Archive for April, 2018

Playful Maths

April 16, 2018

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.

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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.

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Some BCME9 Thoughts

April 7, 2018

I spent Tuesday-Friday at the University of Warwick for the 9th BCME conference. I reckon there’s at least twenty blog posts worth of material from the conversations, thoughts, problems and games of the last few days, the most important of which is that I really need to get into the habit of writing more about maths and maths ed. It has taken me a long time to realise that I have worthwhile things to add to the conversation, and that my community appreciates my contributions even if not everyone agrees with me!

Here are some ideas that I will try to find the time to blog about and flesh out a bit over the next few days:

  1. The importance of play and playfulness in mathematics education at all ages
  2. The tensions that are introduced by high stakes assessment
  3. Public perception of what mathematics is and what mathematics teaching should achieve
  4. The role of computers and calculators
  5. How to engage in respectful dialogue and find common ground when talking about emotive topics within maths ed (and how to pick your battles)
  6. Diversity and representation
  7. How to run a quiz without controversy (or The Time I Lost a Tie Break but am Not Bitter, honest)…

For the most part, the people I talked to at BCME are on the same page as me, trying to improve maths understanding, trying to instill a love of and enjoyment for mathematics, trying to change the notion that maths is for a select few (and that you need grey hair and a white beard to do it…) and I hope by blogging and continuing to tweet I can be part of the ongoing conversations that started last week. Let’s make the world a better place, one maths classroom at a time!