The Value of Algebra
I am so mad right now.
I devote a small part of each and every day to perusing some of the dopiest, most inane websites on the net. There are about a dozen creationist web sites I monitor on a daily basis, not to mention several very right-wing political sites. I've grown so accustomed to their relentless stupidity that I barely notice it anymore.
But I read a number of other sites that are supposedly more reliable. At those sites I expect to read things that will provide some food for thought, even if, in the end, I disagree with them. So encountering breathtaking, creationist-level stupidity at such a site is just too depressing.
I'm sure you've figured out by now that I am referring to this column, by Richard Cohen, from the February 16 edition of The Washington Post. We consider it in full:
I am haunted by Gabriela Ocampo.
Last year, she dropped out of the 12th grade at Birmingham High School in Los Angeles after failing algebra six times in six semesters, trying it a seventh time and finally just despairing over ever getting it. So, according to the Los Angeles Times, she “gathered her textbooks, dropped them at the campus book room and, without telling a soul, vanished from Birmingham High School.”
Gabriela, this is Richard: There's life after algebra.
In truth, I don't know what to tell Gabriela. The L.A. school district now requires all students to pass a year of algebra and a year of geometry in order to graduate. This is something new for Los Angeles (although 17 states require it) and it is the sort of vaunted education reform that is supposed to close the science and math gap and make the U.S. more competitive. All it seems to do, though, is ruin the lives of countless kids. In L.A., more kids drop out of school on account of algebra than any other subject. I can hardly blame them.
I can blame them. I'll bet real money that every one of those kids who dropped out of school on account of algebra had problems that go well beyond difficulties in math. Were these students who were generally doing well in their other subjects but, doggone it, just couldn't pass algebra? Or were these people who didn't take school very seriously, had little in the way of discipline, and were just scraping by in their other, less demanding classes? I'm sorry, but no one of normal intelligence fails algebra six times simply because the subject is just so darn difficult.
I'm glad to hear that LA now requires a year of algebra and a year of geometry to graduate. I'm amazed that only 17 states do likewise.
Incredibly, though, that's not the supid part of the column:
I confess to be one of those people who hate math. I can do my basic arithmetic all right (although not percentages) but I flunked algebra (once), barely passed it the second time -- the only proof I've ever seen of divine intervention -- somehow passed geometry and resolved, with a grateful exhale of breath, that I would never go near math again. I let others go on to intermediate algebra and trigonometry while I busied myself learning how to type. In due course, this came to be the way I made my living. Typing: Best class I ever took.
It is a truism among mathematicians that mathematics is the only subject that people brag about being bad at. Cohen thinks it's just the cutest thing that he has trouble with percentages. Can you think of any other academic subject where he would proudly joke about how bad he is at it?
The following fantasy conversation plays in my mind from time to time:
NICE PERSON AT PARTY: What do you do?
ME: I'm a mathematician.
NICE PERSON: Oh, (giggles), I was never any good at math.
ME: That's because you're an idiot.
I never say that of course. No, usually I say something tactful like, “You just never had the right teacher.” But it really is irritating when otherwise intelligent and well-educated people act like you're the weird one for being good at math.
The fact is that things like math phobia, or the idea that people's brains are wired differently, or that some people just can't do math, are total bilge. Hostility towards mathematics has nothing to do with any of those things. In reality it is just standard anti-intellectualism. Nothing more glamorous or interesting than that.
Actually, though, we still have not reached the truly dumb part of the column:
Here's the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know -- never mind want to know -- how many boys it will take to mow a lawn if one of them quits halfway and two more show up later -- or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note -- or reason even a little bit. If, say, the school asked you for another year of English or, God forbid, history, so that you actually had to know something about your world, I would be on its side. But algebra? Please.
Now that's one of the dumbest things I've read in a while. And remember, I read websites that say things like: “If humans evolved from apes, why do we still have apes?”
First, how on Earth does Cohen know what Ms. Ocampo will need to know later in her life? The fact is that if she wants to pursue any sort of scientific subject she will inevitably need to know algebra to do that.
As evidence that Ms. Ocampo will never need algebra, Cohen presents the fact that he has never had to use it. He's never even rued not knowing it! I have no doubt that Cohen is telling the truth here, but that only proves that Cohen has led an empty, intellectually impoverished, life. It says nothing about what students should learn in high school.
He then presents a standard caricature of what algebra is. He has apparently overlooked the possibility that sometimes you use an unrealistic, contrived situation to illustrate a more general principle.
