First, a little context. I've just finished four days of hands-on workshops for a summer camp of kids ages five to twelve. Our hour-long, mixed age classes have been full of rhythm and patterns in the feet as well as exploration of other kinds of patterns including ones we can find in nature (Fibonacci numbers, hexagons in bee hives, etc.). I've also told some stories about squares who are completely bored with their straight edge/sharp corner existence who want and need a change. (See a version of these stories in a recent post called Scissor Stories: Tales of Transformation.)
This kind of summer programming up in the city finds me working with kids whose backgrounds I know nothing about. I don't know where they came from or where they're going, so I mostly just try and go with the flow, try to meet them every day where they're at instead of where I think we should be.
Although grant sources require some 'evidence' of learning or growth, my job is to do the best I can in four days. To the kids I describe our work as using and making and understanding patterns of all kinds, and we spend most of our time doing just that; instead of explicitly talking about patterns, we're just trying to make and use them. As a result, kids may or may not have absorbed new vocabulary to use when it's time to assess their learning on the final day. I think my goal is simply that they have a reserve of experience to call on when they're back in school learning math with their paper and pencils.
But, like I said, I still need to ask them questions at the beginning and at the end. Here are the questions I asked this week. I'm still not sure that the first question is a helpful one for assessing learning but, as you'll see, it did provide me with some very interesting information:
Question One: "What is a pattern?"
First of four days, summer camp children ages five to twelve:
Something that is ABB and it keeps going...
Two or more things on paper...putting it on paper over and over.
Square then rectangle, keep going.
Something that gets put together.
Numbers -- 1, 2, 1, 2...
Heel, heel, toe, toe... (a clogging step)
Circle, circle, square, hexagon (We studied a hexagon as one of our nature's patterns inquiries.)
Take things and put them in order.
You know it's a pattern when it's the same, something that repeats, like red, yellow, red, yellow...
Question Two: How can you make patterns with your feet?
Different kinds of shoes and socks.
1,2,3 on one foot, 1,2,3 on the other foot.
Mix with other people's feet.
Big foot, small foot...
Number of taps.
Steps, slides, jump, turn.
(Use directions) left right front back diagonal.
(Put your feet) together, split, crossed.
Big, small, big, small (movements)
Heel, heel, toe, toe (a clogging step)
Use toes, heels, kicks.
It's heartening to see that the answers to the second question showed much more understanding after four days of dancing. As for the first question, it's clear to me that, even after four days of playing around with patterns, the idea of pattern these children (and pretty much every other child I've seen this summer) have internalized is a very narrow conceptualization limited to colors and shapes that repeat in a linear way one after another, almost always "on paper."
Driving home today (it's over an hour each way) I had a lot of time to think. I was thinking of all the ways we can harness kids' love of doing and making in the elementary years to the goal of engaging in an deep and meaningful exploration of patterns of all kinds. And that, in the the process of this kind of exploration, kids would get a chance to represent and experiment with this oft perceived 'simple' concept in a multitude of ways: 2D on the page (so many ways to do this), 3D with their bodies as well as all the great math building materials out there, and even 4D using time and rhythm.
While I drove I also had a lot of questions in my head: How can kids learn to see patterns in numbers if all they know is 'red, blue, red, blue'? How can they understand what patterns are if they don't have personal experience with constructing them, taking them apart again to explore the pieces, and transforming them into something completely different?
I am certain it is possible to provide deep, meaningful, artistic, open ended explorations of patterns at the elementary level. We do it all the time in Math in Your Feet with percussive dance; I am starting to understand how I might move this approach toward other mediums. (To see a really nice curated collection of math art, go to the Math Munch blog.)
I have a lot more thinking and learning to do on this topic, but for now I'm clear on one thing:
Almost every one of the 180 kids I encountered this summer, no matter their age or their dancing ability, were unable to identify or describe patterns outside the standard textbook context. I think they can handle more. Not only that, I think they want more.