Breaking the Fundamental Rule of the Math Class Game – and paying the price
The Fundamental Rule of Math Class: I teach something, you go home, open up the homework, do what I showed you in class, and you’ll be fine. Same thing on the test.
If a student gets some math published, should that hurt the teacher’s evaluation?
Many teachers never deviate from the rule. And me? I obey the rule, too. Most of the time. Even those of us who don’t always do it, we do it more than we used to. (thanks to standardized testing and the insane link between standardized test scores and the teacher’s evaluation score.)
I taught you how to simplify square roots? When you look at the home work, you’ll be asked to simplify square roots. Do what we did in class, and you’ll be fine.
Breaking the Rule
But some days are different. I introduce “problems” – little ones that take a few minutes, and big ones, where I have moved ahead in my curriculum so that we can carve out a day or day and a half here or there. I offer problems that do not fit the Math Class Game – always off-topic, usually using skills from prior units, or prior years. How many games will there be in a single elimination tennis tournament (singles) with 73 players? How many times a day do the minute and hour hands point in the same direction? What’s the biggest perfect square with only even digits?
“… I ask a group of you a question, unrelated to what we did yesterday, seemingly out of left field, that requires only math that you already know, but without any of the usual cues about what tool to use… Questions mix counting, arithmetic, organization, and visualization skills. They require reasoning, planning.”
And for the last three years, I have asked the students to do more, and more. Take one of the “problems” that you already solved, and propose an extension. Change it up to make a new problem, and solve that one. Mostly I get variations of the checkerboard, how many subsets, and Ghost the Bunny.
The Price or the Payoff?
As these are the same students whose standardized test scores determine my year-end rating (Thank you Obama, Duncan, Cuomo, Weingarten, and Mulgrew), giving up teaching days is a risky venture. Last year my test scores were “effective” but this year they a) count more than twice as much, and b) could easily end up “developing.” I’m guessing I’ll be ok, but if I am not, and I get TIPped, they’ll pretty much have to put “increase regents scores” in the plan and the first thing they’d look for is “stop throwing away days teaching off-curriculum.” And that’s on top of the TIP already being an unpleasant and fairly useless process. Do I really need to face that so late in my career? Because of test scores that are fine, but do not reach some expectation that is kept secret from me, is set by no one I know, and that no one directly involved actually cares about?
Of course there’s payoff. Kids have fun doing math. That’s worth something. They persevere with an extended task, with the finish line not in clear view at the beginning. That’s big. They propose a new problem, not knowing if they can finish it, and they plow in, hoping to make progress. In some cases students do not complete their problem – in their write up they include advice for the next students to try the same problem. Some finish their problem – they often make suggestions for further inquiry. You know, they are behaving – just a little – like little mathematicians. That’s payoff.
And then there’s M. Her problem this fall generated an alternate interpretation for a known sequence, and will have to be submitted to the Online Encyclopedia of Integer Sequences. Like, published. I want to work with her to help her understand more fully what she’s done before she sends the math in for review. At that point I will share the details in this space.
Hmmph. I’ve been doing math, in one form or another for 40 odd years, and nothing of mine has been published. I’ll take credit for asking the kids to be creative, and for recognizing that her sequence seemed unusual, and for knowing a few combinatoricists. Still, not my name going on the entry.
Thing is, M is a good math student, but works a bit slowly on tests. If we could have the problem solving days back, and turn them into test prep, we could probably raise her score a few points. And given the unpredictability of “growth scores” those few points could make the difference between her hurting my score or helping my score.
As long as I don’t get a “Developing” I will claim I don’t care. But if I get a D? Who knows. It raises an interesting question: If a student gets some math published, should that hurt the teacher’s evaluation?