The devil is in the details, or so they say. But what details are they talking about? Some details are vital to the stories we tell. What would James Bond be like if he drank club soda? How would we recognize Pigpen without the cloud of dust hovering above his head? Hamlet wouldn’t be terribly interesting if he was known for his decisiveness.
On the other hand, some details are simply filler. I think “meaningless” is coming on a bit strong, but that was actually the first word that came to mind. Does it really matter that the curtains are red instead of green? Maybe it does. But if it matters, you’d better make me care passionately about those damn curtains. If I don’t care, I’ll probably forget, because some details are forgettable.
All these thoughts about details in storytelling somehow relate to math of course. Doesn’t everything?
So, forget about the curtains—they really don’t matter—and think about how this relates to teaching: If I don’t care, I’ll probably forget, because some details are forgettable.
My job as a teacher is to make my students care about math. Oh, and to teach them content too, you say? Once more, with feeling: If I don’t care, I’ll probably forget, because some details are forgettable.
What exactly do we teach students? Procedures, formulae, facts, an amorphous blob called “problem solving skills”. Those long dry lists of state standards written in the least kid-friendly language possible. That is what we teach, right?
So…what do students actually learn? Ahh. Well, I taught them the quadratic formula, so they must have learned it. Right? Umm, not exactly. Did they need to know the quadratic formula? Were they wanting it, pleading for it, musthaveitrightnow? Did they care? Okay, some of them might care because you told them to care, or because they know it will be on the quiz next week and they care about doing well and earning their points. But did any of them feel fire in the belly, where they needed a tool to solve a problem they really-truly wanted to solve but couldn’t figure it out without this magical thing? If not, are they really going to remember this formula in a month? For the final? In ten years?
Do I want them to? Do I care?
That last question has been something that I’ve been thinking about for a long time. What do I want my students to remember forever? I admit it—I’ll go on record as saying that I don’t particularly care if my students know all of their trig identities in a decade. I don’t remember them either. I can look them up if I need them. The entire online math community can shun me now if you so desire. But this raises a big hulking question. If the trig identities aren’t what I’m asking kids to learn, what the heck am I getting paid for?
I was introduced to the language “habits of mind” when I was a proto-teacher, not yet pulling a paycheck. I think by now, most teachers have at least heard about this idea. If not, see the expansive list at Without Geometry (though, seriously, if you’re reading this post you’ve already seen it—all 11,000 of you). But these are the things I want my students to NEVER EVER NEVER forget. I want them to look for and see patterns, and to explore new ideas, and ask insightful questions about things that confuse them. That’s what I’m teaching students for reals. That’s what I’m hoping they are learning. If they aren’t learning those strategies and skills, then I don’t deserve to have my job. Period.