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# How to promote valuable discussion in maths.

It’s great to hear the buzz of pupils discussing their ideas during maths lessons and the benefits of this type of interaction are well known by now. Discussion helps learners to clarify and make sense of concepts, provides support for those who are less confident and supplies valuable insight into the levels of students’ understanding.

In addition, listening skills are being honed and there is a need for pupils to use clear language to make themselves understood.

When we factor in the increase in involvement and motivation, it is easy to see why this approach has been adopted so readily in the maths classroom. So we understand the value, but how can we ensure that we are using it to get the greatest advantage during maths sessions?

**Whole Class Discussion**

For this to be successful, the classroom environment needs to be one where pupils understand that mistakes are useful since they provide an opportunity for us to learn and can help the teacher pick up on any misconceptions.

Pupils often need time to think on their own first, followed by sharing their thoughts with their partner. To avoid always asking the more confident pupils, a die can be rolled to obtain an odd or even number. In each pair, one person is odd while the other is even, so the relevant pupil starts the explanation.

The type of questions that teachers use is also important. Rather than asking closed questions such as, ‘What is 4 times 5?’, the teacher could ask an open question such as which multiplication facts have an answer of 20. This also allows for more confident pupils to consider decimals and fractions.

Questions that pupils have about a topic or concept could be added to a maths learning wall and could be material for class discussions. Alternatively, a student may have provided an answer by adding it to the wall and the class could discuss whether they agree or disagree with the explanation.

**Paired and Group Discussion**

**Explanations**

It can be interesting to ask pupils to explain a task to their partner since pupils can appear to be listening but in fact have switched off, despite your best efforts, particularly as they get older.

Once a group challenge is complete, one person or pair from the group can visit another table to listen to how they reached a solution. They then need to share the explanation on return to their original group who can then decide, within a specified time, whether they should amend their work and be ready to show why.

On a practical note, this reduces the time that would be required if every group was to share their solution with the whole class. So ask learners to be ready to explain, using resources, images and diagrams, how they solved a problem.

**Games**

Apart from being something that most pupils enjoy, games are a great way to get pupils discussing maths, especially if they play in paired teams. It is most effective if the game involves some decisions but there can still be discussion if pupils, for example, are using larger numbers that have to be multiplied together. The conversation could then involve the best way to perform the calculation or how to check that the answer is sensible by using estimation.

It is also worth allowing situations that raise questions such as a division game where it is possible to roll a zero. This is likely to result in a decision whether a denominator can, in fact, be zero.

**Reasoning**

Activities such as providing a calculation with an incorrect answer and asking why it is incorrect can promote interesting conversations while also yield insight into understanding and misconceptions. This can also be achieved by presenting pupils with a statement which they have to decide is true or false or is always, sometimes or never true. The important aspect is the reasoning behind their decisions.

Other activities that promote reasoning through discussion include asking what is the same and what is different about two entities or providing four possible answers to a problem. The teacher can place the answers in four corners of the workspace and pupils then move to the corner where they think the answer sits. After a few minutes of discussion, they can move to another corner if the discussion has changed their mind. Pupils are then chosen to share their thoughts.

**Activities at Home**

To encourage maths dialogue at home, pupils could take a statement they need to discuss with someone or the task could be to explain a procedure. Alternatively, they could explore a question with someone, or several others, at home such as, ‘What is a fraction?’. Talking through a puzzle or problem can also help them think about ways to approach the problem. Parents or carers can then provide brief feedback about the conversations they have shared.

**Ground Rules for Success**

Time constraints are important for any task that involves discussion since pupils are then less likely to wander off task. When working in groups it is worthwhile allocating roles and one of these should be a timekeeper.

Low threshold, high ceiling tasks allow all pupils to get started but you may need to still adapt the task for less confident pupils to get started. Open-ended questions help here.

Tasks do not have to take a long time; quick starters or mini plenaries can provide fruitful opportunities for discussion.

Try not to rush the end of a longer task. Can they have ten minutes to finish after lunch or skip the starter the following day to allow time for the conclusion if it wasn’t reached in the previous lesson?

Be confident about presenting students with a challenge. If pupils haven’t worked this way before, there may be some pushback when faced with longer problems where they have to think about how to approach the task but through discussion, learners are often surprised at how their ability to tackle longer problems increases over time.

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