The Map is Not the Territory

I recently had the opportunity to have my teaching work critiqued by a group of colleagues.  They viewed a ten-minute video I produced which illustrated what success looks like in my classroom. The feedback I received was all at once enthusiastic, thought provoking and puzzling.   

I teach elementary students the elements of percussive dance and then, within a structured framework, give them the freedom to create their own percussive patterns.  Along the way we use and talk about a lot of math which both describes their patterns and informs their creative choices.  It seems straightforward to me, so I think that is why I was flummoxed by a question they all had:

“When your students are choreographing their percussive dance patterns, how much of that activity is about their math understanding?”

I can answer that question.  The answer is, “All of it.”  I don’t see a separation between the two.   In fact, I think the dance and the math are essentially the same activity.

Here is an example:  a video of some traditional Irish figure dancing with accompanying percussive footwork.  You only have to watch a minute of the dancing to notice it is full of geometry and symmetry and all sorts of other wonderful kinds of math:

The shifting, curving patterns move through space and time while undergoing symmetrical transformations.  The dance choreography explores permutations and combinations of moves and steps by arranging and rearranging dancers at a dizzying rate in time to the music.  The footwork traces invisible maps on the floor.  The math in the percussive footwork is a reiteration of the figure dancing, but on a smaller scale with more specific and precise patterns.  Unsurprisingly, precision is a hallmark of mathematics which has, by a popular meme, been called ‘the science of patterns’.  

All this is well and good, but what my colleagues really wanted were more specifics about my evaluative criteria.  How exactly do I gauge my students --within the medium of percussive dance or with regard to the math?  Again my, possibly controversial, answer:  Both.  

And a question back: Why do we think of them as separate activities?  I think part of the issue might have a lot to do with how we, on the whole, perceive mathematical activity.

Generally conceived, dance is a three-dimensional, kinesthetic endeavor.  Math is rote memorization of algorithms and concepts and inhabits a two-dimensional symbolic realm.  Everything we’ve learned in school bears this out, except that it’s really not true!  When I started to really investigate what it means to do math I found that it’s completely different than what I did in school when I was a kid (and you too, probably).   

And, as I dug deeper, I also realized I had been thinking mathematically all my life – I just never recognized it as a mathematical activity.

One of the things I’ve come to realize is that, really, people who do math don’t spend a lot of time plugging numbers into memorized algorithms.  Instead,they formulate and/or approach questions that don’t have immediate solutions.  They spend time thinking, talk to others, sketch out ideas on napkins (or whatever), and build models.  And then, when they think they’ve got something that resembles a solution, that’s when they start writing it down.  The notation is the end result of a process of questions, trial and error, and conversations.  Sounds a lot like what we do in Math in Your Feet, actually.  Take a look:

When I first started wondering about whether or not there was math in the dancing I did with students, I knew I needed an interpreter, someone who really understood math and how it was taught to children. I was lucky to be connected with Jane Cooney, a classroom teacher with deep experience and love for teaching math.  Our collaboration in creating Math in Your Feet included long discussions about the best ways to retain the integrity of both content areas.  We weren’t going to make up the dance to fit the math and I wasn’t going to make up the math to fit the dance.

We didn’t and I haven’t.  There was no need. There is enough overlap between the two that, if you hit it right, you often can’t tell where one starts and the other ends.  However, I have consciously created specific lessons to identify and learn the math that we’re going to use in our dancing.  Not only is math a tool we need to understand in order to use it properly, but I think it’s also important to know exactly how math is involved in our physical and creative work.     

Like the old chicken/egg conundrum, it really doesn’t matter which one comes first because they’re both part of the same process.   And that is why, when I watch my students share their work throughout the week, I can see clearly if they have both the dance and the math and to what degree.  But that’s another story!