they find personally difficult about teaching problem solving and what works for them, before exploring some research-based strategies. Many teachers find it challenging to teach problem solving lessons, partly because it is difficult to predict how students will tackle the problem and partly because they find it difficult to allow students to choose their own approaches. Teachers often find it difficult to know when to give help and when to leave students to overcome their own difficulties and find their own solutions. If they intervene too quickly, then the students have no chance to experience what it is like to pursue an unfruitful idea, or to puzzle out a solution for themselves. If they intervene too slowly, then students become frustrated, bored and disengaged. 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. This support may involve reducing their choices, drawing attention to important features through questioning, or even at times demonstrating what to do. In his work with young children, Wood (1988) categorised different levels of scaffolding, from less directive to more directive: giving general verbal advice, giving specific verbal instructions, breaking the problem down, demonstrating a solution. Wood also introduced two rules of contingency: “Any failure by a child to succeed in an action after a given level of help should be met by an immediate increase in help or control. Success by a child then indicates that any subsequent instruction should offer less help than that which preceded the success, to allow the child to develop independence.” Wood (1988) The important idea here is that scaffolding should be removed as the student begins to cope, otherwise it reinforces dependency.

Teaching problem solving In your own experience of teaching problem solving: What is challenging? Why is it challenging? What works well? Hold a discussion with the teachers. Ask them to share their thoughts about teaching problem solving: what do they find challenging? Why? What works well? If the points made in the introduction (above) are not covered in the discussion, end by sharing anything that has not been covered.

Exploring strategies Read the handout and discuss: Which ideas do you find most difficult to implement? What could you say to your students? The handout Problem solving handout 2 suggests provides some practical strategies for teachers when they use  unstructured problems in the classroom. Ask teachers to work together in small groups and give each small group a copy of the handout. Ask them to discuss which ideas they find most difficult to implement; and think of examples of what they could say to the students and to add these to the cells in the right hand column.

Finishing off Share some of your ideas with the group and add any new strategies to your handout. Think about one new strategy that you can use with a class with a problem-solving activity. Try this before the next session and be ready to report back on how it worked. Bring everyone together, and ask each small group or pair to share one or two of their ideas. Encourage teachers to write the ideas into their sheet if they like them. To finish off, ask the teachers to think how they could adopt one new strategy into their problem solving lessons. Ask them to do this before the next professional development meeting, and to be ready to feed back to the group.