Introduction

The importance of discussion

We know from research that mathematical discussion is an essential component of thinking and reasoning. Yet, as many OfSTED reports confirm, collaborative discussion is rare among pupils in most mathematics classrooms. This module is intended to help you:

• consider the characteristics of an effective pupil-pupil discussion;
• explore techniques for promoting pupil-pupil discussion;
• discuss the teacher's role in managing pupil-pupil discussion.

• 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.

Activity 1

Experience a mathematical discussion

What are the characteristics of helpful and unhelpful classroom talk? Before discussing this question in detail, we suggest that you experience a mathematical discussion for yourself with a small group of colleagues. Discuss the following problem together: How many people can stand comfortably on a football pitch? Alternatively, you may prefer to tackle one of the problems on Handout 1. These problems are similar to those found in the Bowland Case Studies. You may like to compare your discussion with that held by three teachers: Marc, Eve and Angela.

Activity 2

Reflect on your discussion

Take some time to reflect on the experience you have just had.

• What roles did you and your colleagues play in the discussion?

Not all kinds of classroom talk are helpful for learning. Refer to characteristics of helpful and unhelpful talk on Handout 2.

• Which of these characteristics do you recognise in your own discussion?
• Was your discussion Collective, Reciprocal, Cumulative, Supportive, Purposeful?
• Would you describe your talk as Disputational, Cumulative or Exploratory?
• What did you learn mathematically from this experience?
• What concepts, skills and problem solving strategies were being developed?

Activity 3

Observe a discussion lesson

The video clips show three teachers; Eve, Angela and Marc teaching with the three problems shown on Handout 1. We suggest that you watch Eve's lesson first. Later, you may wish to come back and watch Angela and Marc's lessons. Watch the video clip, and then consider the following issues, referring again to Handout 2:

• How does the teacher introduce the problem?
• What different approaches are being used by pupils?
• How does the teacher help pupils to discuss productively?
• Can you characterise the types of talk they are using?

Activity 4

Discuss implications for teaching

Pupils (and adults!) do not always discuss in helpful ways. Some are reluctant to talk at all, while others take over and dominate. Pupils may therefore need to be taught how to discuss. Some teachers have found it helpful to introduce a list of 'ground rules for discussion' into their classes. These ground rules should, in appropriate language, give explicit guidance to pupils on how to talk together profitably.

• Together in your group, prepare your own list of "Ground rules for discussion".
• Compare your list with that offered on Handout 3.
• How could you encourage your pupils to follow these rules?
• Could you involve your pupils in drawing up such a list?

Activity 5

Plan a lesson using one of the problems

Choose one problem from Handout 1 that would be appropriate for your class and plan a lesson.

• How will you organise the classroom and the resources needed?
• How will you group pupils?
• How will you introduce the problem?
• How will you explain how you want pupils to discuss; which ground rules will you introduce?
• How will you manage the discussion?
• Will you hold a plenary discussion towards the end of the lesson?

You may like to watch the video of Eve planning her lesson using Schoolteachers and dentists.