But the idea that calculators and computers can do “most of math” is really just too much. Calculators and computers do not do math at all. They do computation. It's clear at this point that Cohen thinks algebra, and mathematics generally, is just about manipulating symbols according to arbitrary rules. That's like saying that carpentry is about hammering nails and sawing wood. Mathematics is about the reasoning process you go through in taking the information you have and inferring the things that you need. Algebra and computations are just tools you use in the course of implementing such reasoning.
Incredibly, Cohen then tells us that computers can't reason - not even a little bit. Well, duh! That's the whole point!
And then, to cap off this masterpiece of inanity, Cohen offers up his examples of genuinely useful subjects: History and English. Oh, for heaven's sake. Thirty seconds with a good internet connection is enough to learn any bit of history you might be interested in. And English? Has anyone other than an English professor ever needed to read Dickens or Shakespeare?
Of course, the problem here is that Cohen has a pathetically empty idea of what education is all about. Education isn't job training. Education isn't about teaching you how to use an ATM, or balance a checkbook, or any of those other things you need to know in your day-to-day life. You don't need school to teach you those things.
The reason you learn about history, or read great literature, or study math and science when you're in school is precisely because you won't do these things in your day-to-day life. You don't read Dickens because you think it is going to get you a job someday. You read Dickens because the man could write, and your life will be just a little richer for being shown what the English language can be made to do. You read Dickens because by doing so you realize that the things people worried about a hundred years ago are mostly the same things they worry about today. Likewise for any of the other things you learn in school.
Cohen seems to have this idea that education is about learning a bunch of facts. And if those facts don't materially help you in the course of your professional life, then it was a waste of time to learn them in the first place. When teenagers display attitudes like that we chalk it up to immaturity and the lack of a long-term perspective. Columnists for major newspapers don't have that excuse.
Gabriela, sooner or later someone's going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers. Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence. I can cite Shelly, whose last name will not be mentioned, who aced algebra but when called to the board in geography class, located the Sahara Desert right where the Gobi usually is. She was off by a whole continent.
And this paragraph isn't even coherent. Writing is the highest from of reasoning? What? The proof of this is that some old classmate of his aced algebra but couldn't find the Sahara Desert on a map? Does this guy understand what reasoning is? Reasoning is what you do when you are told that a hen and a half can lay an egg in a half in day and a half and want to determine how long it will take seven hens to lay seven eggs. Finding the Sahara Desert on a map is just a matter of being in possession of certain facts.
Look, Gabriela, I am not anti-algebra. It has its uses, I suppose, and I think it should be available for people who want to take it. Maybe students should even be compelled to take it, but it should not be a requirement for graduation. There are those of you, and Gabriela you are one, who know what it is like to stare at an algebra problem until you have eyeballed a hole in the page and not understand a thing you're seeing. There are those of us who know the sweat, the panic, the trembling, cold fear that comes from the teacher casting an eye in your direction and calling you to the blackboard. It is like being summoned to your own execution.
Why not take that attitude with every subject? Maybe we should just make every subject available to students who want to study it, but then leave it up to the kids to decide what they need to know?
As for the uses of algebra, do I really need to point out that every bit of technology Cohen uses every day was invented by scientists, that virtually every major branch of science has mathematics at its core, and that no matter what branch of mathematics you are using it is certain that algebraic manipulations reside at its foundation? Of all the subjects he could have labelled as useless, Cohen could not possibly have made a worse choice.
As for the rest of this paragraph, I'm getting weepy. When you're not understanding what you are reading in your textbook, the solution is to work harder and ask questions. Everyone has subjects they're not good at. But we don't whine and blame the subject. As for being called to the blackboard, I don't know many algebra teachers who actually do that. And I know even fewer who, when the student says he doesn't know how to do the problem, ridicules the student for his ignorance.
Cohen closes with:
Almost 20 years ago, I wrote a similar column about algebra. Math teachers struck back with a vengeance. They made so many claims for algebra's intrinsic worth that I felt, as I once had in class, like a dummy. Once again, I just didn't get it. Still, in the two decades since, I have lived a pretty full life and never, ever used -- or wanted to use -- algebra. I was lucky, though. I had graduated from high school and gone on to college. It's different for you, Gabriela. Algebra ruined many a day for me. Now it could ruin your life.
Sorry, but I don't think it's unreasonable for a high school diploma to certify that you know a tiny amount of higher mathematics.
As I said, I expect this sort of stupidity and short-sightedness from the creationists and the right-wingers. But Cohen is supposed to be one of the Post's liberal columnists. Yet here he is promoting the very silliness he's supposed to be fighting against. Ugh.