For a quick diversion from the immediately relevant tasks of quantifying legislator votes and charting the ebbs and flows of Rhode Island civilization, I can’t resist commenting on Andrew Hacker’s New York Times question, “Is Algebra Necessary?“:
My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.
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.)
My experience was somewhat like that of Glenn Reynolds: I was good at math but didn’t become a fan until I began putting it into practice. That practice rolled out in many different phases: Music, for one, is built on mathematical concepts; analyzing public policy as a hobby in my mid-20s lent a new relevance to calculations and proofs; but the visceral love of math only came when all of my preferred career paths came to a dead end of unemployment.
When you can double your salary in a year because you’re the only guy on the construction site who can find a radius from any two points on a circle, you look back very fondly on those silly courses in quantitative abstractions. I should note, especially, that I didn’t remember any but the most basic formulas; the key was a general recollection of the concepts, fleshed out with Internet searches as necessary.
Ultimately, Hacker’s question is far too limited. First, we must know: What is public education for? Not mentioned once in his article is how students are to discover either (1) what their academic interests are, or (2) what they’ll actually be able to make a living doing.
He writes, “a definitive analysis … forecasts that in the decade ahead a mere 5 percent of entry-level workers will need to be proficient in algebra or above.” Put aside the question of whether such trades as carpentry are included in the estimate. The relevant question for a society determining what its students must master is: What percentage of that 5% will know, in seventh grade, that they will be among the 5%?
That question leads to critical considerations. Some subjects, for some students, require a mandatory minimum exposure before they become hooked. More importantly, extensive exposure to a topic is perhaps the only way to ensure that (for my personal example) a creative writer will recognize what sorts of problems he’s tackling when he’s staring at a sheet of plywood in his early 30s.
In these terms, is algebra one of the topics that all students should have beaten into them at least thoroughly enough that they’ll know it when they see it, even if they don’t remember how to do it? Our society appears to think so. Perhaps some of the screws could be loosened, particularly when it comes to college entry and graduation; at that point, students should have more of a sense where they’re headed.
But consider Hacker’s compromise:
… mathematics teachers at every level could create exciting courses in what I call “citizen statistics.” This would not be a backdoor version of algebra, as in the Advanced Placement syllabus. Nor would it focus on equations used by scholars when they write for one another. Instead, it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.
It may be that my radar is more sensitive to such things, as a blue-state conservative, than that of a New York Times op-ed writer, but such a course summary strikes me as fatally susceptible to the sorts of bias that establishment voices like to define as not a bias. Indeed, it brings to mind another value of slogging through algebra courses: It gives young Americans a sense that there is an objective logic to any subject without regard to its application.
For any school in which I have an interest, I’d suggest that, rather than eliminating algebra, it would be better to reallocate resources from fluffier concerns in order to hire teachers who are up to the task of teaching it. Of course, that might require rethinking the principle that all subjects ought to cost the same amount to have taught, depending on the longevity of the union member at the blackboard.
But then, I believe that making a national issue of the fundamentals of education is a miscalculation. If Jane’s parents in Maine attribute greater value to a than to b, and Tom’s in Arizona believe that c is the greatest of all, why should Andrew in Washington, D.C., have a say in whose school requires what?