In my BCME thoughts post, I kind of promised that I might maybe do a bit more blogging, and one of the topics that I did quite a bit of musing on at BCME was playfulness and its importance in understanding mathematics. So I guess I should flesh out some of those thoughts a bit…

Firstly, some moments from BCME that got me thinking about playfulness. I attended an excellent session by Helen Williams and Mike Ollerton about using Cuisenaire rods at all ages. All good practice with Cuisenaire seems to be rooted in giving learners lots of time to play and become very very familiar with the rods, the way they feel, the way they fit together, and the colours, before starting to write things down more formally. I went to the second of their two sessions, and those who’d attended both sessions had a whole wealth of shared experience to draw on from having had “playtime” in the first session. And in videos where children work with Cuisenaire, it is a joy to watch the almost instinctive way in which they reach for the piece they want.

Talking of joy, I grabbed a lovely snap of John Mason after he’d completed the snake puzzle challenge from one of the stands at coffee time. He had been challenged to turn the snake into the ball-shape. I was familiar with the puzzle as I’d played with one before, and I can’t help thinking John would have been less frustrated if he’d had five minutes of being playful with the snake first before trying to make a particular given object! But he showed perseverance and resilience, and enjoyed a feeling of success at the end, so that’s OK.

Becky and I did quite a lot of playing with Pattern Blocks at the BCME workshop. Becky has written up some of the experience on her own blog, but I would like to add a little – we created some cards as a prototype of a game that can be played with squares, rhombuses, hexagons and equilateral triangles. While trying to formalise the rules of our game, lots of people joined us at different times and wanted to join in, make suggestions, and talk about the maths classroom implications. The context of a game and the associated playfulness can direct attention and awareness to particular attributes of a situation; by focussing on shapes meeting at a point, our game provided a natural way to think about angles and tesselations. (I really hope we can find the time to write our game up properly at some point.)

Ruth Bull led a session about geometry and paper folding. Many of the ideas were ones I’d seen before, but what was really valuable for me was seeing them woven in together, with time allowed for me to fold, play, think, and reflect on old ideas in new ways. In fact, I used one of the ideas, folding a hexagon, with a workshop group of my own last week – a story for another blog post, perhaps.

Now, thinking more generally about playfulness and why these moments at BCME were important. When I talk with students and teachers about problem solving, I talk about understanding the problem. Some mathematicians talk about getting stuck in, getting their hands dirty, digging into a problem. For me, my mindset when I am first working on some new mathematics feels very similar to my mindest when I am trying out a new craft, or exploring a new place. I am excited, a little apprehensive perhaps, thinking about all the possibilities ahead, ready to make a start. Perhaps I take a left turn over a bridge, to see where it goes! Or prepare some materials, and try to join them together. If I make a mistake, it doesn’t matter – there are no wrong answers at this point. If the bridge leads nowhere, I can turn back. If I cut out something and it doesn’t fit, I can cut again. I am being playful, and I learn a lot from the early explorations. Then I can draw on that experience of being playful later on. When I get down to work – trying to find a route, or make a particular item, or solve a particular problem, I can draw on my explorations and make plans based on the experiences I had. I know where the dead ends are, what will work and what probably won’t.

Sometimes, having a problem to solve can be a really good motivation for learning. Without knowing the problem, there can be too much open space, too little direction. But there has to be room to play too. If the space is closed right down and the paths are prescribed, some of the joy goes out of learning, and the opportunity to make connections is lost.