"An Object to Think With"

The point of this post is to push back a little on the idea that simply being out of one's desk and on your feet will create what Seymour Papert termed 'body knowledge'. Specifically, my goal, now and in the future, is clarification of what it looks like to combine movement/dance with math learning in meaningful ways.

This post is the result of conversations inspired by this video from Simon Gregg showing an activity he did on factors and primes on the playground with his 8 and 9 year old students.

After he posted it, there was a Twitter conversation between myself and Christopher Danielson which I Storified here. This led to my post Starting the Conversation: Meaningful Movement and Math Learning (including a video using modern dance to illustrate statistics concepts). A day later there was a blog response from Simon and, finally, here is my response.
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First of all, I really don't buy the idea that just by being on one's feet means there is opportunity for body knowledge. Simon said in his blog post:

"Another thing - one Malke and Christopher didn't mention - to focus attention, it might work well if some kind of game was involved at some point."

This sort of makes my point all on it's own -- Simon's Year 4 students were on their feet but there were a lot of distractions and, as I'm sure he knows, no opportunity for focused movement. Meaningful movement is created when the focus of the lesson is on a body task and the mathematical concept at the same time – the two together create the focus for each other.  In addition, both need to be developmentally appropriate. What Christopher described doing with the school yard hundreds chart (noticing pathways and the distances between numbers by standing and moving on the chart) highlight, among other things, important numeracy skills but I am looking at it as a movement activity as well.  The kind of body activity Simon and Christopher proposed in concert would, I think, be better suited for 5, 6 and 7 year olds and probably provide very little physical challenge for the upper elementary students in question.

So, if you're interested in creating more focus during 'stand up' math learning, what kind of movement skills can you embed into a hundreds chart activity like the one shown in Simon's video? What is the most important concept you would want your students to understand about primes? When you think of prime numbers, does your mind go to the intervals between them? If so, is the hundreds chart itself really the best visualization for that particular idea? What exactly is the big idea connected to prime numbers? And, if you were going to create a movement game what would be the point of the game physically and mathematically? 

If you are having trouble thinking of answers to these questions I think I know why. There is a perception I think many people hold about using movement in concert with math learning -- that they are primarily thinking of the body as a drawing tool. 

My standpoint on all this is deeply tied to what I see as a huge qualitative difference between mathematical representation and modeling and more literal illustrations of mathematical procedures or definitions (watch this video where the dance is little more than animated illustration for basic ideas of statistics). For one thing, definitions and procedural concerns are not math and dance is much more than literal interpretation. I know I need to develop my argument a little more but, for now, my point is that you are not creating body knowledge if you can just as easily illustrate (draw or identify) a math idea (like a right angle) using your eyes or a pencil and paper. If you can, there is probably no need to do a similar activity with your body.

Your body is an expressive vehicle and, as Papert intuited, an "object-to-think-with" capable of deep knowing that is rarely called upon or valued in academic learning. The body can be the perfect math manipulative, the perfect tool for children to use as they explore and experience the big ideas underlying mathematical activity – if used properly. Simon mentioned Dienes' principle of multiple embodiment. Here's what I took away from an article about Dienes' work I found on the Rational Number Project site regarding the use of math manipulatives (bolding emphasis and brackets mine):

“When individual activities [in this case with the body] cease to be treated as isolated actions and start to be treated as part of a systematic pattern of activities, the student begins to shift from playing with blocks to playing with mathematical structures [that's what we want] … Yet, when concrete materials have been used in instruction, more concern is often given to the "concreteness" of the materials than to the "activeness" of the activity - as though the abstraction were from the materials rather than from the structure that must be imposed on the materials.”

This takes me back to my original point. If using math manipulatives does not automatically connect you to the underlying mathematical meaning then being on your feet is not a guarantee of building ‘body knowledge’ in mathematics or any other domain. It goes the other way, too. Just because you’re a skilled mover does not necessarily guarantee you will be good at math. The meaning is created through thoughtful construction of activities or even whole sequences of investigations where both modes, mathematical and movement, come to influence the understanding of the other. Easier said than done, bu it is totally worth the effort, so let's keep thinking and talking.

In the end, you may disagree with me and that's okay -- as Christopher said during our recent Twitter conversation, “I would love to hear you argue back."