Thinking mathematically through games

If you ask mathematicians what they do, you always get the same answer. They think. M. Egrafov

6 + 4 = take away 9 makes 1 1 add 17 is 18 18…… Competitive aim – stop your partner from going

Collaborative aim – cross off as many as possible What’s the longest chain? Is it possible to strike them all out? If so how? If not why not?

 What is the mathematical knowledge that is needed to play?  Who would this game be for?  What is the value added of playing the game?  Could you adapt it to use it in your classroom?

Low threshold high ceiling  Accessible to all at the start  Plenty of supporting activity for those who benefit from it  Lots of opportunities for challenge for those who decide they are ready for it  Lots of opportunities for teacher to tweak both the mathematical knowledge needed and the mathematical thinking

 Children can do more than you think  Children’s own problems  Importance of talk and questioning  Children as mathematicians

‘Effective teaching requires practitioners to help children see themselves as mathematicians. For children to become (young) mathematicians requires creative thinking, an element of risk-taking, imagination and invention - dispositions that are impossible to develop within the confines of a work-sheet or teacher-led written mathematics.’ Worthington and Curruthers 2007

Valuing mathematical thinking Creative climate and conjecturing atmosphere Purposeful activity and discussion Conditions for learning

Purposeful activity Give the pupils something to do, not something to learn; and if the doing is of such a nature as to demand thinking; learning naturally results. John Dewey

Liz Woodham Bernard Bagnall Fran Watson nrich.maths.org