For two years at the Centre for Mathematics Education at the University of Manchester, we have been working with children and teachers, discussing“errors” and the methods used by children in SATs at KS2 and 3. We encouraged them to listen to each other, build on what someone else said and share responsibility for ensuring that everyone understood. In the process, we learned many things about the children’s thinking.

Expressing different points of view led to the need for children to explain mathematically the best methods and answers. They were very positive about the discussion; one of them said: “It’s easier listening to other people because it persuades you, and it makes you think about the mistakes you’ve made ... because you’ve got different ideas.”

It is through active lanuage that children learn best. Maths has often been used as a received body of knowledge. Reflective discussion turns this idea on its head. There should be less “How do you do it?” and more “Why do you do it that way?” There can be problems with developing discussion as a teaching strategy. We must be sensitive to children’s vulnerability when they express ideas publicly. But if we listen carefully, we will gain insights. Often the language of a question may be peculiarly mathematical and children, sensibly, draw on their everyday language to find meaning for it.

There was an added bonus. Watching those children struggling to speak maths in dialogue and enjoying it was illuminating. We hope that discussion will become a common learning strategy. As one of the children said: “I’ve listened to everyone else and their methods of doing it. I think I have a different answer now.”

Julie Ryan is test development officersenior lecturer in maths education at the University of Manchester. Mathematical Discussions with Children, by Julie Ryan and Julian Williams, pound;10. Tel: 0161 275 3409. Web: www.man.ac.ukcmeResources