Figuring out a problem yourself is better than copying someone else’s down because then it stays processed in your brain. And once it’s processed in your brain, you can’t lose it because you did it on your own.

-A student, reflecting on her first term.

Since September I’ve been dealing with two things that are forcing me to grow. First, I’ve been doing what I’ve done for a year or two, only this year, the response is different. Students are more restless, with shorter attention spans, so giving them long periods of independent work time results in little work from them and little coaching from me because I am spending all my time redirecting. So it’s back to table groups and roles and more, shorter tasks and putting things in front of them to complete instead of writing a broad direction on the board.

Second, I’ve been trying to learn how to develop fluency with some basic skills. My current experiment is in learning how to teach graphing quadratics. There’s lots of great material out there. (Check out James Tanton’s course at G’Day Math). But I thought they would be able to do it as easily as me walking them through it. The skill that common core calls “Seeing Structure in Equations” seems to take time and repetition to build. It’s something I do without realizing I’m doing it. How did I not know this? Seriously, I thought we’d do one day on graphing from vertex form and maybe one additional day to review, then on to the next standard. What’s required, at least for this group this year, is one day on where’s the vertex. One day on width. One day on finding intercepts. One day on synthesis of the above. So good: that’s what it takes. But I’m inventing as I go. It feels a lot like I am just now figuring out how to do what every other teacher already knows how to do.

The student quoted above came to see me after school to get coaching on a problem because she didn’t present any original solutions last term and wants to start 2nd term off by presenting. She announced to me as she arrived that she’s “really horrible at math.” As we worked through some background problems and re-discovered what her classmates had discovered, she lit up (“Whoa! That’s really smart!”), and as she got into the new problem she wants to present, she was really enjoying it. She told me she’s been doing what a lot of students do: waiting for other people to present and then just writing reports of their solutions (which I allow, though I will taper that off as winter turns to spring). Then out of the blue, she said what’s quoted above. I said, “Wait, I want to write that down. You just reminded me what I’m doing here.”