This dude is strong. No question about it. He can lift very heavy things. Every day he hits the gym, spends an hour or so on the bench, probably another hour doing lat pull-downs. He may vary it up, doing chest/back on even days, arms/shoulders/legs on odd. Whatever his routine, clearly it's working. And maybe that's great. Maybe there's a certain utility in being able to curl 300 pounds today, in order that you can curl 305 tomorrow.
But are all strengths the same? Indeed, could we even say that this guy is strong in a real-world way? The dictionary definition of "strength" is the capacity for exertion or endurance, which suggests an application, some activity for which you're using all this strength. So is he a rock-climber? A boxer? Is he a firefighter responsible for dragging hoses into burning buildings? Put another way: what's the point? Beyond body building competitions, is there some reason why he's lifting all this weight?
I read an article in yesterday's New York Times about Jump Math, a math curriculum designed by John Mighton, hailed by some as a "kind of math miracle worker." Teachers in England and Canada praise Jump Math's effect on student performance, including dramatic gains in standardized test scores. Curious what a miracle looks like, I downloaded the student workbook for Grade 8, and was surprised by what I found:
It seems very traditional, your run-of-the-mill skills-based approach to math instruction. In this sense, it's not unlike most curricula that students see every day, in that it takes math, breaks it into a bunch of smaller skills, and addresses those individually. As described by the article, a key difference is that Jump Math takes this even farther, "break[ing] things down into minute steps and assess[ing] each student’s understanding at each micro-level before moving on." LCM today. GCF tomorrow. Then prime factorization, order of operations, identifying fractions, etc., etc. Bench press. Flat bench fly. Incline press. Decline flies.... It's hyper-focused--every muscle group is covered!--and, at least judging by the test scores, very effective.
But that's the crux, right? What are we measuring? Of course, standardized tests aren't going anywhere. Like it or not, they're a fundamental part of what it means to be a teacher these days, and bemoaning this reality prompts the Don't hate the player, hate the game truism. Still, in the same way that being big and being strong are different, knowing how to do skills and knowing how to do math are not the same. Skills are a subset of math, just like grammar is a subset of language. Necessary? Yes. Sufficient? Hardly.
Which gets to the question that arguably matters most: what's the purpose of a teacher? What's the point? Does a teacher train for training's sake, or does he/she prepare students for what comes next: the game of life? Breaking math into discrete skills is good...until it's not. You can't build a house from a whole tree, so you cut it into boards. Fine. But maybe those boards are still too big, too unwieldy, so you cut them down further. Okay. But if you keep going, and going, and going, then ultimately you're going to be left with sawdust, and that's pretty tough to build with.
Quarry, stone, rock, pebble, sand. If the purpose of math is ultimately to construct something larger and more meaningful--if the purpose of being strong is to apply that strength to some real-world activity--then at what point do we draw a line in the road, lest we end up in the sand?
Teaching is incredibly liberating, but can be a drag when we feel like we're just implementing someone else's agenda, someone else's priorities (especially when those priorities seem to change each year). Again, standardized tests aren't going anywhere, but what if they did? How many of these "miraculous" programs would disappear with them? Look at a textbook, a Mathalicious lesson, your own approach to math. Look at everything there is to look at. And then ask: "If the rules were different, would this still exist?" You still have to be able to lift heavy things, but now you have to run, too.
Math is timeless, and trumps legislation. Real teaching is timeless, and doesn't require outsourcing autonomy simply to meet AYP. Yes, there's a game to play, and yes, we have to play it. But let's remember something, something that's always been--something that will always be--true:
Cogs spin. Teachers teach.