Is Our Kids Learnding, Algebra Edition

by evanmcmurry

Thoughts on Andrew Hacker’s op-ed in Sunday’s New York Times arguing that we should 86 algebra from core high school curriculum:

1. I definitely think Hacker’s talking more about algebra II, and higher-level stuff like trig and calculus, than he is straight-up freshman-year algebra. He makes the distinction, in a blink-and-you’ll-miss-it way, but the article explicitly talks about algebra for the most part.

However, if we confine Hacker’s article to algebra II, then he’s got a point: a mathematician friend of mine with experience teaching at Hacker’s exact level recounted

a foundations class that (college) freshmen could take in lieu of an algebra II-type thing. It had *some* algebra but mostly combinatorics, probability, and logic. It will be infinitely more useful to them in their lives, and I think some research needs to go into whether those types of courses should be offered in high schools FOR THOSE TYPES OF STUDENTS.

That sounds perfectly reasonable to me. It’s a much narrower reading of Hacker’s article than his own thesis allows; whether Hacker meant to make the broader argument, or the Times thought the more sensational headline would increase traffic, I have no idea. But I wonder if this debate would be more helpful if he’d tailored his argument to be less risible.

2. This piece seems missing a lot of context. Like, all context. Are the problems students are experiencing with algebra new? Were students having just as much trouble with the subject ten, twenty-five, fifty years ago? If they were, but graduation rates were higher then, what were we doing differently, if anything? If the curriculum hasn’t changed, but the results have, wouldn’t that suggest that the problem is not algebra, but something extrinsic to schooling? Along the same lines, are other countries having this problem? (Dana Goldstein suggests not.) If not, why not? If they’re teaching algebra and getting different results, again, that would suggest the problem isn’t algebra but something either endemic to our education system as a whole, or to our society’s relationship to it. In short, Hacker seems uninterested as to why we’re doing poorly at algebra; he seems content to point at it and say “there’s the problem.” This strikes me as classic mistaking-the-symptom-for-the-disease.

(Hacker tags the international argument, briefly: “It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.” Anybody who knows what that means, lemme in on it.)

3. Check out this paragraph:

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.

That’s called reasoning. Good thing somebody, probably a teacher, taught Hacker how to do it. I doubt that teacher taught Hacker reasoning by using this exact example (“Suppose that X believes P, wherein P is the proposition that algebra is valuable”) but probably used similar examples from which Hacker eventually assembled the skill. Hacker may never have encountered the exact problem his teacher used, but that doesn’t make the problem irrelevant to Hacker’s life; in fact, it enabled him to get published in the New York Times.

So when Hacker writes, “But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis,” he’s being too clever by half. No, knowing how to solve that equation probably doesn’t help you project the funding effects of the Affordable Care Act on the deficit. Knowing how to solve complex equations with multiple variables sure does, though. Which is to say, learning to solve (x² + y²)² = (x² – y²)² + (2xy)² is valuable, even if it’s never encountered in real life. In this case, it’s the skill, not the knowledge, that matters.

4. John Locke, Book IV of An Essay Concerning Human Understanding, hit it:

There could be no room for any positive knowledge at all, if we could not perceive any relation between our ideas, and found out the agreement or disagreement the have one with another, in several ways the mind takes of comparing them. (IV.v)

That reads like a simulacrum of algebra to me. I know, Locke is dead ol’ white guy, and his formulation of knowledge, of which the above is 25%, was by definition elite. But still. There’s something foundational about algebra, no matter how unpleasant it is, something that girds it against passing educational fads, shifting socio-economic concerns, and, well, popularity. Or, as my mother used to say when I complained about doing problems 1-99 from my Algebra II textbook, “Math doesn’t care whether you like it.” She was right; the quadratic equation persists whether we learn it or not, and the laws of mathematics participate in the governance our lives whether we enjoy them or not; refusing to learn math because it’s obtuse only disadvantages you. Hacker knows this:

Mathematics, both pure and applied, is integral to our civilization, whether the realm is aesthetic or electronic. But for most adults, it is more feared or revered than understood.

But if this last part is truly the problem, it seems like more education is called for, not less, right? (h/t Kasia for pulling that quote out.)

5. If I were a nineteen year old who’d just read Marx (or a 24 year old who’d just read Althusser) I’d point out that this essay sure seems to be calling for the disabling of the proletariat of any ability to navigate an increasing complex economic system of which they are very much the victims. While I normally think that those who describe Republican attempts to remove humanities and such from the curriculum as “preparing new Republican voters by sowing ignorance in the populace” are assigning too much intention to the GOP, a call for not teaching complicated mathematics just after an historic financial collapse involving derivatives that were commonly described as “complex” sure seems a little off. In short: if you wanted to make sure nobody could understand your crimes well enough to be outraged over them, this would be a good way to do it. That’s IF I were a nineteen year old who’d just read Marx.

Which brings me to my next thought:

6. The two states Hacker highlights as having the worst attrition problems are Nevada and North Carolina. Those two states have some of the worst unemployment rates, with Nevada holding the ignoble record. I have no idea what the causation would be between those two facts, if there were one; something tells me there’s a chicken-and-an-egg thing with education and unemployment. But this ain’t the causation:

Toyota, for example, recently chose to locate a plant in a remote Mississippi county, even though its schools are far from stellar.

Huh, it’s almost as if there’s another explanation for that or something. Either way, that a manufacturer decides to bless a municipality producing poor education rates with a factory is not an endorsement of that area’s education policy, nor is its long-term consequences beneficial to that region’s educational performance. Striking algebra as a requirement because it’s not necessary for the local economy is a good way to ensure you produce workers who are able only to satisfy the needs of the current economy, not the potential needs of a future one. In other words, you don’t want to have a city full of factory workers when your economy suddenly goes high-tech.

Hacker also makes this argument in reverse:

An equally crucial issue is how many available positions there are for men and women with these skills. A January 2012 analysis from the Georgetown center found 7.5 percent unemployment for engineering graduates and 8.2 percent among computer scientists.

But will the unemployment rates for those jobs now be the rates forever? What happens when our economy rights itself and we suddenly find that we need high-tech jobs to compete? I think the internet bubble is a good example of the unpredictability of of required skills in an economy: who knew people would one day be making billions over competing search algorithms? If you had been designing an education system in the 80s using Hacker’s article as your guide, you would probably conclude that the America is headed towards a service-oriented economy, and needs real-world math skills along the lines of working a register or a database. All well and good, but there goes your job force capable of staffing the high-tech industry. Education is by definition a long-term enterprise; trying to game the skills of the future based off the job requirements and unemployment rates of the present seems like a losing tactic.

The rest of you, thoughts?