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.

Well said, and very sad that this is the situation. A capitulation by the “teachers” who prefer to idolize the sports and gambling worlds.

Regarding the primacy of calculus: there have been musings at the college level, too, about moving away from the idea that calculus should be the first (and, often, only) math course students take. Specifically, Prof. Strang at MIT has an essay that suggests linear algebra instead. I tend to think that at least providing the option is a good idea:

- Arguably, linear algebra is just as useful/important to engineers and scientists as calculus is.

- For computer scientists, linear algebra is much more central.

- For potential math majors, one could argue that calculus is fundamentally “similar” to everything they learned in high school. Exposing these students to linear algebra (or another type of “discrete” math) might show them what else math has to offer.

- The same argument goes for students in non-technical disciplines who want exposure to some of the nice ideas math has to offer (though I’m not sure such students exist in any appreciable numbers!).

Little was said about the student who failed Algebra I six times. Did she have a language problem? And the “six times” sounds bizarre. The article about the student taking Algebra I six times has a lot of explaining to do to be trustworthy. The writer seems to have a bias against mathematics. The journalist who wrote the article is fooling himself if he thinks you don’t need skills in algebra in today’s world. His skills seem to be in avoiding the more challenging areas of learning.

Algebra I is a year long course. Did the student stay in high school for six years? That doesn’t sound right. Did the student pass the prerequisites for Algebra I? Why wasn’t she routed into some special assistance? Did she have the mental capability of understanding simple mathematics? Did she know how to study and that work by her was required to learn? Did the student actually read the book and do the homework? Did she ask questions in class? Did she ask the teacher to show how to do homework problems she didn’t understand? Did she take notes? Did she write anything down? Did she keep a notebook and save her homework to study for the test? Did she study for the test? Did she use the extra tutoring that is available after school at most schools? Learning is not a passive event for the student and the student must take the initiative in engaging themselves. In high school students should not be spoon fed.

And did she work after school? Did she participate in activities after school that prevented her from setting aside the amount of time she needed to study? We don’t know. But school work should be any student’s top priority.

Since Algebra I is taught to 9th graders there are often immaturity issues that prevent the student from learning to their fullest. They come out of middle school thinking that the courses will be easy and that they can copy some other student’s homework and pass the exams anyway. This is a very common attitude. Whether it results in 44% failure rate, I don’t know (not my experience). But much of the 9th grade is spent in learning that teachers require real work from the student and that the easy grades are over. That is a shock that some students don’t recover from and end up holding a grudge against the school system for the rest of their lives.

I am a high school teacher. I teach chemistry and expect my students to have a firm understanding of Algebra I (and Biology) as a prerequisite. I don’t give grades, they earn them. I have not taught Algebra I but have taught Geometry and Java Programming. (I’m certified in mathematics, computer science, and chemistry.)

Admittedly, Algebra I is boring to students who expect to be entertained. And a few students have the attitude that if they are not entertained they will shut down and not put the work into learning that is necessary. While a teacher tries to motivate, it is not the job of a teacher to entertain. So an attitude adjustment for those students who expect to be entertained is sometimes in order.

The article appears to contradict another article I read yesterday that says that students who drop out do that because they are bored and need more of a challenge. One of those articles must be off base. Unfortunately, I see a lot of contradictory stuff in the educational field.

Part of the problem that I see as a teacher is that everyone is at fault except the student. The student is often off the hook when it comes to responsibility. While there are bound to be a few students who simply don’t have the mental capability of learning most anything, including algebra, the far majority of students can learn Algebra I with only a minor amount of effort. With our world becoming increasingly complex, students will need far more math than their parents did. Get used to it; the need is not going away!

That said, there might have been something wrong with the guidance department in the case of this student who took Algebra I six times (?!). The student should have been flagged as ESE (learning disability), or ESOL (limited English knowledge) or some other educational problem and been given the proper guidance to deal with their problem.

And, finally, she can always become a journalist! Apparently they don’t need to know very much, report in any depth, or clearly explain what the real problem was.