Day 2 of the Math in Your Feet primary project was super interesting and provoked a lot of thinking on everyone's part, myself included. (See my Day 1a and Day 1b posts for an overview of this project if you need some context.)
I enjoyed myself and the kids were excited to do their work but throughout the sessions I had an odd sense of dis-ease. This sense was difficult for me to articulate until I transcribed the video footage from both schools but now I'm pretty clear: it's (mostly) all about units.
At the heart of our work in Math in Your Feet is the pattern unit and all the things you can do with it (make it, change it, compare it, transform it, perform it). With my new audience of K-2 kids I'm getting to see what happens when I work with humans who are still developing a sense of wholes and parts. It's especially interesting to observe their work when I challenge them to 1) dance a pattern the same way every time and 2) take a familiar-ish pattern and re-unitize it (which requires them to make different combinations/units using the movement pieces from the original pattern). Here's an example from the K-2 class:
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| This group came up with [Jump Step Jump Step] |
Me to class: I have a question. We have two different patterns up on the board. Let's do them w/ our hands...jump jump step step. Good. Now let's see if we can do the second one...Let's do it with our hands...jump, step, jump, step...[kids keep going...jump, step, jump...] Oh wait! How many times do I do that? [This is where I really started thinking about units; they need to have a sense of where the pattern starts and where it ends.] I do Jump Step twice, so there are how many beats? [Kids say Four!] Let's try that with our hands together! [speaking and moving slowly] Jump...Step...Jump...Step.
Me: Now. I have a question for you. Can you think of another way to combine two jumps and two steps to make a different pattern?
The kids jump to their feet and start working enthusiastically. I stop the group after 2-3 minutes.
Me: Before we're done today, if everybody has a pattern that's
new to them I want to get it down on the board. Who wants to show their work?
1st grade girls 1 & 2 (dancing and talking): Jump, Step, Jump, Step, Jump, Jump, Jump, Jump
Me: I put a line between JSJS and JJJJ. So really, how many patterns is that?
Girl 2: Two!
I write it on the board and then ask the girls: There's pattern A and there's pattern B. Nice! Give them a
round of applause! Who's next?!
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| Jump Nod Step Jump Nod Step |
Two little K girls (dancing and talking): Jump Nod Step Jump Nod Step
Me at the board: So what was the first thing they did? [getting feedback from the class, writing down their pattern] And now my question is, is JNSJNS the whole pattern or is it two two of these [JNS]?
At this point I should say that adding in movements other than the jumps and steps I've introduced has become a bit of a theme with all the Ks and 1s I'm working with. Although I am being as explicit as possible about What Makes A Unit (right now that means steps and jumps done in 2 or 4 beat combinations) K-1 kids have been extrapolating that to mean "Any move you can make on an individual beat." I actually think this is kind of cool and am trying to figure out how to harness this in future lessons. But, I also think it might be related to the conceptual/cognitive development of both units and sets of things.
After all, WHAT MAKES A UNIT? To me, a 4-beat foot-based dance pattern is a unit that includes certain inventory of things you can use to decide:
- where your feet are
-how you move your feet, and
- the direction you move in.
And this is why it's fascinating to have these other moves (nod, clap, shoulder movements, toe touches, jumping jacks...some of them from our warm ups, some of them not) show up in the patterns like unexpected wild poppies in the garden. Gorgeous, but because they're prone to reseed like weeds, how will you deal with them in the context of your larger garden plan?
In other words, what's the balance between my agenda and their lovely sense of personal and creative agency?
None of this bothers me, by the way; I actually find their verbal and movement answers surprising and delightful. But it does make me wonder about my expectations for K-2s in general and these K-2s in particular.
But, the good news is, it's clear they've got the main point: we're using rhythm and movement to make our dance patterns; we can experiment and make new patterns; we need to remember and repeat these patterns; Malke asks us to notice things and talk about our patterns; there are special words we use to describe our work. To be continued...
Me at the board: So what was the first thing they did? [getting feedback from the class, writing down their pattern] And now my question is, is JNSJNS the whole pattern or is it two two of these [JNS]?
One of the K girls: JumpNodStepJumpNodStep.
Me: ...is the whole thing? (she nods) Okay, so we're going to call that one pattern and I'm wondering how many beats this pattern is? [Random answers from the group including TWO!]
Me: Let's count them (using my fingers while I say) JNSJNS...it's...?
Class: Two! Six!
Me: ...each time I say a movement it's a beat. J N S J N S. How many?
Class: SIX!
Me: It equal's six. And these [pointing to the JS combos written on the board] are four...Okay.
At this point I should say that adding in movements other than the jumps and steps I've introduced has become a bit of a theme with all the Ks and 1s I'm working with. Although I am being as explicit as possible about What Makes A Unit (right now that means steps and jumps done in 2 or 4 beat combinations) K-1 kids have been extrapolating that to mean "Any move you can make on an individual beat." I actually think this is kind of cool and am trying to figure out how to harness this in future lessons. But, I also think it might be related to the conceptual/cognitive development of both units and sets of things.
After all, WHAT MAKES A UNIT? To me, a 4-beat foot-based dance pattern is a unit that includes certain inventory of things you can use to decide:
- where your feet are
-how you move your feet, and
- the direction you move in.
And this is why it's fascinating to have these other moves (nod, clap, shoulder movements, toe touches, jumping jacks...some of them from our warm ups, some of them not) show up in the patterns like unexpected wild poppies in the garden. Gorgeous, but because they're prone to reseed like weeds, how will you deal with them in the context of your larger garden plan?
In other words, what's the balance between my agenda and their lovely sense of personal and creative agency?
None of this bothers me, by the way; I actually find their verbal and movement answers surprising and delightful. But it does make me wonder about my expectations for K-2s in general and these K-2s in particular.
But, the good news is, it's clear they've got the main point: we're using rhythm and movement to make our dance patterns; we can experiment and make new patterns; we need to remember and repeat these patterns; Malke asks us to notice things and talk about our patterns; there are special words we use to describe our work. To be continued...
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| I love that this girl drew the white board. It looks exactly the same as the real one! |
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