“How do you know?” asked Mr Bell.
“I just did it in my head,” replied Joey.
This is a comment we’ve all come across in our classrooms when asking a pupil to explain how they got to an answer.
Overcoming this barrier is important: as teachers we know how crucial it is to encourage children to vocalise their thinking, helping them to articulate their reasoning and deepening their understanding.
When children explain, they become much more aware of their thinking, and they understand their own reasoning better.
Recommendation 3 of EEF’s ‘Improving Mathematics in the Early Years and Key Stage 1’ guidance report suggests manipulatives and representations can encourage discussion about mathematics, prompting children to share and compare different approaches.
Using manipulatives and representations can also support reasoning for problems children don’t have words for.
A reason to reason
There is a wealth of evidence which indicates that talk can play an important role in supporting mathematical learning. Promoting mathematical discussion in lessons can help children make connections.
But are there specific ways we can motivate children to engage in meaningful mathematical discussions and see the need to reason?
Well-designed mathematical games can be valuable for stimulating rich mathematical discussion. Using the context of a game can be an instant hook to engage learners in purposeful talk.
They can be a motivating context to justify and prove an answer is correct. If it is a competitive game, winning is at stake.
Who is closer to 7 ½?
Let’s take the game 7 ½ used in ‘Mathematical Reasoning Programme’ as an example.
The children play the game in pairs. Each child picks 3 cards randomly (numbered 1, 2, 3, 4 or ½) and adds or subtracts the numbers to get as close to 7 ½ as possible without going over.
Each child writes down the numbers on their cards and the total they have by adding and / or subtracting.
The children should be encouraged to try different ways of adding and subtracting to find the number that is closest to 7 ½. The child who is closest to 7 ½ without going over is the winner.
Representing mathematical ideas using visual representations can support pupils’ understanding of concepts and their ability to transfer between these and the abstract. For example in this game children can use visual representations – circles and half circles ‑to support their understanding of the concept of half. Children are encouraged to talk through their decisions. Why have they added or subtracted? How do they know that is the best solution?
They are motivated to justify their thinking as they want to prove they are correct. They want to win.
Pupils listen intently as they want to check their partner’s reasoning is correct, sharing and comparing their approaches.
Playing mathematical games can be a way of encouraging all children to explain and justify their thinking. It may support them to see ‘the reason to reason’ and help the familiar response ‘I just did it in my head,’ become a thing of the past.