Over at the Times they’ve got a big piece on Almighty Algebra by Andrew Hacker and how it’s crushing our students:
A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t…
There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)
The obvious question here is just how far “algebra” reaches into “quantitative skills.” Hacker is somewhat unclear on this point. “My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus,” he says. But that represents three to four years of mathematics. If we’re talking advanced algebra, trig, and calculus, I agree, despite their massive scientific utility, those are probably outside the reach of the average student. But throughout the rest of the piece he’s talking just “algebra.” Even the simplest bit of quantitative reasoning—trying to figure out which credit card offer is screwing you the least, say—needs some variable work. Just where do we stop with that? Hacker isn’t clear.
In any case, this got me wondering. Suppose Hacker really is talking about basic algebra. I did that in eighth grade. From there I went through the usual cycle, through geometry and calculus, and then a couple math classes in college required for a chemistry degree, which were by far the hardest classes I’ve ever taken, leading to existential panics and profound self-reevaluations. And that barely scratched the surface of college-level material, which in turn isn’t even close to the work that real mathematicians do.
I would estimate that in my school career I made it about 5 percent of the way to an actual high-level understanding of some kind of mathematics (since of course no one person can be an expert in every sub-field). In turn, I would estimate that basic algebra represents about one percent of my understanding at its peak (now significantly decayed), or roughly 0.05% of a full math education. Is the average person really so rubbish at math that they can’t handle that? Or, perhaps our culture has such an inferiority complex about math that we hamstring ourselves? What do you think?
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