As you read, I invite you enjoy this blogpost multimedia style while you listen to K.D. Lang.
Walking home from dinner tonight, I was teased mercilessly by my comrades for crying and blogging about crying. While I am not the caricature they perform, I will admit that I have been crying with a lot more frequency of late. Back in May, of course, the crying wasn't so fun. But here at PCMI, it's been joyful bursts of awe and deep heart opening, mostly to do with mathematics. Not even talking about teaching, just straight up math. This has never happened to me before, and it's cool, even if people do make fun of me for it. I like it. I like being surprised in my own skin.
So I will tell you about two more recent tales of my mathematical emoting here at PCMI, where kids & families are welcome and all levels of mathematical experience will thrive and blossom. You yourselves are not guaranteed to cry, whether you want to or not: crying seems to be the way that this experience is manifesting my new levels of engagement and joy in my mathematical practice, but it would manifest differently for others, I'm sure.
In the afternoons, we all work in smaller groups to do some math and create a product that could be used by other teachers. I'm in the Discrete working group, and we've been looking at these jug problems, which are apparently iconically represented in mathematics curricula by hooking kids with the Die Hard with a vengeance clip. The basic problem: you've got a fountain, a 3 gallon jug, and a 5 gallon jug. How do you get 4 gallons? Last week, we worked, solved and extended this and other related problems, and enjoyed employing M.C.K Tweedie's graphical solution method on a triangular grid. I had been frustrated if excited by this method, because our leader just sort of showed it to us, and I couldn't figure out how on earth anyone would have just come up with it. But yesterday, our fearless leader gracefully and patiently talked us through how you can think of the possible states of the jug's as coordinates in three space, and when you do that, all those states lie in the same plane, which, if you connect the coordinates, makes precisely the triangular grid we had been working with. Let me tell you, I was the most surprised person there, but as soon as I saw it, I had to take my glasses off and wipe my eyes as I CRIED. Ridiculous, amazing, laughable, tender, wow. That's all I know to say.
Also, this morning the group had a nice conversation in our Reflection on Teaching Practice session about how to watch teacher videos, and I got to process a lot more about what Rob and Ben (in his comments here) said.
Here are the things I've been integrating from all this:
1- When we hang out with kids who haven't yet learned their times tables, do we ridicule and points fingers? Do we politely snub and dismiss them? Do we secretly feel superior because we have already mastered this amazing skill and they haven't? Mostly, I'm thinking the answer is no. When someone next to me is working faster than me, or straight up knows more math than I do, it is (mostly, at least) because they have spent more time doing it, they've seen it before, and/or they have already learned it. Ben Blum-Smith taught me this idea.
2- Learning to teach is like learning to do math. In fact (hats off to Ben here as well) you could say that the process is entirely parallel, within our own lives and between us and our students. In both, we need to be generous and kind to ourselves and our peers as we reflect and learn how to teach (do math) better, more fluently, more efficiently, more creatively. Just like we wouldn't ridicule the kid who hasn't learned something yet, we don't need to batter a teacher who hasn't learned to do a particular teacher move yet. It doesn't mean they are a bad teacher, or even that they are doing "bad teaching" necessarily. I won't even venture to say what it means, only that it seems worthwhile to hold back our judgment instincts and just practice noticing. Ben's comments address this specifically and beautifully. I'm linking to them again and again because they're so good.
3- In A New Earth, Eckhart Tolle writes, "In essence, you are neither inferior nor superior to anyone. True self-esteem and true humility arise out of that realization. In the eyes of the ego, self-esteem and humility are contradictory. In truth, they are one and the same." We can enter into viewing other teachers with the humility that we all have had many minutes in our teaching (maybe most of them) when we would, upon reflection, given more time or more experience, have made other choices. We can enter into viewing other teachers with the confidence that we are smart, capable, generous and qualified to be doing this job, which is one of constant learning and growth. A process.
I'm off to the ice cream social. I've been doing math what feels like 24-7, writing about it with urgency when I'm not doing it, learning it, eating it, sleeping it, teaching it, walking it, loving it. Mathematics has become my spiritual practice. Thanks for everyone who is holding space and supporting me through it. I am changing on the insides. May your nights be bountiful and delicious, whatever the weather.