What is an 'unstructured' problem?
In mathematics lessons most 'problems' are highly structured exercises. Pupils are given the exact information they need and told which techniques to use. In this module, we compare structured and unstructured versions of problems and consider the demands and challenges they present to pupils and teachers. We try out one or two unstructured problems with a Key Stage 3 class and then go on to consider the support pupils need to work on more 'open' problems of this type.
- If you are leading a session, or working alone you may wish to print a copy of the module handbook.
- Session leaders should make copies of the handouts for all participants.
Critique and revise structured tasks
Work through one of the structured problems carefully.
- List all the decisions that are being made for the pupils.
- Revise the problems so that some of these decisions are handed back to pupils. This will make them less structured.
Compare structured and unstructured problems
Compare the unstructured versions of the problems (Handout 2) with the structured versions (Handout 1).
- What are the essential differences?
- What pedagogical issues will arise when you start to use unstructured problems like this?
Observe teachers using unstructured problems
The three videos below show pupils working with the unstructured versions of the same problems you have worked on. The first time through, we suggest you watch Michelle using Organising a table tennis tournament . You may like to return to the other clips another time. As you watch the video, consider:
- How did the teachers organise the classroom?
- Why were pupils expected to work in pairs/small groups?
- How did the teachers introduce the problems to pupils?
- What different approaches were being used by pupils?
- How did the teachers support the pupils that were struggling?
- How did the teachers encourage the sharing of approaches and strategies?
- What do you think these pupils were learning?
Discuss pedagogical implications
Watch the three teachers talking about how they will introduce the unstructured problems to their pupils.
- What culture are these teachers trying to create in the classroom?
- How did the teachers plan to make the problem more accessible to pupils?
- What do they plan for pupils that finish quickly?
Handout 4 offers general practical advice for teaching problem solving.
- What aspects of this advice were the teachers considering?
- Discuss the advice and consider the implications.
- Add your own ideas for advice to the bottom of the handout.
Plan a lesson using one of the problems
Choose one of the three problems that you feel would be appropriate for your class. Discuss how you will:
- Organise the classroom and the resources needed.
- Introduce the problem to pupils.
- Explain to pupils how you want them to work together.
- Challenge/assist pupils that find the problem straightforward/difficult.
- Help them share and learn from alternative problem-solving strategies.
- Conclude the lesson.