play

In Kate's math class, they've been coloring in grids that look like this:

0+0    0+1    0+2    0+3    0+4 ...

1+0    1+1    1+2    1+3    1+4...

2+0    2+1    2+2    2+3    2+4...

to color in all the boxes that sum to, say, 6. Students should (I'm assuming) realize that if 3 + 3 is 6, then so is 4 + 2 (up one, down one)... and so is 2+4 (down one, up one). And so on. and then if they want the ones that sum up to 7, they notice those are always one box below the sum-to-six. Etc. etc. 

But when she "plays" math and gives me a problem to solve, it looks like this (see left) - random addends in random boxes with random rules for coloring: 

She also created a problem for me about 10 cupcakes, and 7 cupcakes went into the cupcakehole. And she knows that's a funny twist on "piehole" (which she knows is one of my favorite words). 

And then this week during her piano lesson, she decided that she wanted to play every piece two ways: the "right" way, and then with her left hand up "up" 4 keys from where it ought to be. (she's only playng the white keys so she's not transposing anything!) And we played it that way and it was fun and at the end of each piece it didn't sound "right" so I would plunk the "C" so that it sounded like an ending!

I want to say that cupcakehole is playing with language in a way that says to me that she "gets" it... or get something. And her piano today was real music-theory play. But her math play isn't math, right? Her inability to play with addition suggests to me (weakly) that she doesn't "get it." She can add and subtract but she doesn't get the patterns of it all and why different sets fo numbers can combine to make the same number. But not that - that's big stuff - she doesn't get the POINT of what she's doing in math.

I think of a paper I just submitted on aesthetics -- I claim that a physics class should give students a new way to play in the world. 

And my students and I are thinking about this sense of play in theory-building ... but mostly I'm just thinking lots about capacity for play as a marker? goal? for learning. And what such play looks like in physics v. other settings. And how much the monks in India were clearly, delightfully playing with their ideas. And where I see Kate playing with ideas v. "just" playing/playing with routines/playing with "school."