I know I'm late to the game here, but I can't resist taking a moment to dive in to the furor surrounding yesterday's appalling NY Times op-ed, "Is Algebra Necessary?". (Yesterday was my birthday, and I just couldn't face reading something that I knew would make me so angry.)
In case you haven't seen it yet, let's start with a quick look at the argument:
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.
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.)
Already, this is a total disgrace. The number of cheap fallacies in this little excerpt is just amazing. To point out a couple:
- Blame the victim. We do a lousy job teaching math. Therefore, math is bad, and we should stop teaching it.
- Obfuscation. The author really wants to make it look like math is really terribly difficult. So he chooses a couple of silly phrases that take simple mathematical concepts, and express them in ways that make them sound much more complicated and difficult. It's not just algebra: It's polynomial functions and parametric equations. What do those two terms really mean? Basically, "simple algebra". "Parametric equations" means "equations with variables". "Polynomial equations" means equations that include variables with exponents. Which are, of course, really immensely terrifying and complex things that absolutely never come up in the real world. (Except, of course, in compound interest, investment, taxes, mortgages....)
- Qualification. The last paragraph essentially says "There are no valid arguments to support the teaching of math, except for the valid ones, but I'm going to exclude those."
and from there, it just keeps getting worse. The bulk of the argument can be reduced to the first point above: lots of students fail high-school level math, and therefore, we should give up and stop teaching it. It repeats the same thing over and over again: algebra is so terribly hard, students keep failing it, and it's just not useful (except for all of the places where it is)
One way of addressing the stupidity of this is to just take what the moron says, and try applying it to any other subject:
A typical American school day finds some six million high school students and two million college freshmen struggling with grammatical writing. 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.
My question extends beyond just simple sentence construction and applies more broadly to the usual english sequence - from basic sentence structure and grammar through writing full-length papers and essays. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master rhetoric, thesis construction, and logical synthesis.
Would any newspaper in the US, much less one as obsessed with its own status as the New York Times, ever consider publishing an article like that claiming that we shouldn't bother to teach students to write? It's an utter disgrace, but in America, land of the mathematically illiterate, this is an acceptable, respectable argument when applied to mathematics.
Is algebra really so difficult? No.
But more substantial, is it really useful? Yes. Here's a typical example, from real life. My wife and I bought our first house back in 1997. Two years later, the interest rate had gone down by a substantial amount, so we wanted to refinance. We had a choice between two refinance plans: one had an interest rate 1/4% lower, but required pre-paying of 2% of the principal in a special lump interest payment. Which mortgage should we have taken?
The answer is, it depends on how long we planned to own the house. The idea is that we needed to figure out when the amount of money saved by the lower interest rate would exceed the 2% pre-payment.
How do you figure that out?
Well, the amortization equation describing the mortgage is:
- m is the monthly payment on the mortgage.
- p is the amount of money being borrowed on the loan.
- i is the interest rate per payment period.
- n is the number of payments.
Using that equation, we can see the monthly payment. If we calculate that for both mortgages, we get two values, and . Now, how many months before it pays off? If is the amount of the pre-payment to get the lower interest rate, then , where is the number of months - so it would take months. It happened that for us, worked out to around 60 - that is, about 5 years. We did make the pre-payment. (And that was a mistake; we didn't stay in that house as long as we'd planned.)
But whoa.... Quadratic equations!
According to our idiotic author, expecting the average american to be capable of figuring out the right choice in that situation is completely unreasonable. We're screwing over students all over the country by expecting them to be capable of dealing with parametric polynomial equations like this.
Of course, the jackass goes on to talk about how we should offer courses in things like statistics instead of algebra. How on earth are you going to explain bell curves, standard deviations, margins of error, etc., without using any algebra? The guy is so totally clueless that he doesn't even understand when he's using it.
Total crap. I'm going to leave it with that, because writing about this is just making me so damned angry. Mathematical illiteracy is just as bad