Three weeks ago, Duke Helfand of the Los Angeles Times wrote a thoughtful article on high school algebra. A one-semester course in algebra has recently become a requirement for graduation in the Los Angeles unified school district, and many students are having a hard time with it. The Times article tells the story of Gabriela Ocampo, who failed the course six times and finally dropped out of school when it became apparent she would have no more success on her seventh attempt.
Last Wednesday, Richard Cohen, an op-ed columnist for the Washington Post, was inspired by Ocampo’s plight to publish his own thoughts on mathematics education, from which I extract a few sentences:
Gabriela, this is Richard: There’s life after algebra….
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….
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…. Most of math can now be done by a computer or a calculator….
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.
Richard, this is Brian. Although I’d sooner swallow Drano than speak these words, I have to admit it: You’re right. There is life after algebra. Millions of our compatriots are living proof—contented and productive citizens who couldn’t solve a quadratic equation to save their lives. But, Richard, you don’t go far enough. Why stop at algebra? Elementary arithmetic is also highly overrated as a passport to riches and fulfillment. On this point I can offer personal testimony: I’m very shaky on my multiplication tables (in spite of the valiant efforts of Miss Cross, who drilled me relentlessly in the second grade), and yet I have managed to stay off the welfare rolls, and I even file my own income-tax returns. Although your claim that computers and calculators can do “most” math strikes me as a little ahead of its time, those machines sure are handy for +, –, × and ÷, not to mention those irksome percentages. Come to think of it, maybe we can cut off the mathematics curriculum even before the kids get as far as arithmetic. After all, unless your ambitions tend toward professional gambling or ballroom dancing, you can probably get through life today without even knowing how to count. Why demand that our children learn such frivolous skills?
“You will never need to know algebra,” you tell Gabriela Ocampo. But what do you mean by “need to know”? Apply a strict enough standard, and very little of what we teach in the schools would survive the test of need. Who really needs to know the names of the planets or what happened in 1066 or why Achilles sulked in his tent. Does anyone’s life depend on memorizing the prelude to “Evangeline” or knowing the price of the Louisiana Purchase? Reason not the need, Richard. Culture begins just beyond where need ends.
I too have a gripe with algebra in high school. My complaint is not that schools insist on teaching it, but that they teach too litttle else of mathematics. Even for the enthusiastic students, there’s nothing on offer but a year or two of algebra, some geometry and trigonometry, then finally calculus, which is viewed as the culmination and capstone of the whole enterprise, the end point toward which everyone have been striving from kindergarten on. There’s something musty and 18th century about this curriculum. It bears no resemblance to the much broader spectrum of interests among mathematicians today. Where are the courses on combinatorics and number theory (the “higher arithmetic”)? How about spending a semester on topology, a field with beautiful and mystifying ideas that might appeal to some kids who don’t go for the standard lineup. A course in probability and statistics might score well on the need-to-know scale for certain students. Then there’s the matter of computers in mathematics and the mathematics of computation. Even the algebra of traditional high school courses is only a pale shadow of what that word really encompasses; there’s more to it, Richard, than just doing arithmetic with x’s and y’s.
Finally, I have a further gripe about the school that failed Gabriela Ocampo. How could they let a student flunk the same course six times—whether the course is algebra or anything else—and not intervene in some way? According to Helfand, 48,000 ninth-grade students enrolled in algebra in the fall semester of 2004, and 44 percent of those students failed the course. If only you could do percentages, Richard, you’d see there is something desperately wrong with the mathematics of that situation, and the problem lies elsewhere than in the algebra.