Playfulness and invention as aspects of mathematical thought

I serendipped my way to these "Notes from a session discussing Mathematical Thinking: October 16th 2002," sponsored by the University of Oxford Center for Mathematics Education Research. It's been a long time (maybe 35 years) since I thought about math education. Probably because when I last did, I found that my uses of games and play resulted in massive parental angst. I may have been helping kids develop a love for mathematical thinking, but I was doing them a disservice by not focusing their love on the SATs. So the following extract comes as a much-welcome, though somewhat belated balm to my faith in the fun/learning connection.

A treatment of imagination as an integral component of thought, rather than as a separate type of thinking, led us to see playfulness and invention as aspects of mathematical thought. Indeed, these aspects help us avoid reducing thinking to a list of things one must show the teacher one can do. Freedom to play, to look for many possible methods and answers, may be hard to use at first if students have not been used to it. Sometimes they react by playing well outside normal mathematical parameters. But we retain the word ‘play’ to indicate this creative dimension to mathematics, believing it to be an important approach to learning and working. We did several exercises to explore the effects of being asked to ‘imagine’ and ‘visualise’. (One exercise was to imagine identical twins imitating each other.) From these we found that the ways in which we imagine are very varied, and the norms we choose to impose on our imaginations come not only from knowledge and intellect but from emotional and social directions as well.

"Playfulness and inventions as components of mathematical thought." Yeah, baby.

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