My first year teaching, vocabulary was about as far from my mind as possible. I was in the business of figuring out which battles to fight, and competing for my attention were things like kids who couldn’t add and classrooms that operated at a dull roar while I tried to talk. If a kid was doing good work and happened to say “the little 2″ instead of “exponent”, what did I care? In a situation like that, I would already have been winning so many fights that I hardly wanted to start a new one. I went to PDs where they told me that I needed to care, but I thought of plenty of reasons to ignore them. Didn’t they just have to say that? Isn’t caring about literacy The Thing To Do, no matter what? Aren’t they saying this for teachers of kids on grade-level? If my kids barely speak English, is this really useful? Do these people have any idea what my teaching situation is like?
It didn’t hit me that I was deeply and entirely misguided until the very end of my first year. I was working after school with a really sweet student who desperately wanted to pass math and couldn’t. Both his math and his English-language skills were very low, and I was letting him cut every corner I could find in hopes that he could accomplish just the basics of the current unit. We were working on the Pythagorean Theorem, and we were trying simple problems again and again and again and again and again. As the afternoon wore on, I was startled by how well I could get him doing one problem and how immediately he got all caught up and confused in the steps just minutes later. Finally, I had him put down the pencil and just try to explain to me the steps of a problem we’d just done (in whichever language he wanted).
He couldn’t. As he struggled, it dawned on me that he had no words for what he was trying to explain. There was a sea of numbers and pictures in front of him, but humans have a tendency to name things for a reason. He needed something to identify what he was doing, something to latch on to, something to make connections with in his brain. Instead, I had spent all year focused on the calculations happening in front of us, and I’d never taken the time to stop and give him language for it. The Pythagorean Theorem requires more than “that little 2″ – it requires an understanding of exponents. Just that word, “exponent”, actually carries with it a concept, a connection to previous problems, and directions for what to do in the case in front of you. “The little 2″ brings nothing but a weak description of marks on the paper. That is a distinction that a million PD sessions could never teach me, but watching that boy struggle was enough to make me feel slapped in the face with understanding. (Cue the classic first-year-teacher feelings of guilt and regret.)
Today, I’m far from the vocabulary expert, but it has at least become a no-exceptions part of my classroom. If you say something without mathematical language, you need to say it again. If you can’t fix your mistake, someone else in class will fix it for you and then you can try it yourself. If you can’t pronounce or spell a word, you and I will sit together and practice. When I pick battles in my classroom today, I choose things like fighting for the word “proportion”, not “poorpotion”.
Yesterday, one of our lowest students asked me for help with an order of operations homework problem after school. I was late for a meeting and rushed him through the steps instead of doing a good job with him. With some shame, I’ll admit that when we got to 2^2, all I said was, “Now what’s two times two?”
He looked at me like I’d grown another head. “Miss, that’s not two times two! That’s an exponent. It means we do two squared!”
Sure, I wish he’d recognized that we were doing the same thing, but that’s not the point. What stopped me in my tracks was his confidence in both the content and the language. The fact that he recognized the exponent, had a word for it in his head, and from there could tie it back to all the problems where I begged kids not to multiply base times exponent. It had meaning to him, it had history for him, and it represented something where he knew what to do next. You can’t tell me that learning vocabulary didn’t play a significant role in that.