Quick, when was the last time you solved a quadratic equation? Quick, given ax 2 + bx + c = 0, derive the formula for solving quadratic equations. What does “quadratic” mean, anyway? (Hint: It’s not the same as in “quadraphonic.”)
Quadratic equations are something that students learn when they take a subject called algebra. Although people have long said that there will be prayer in school as long as there is algebra, today, algebra rules. If physics is the Queen of Sciences, algebra is currently the King of All It Surveys.
Although algebra is all about finding values in equations, it has no value for most people. Its actual uselessness in most people’s lives was wonderfully revealed in a Washington Post article from several years back. The story described how parents in Fairfax County, Va., were rushing home from work, bolting down dinner, and going to school to learn ... algebra. “They came not for their benefit,” the reporter wrote. “They had learned algebra years ago and most of them had no use for X’s and Y’s in their current lives.”
That sure gives the game away: “Most of them had no use for X’s and Y’s in their current lives.” Yet, they are inflicting those useless X’s and Y’s on themselves for the second time. This time, they’re doing it so they can help their kids get through algebra. Apparently, it didn’t occur to these parents to ask, “If I didn’t need it, why am I suffering through it again just to help my kid successfully suffer through it?”
Why has algebra taken on such dimensions lately? Why do students in Virginia have to take algebra to graduate from high school? Why does the Montgomery County, Md., schools superintendent, Jerry Weast, fret over the failure rate on his algebra test? Why did Lee Stiff, the president of the National Council of Teachers of Mathematics, recently tell Brigid Shulte, a Post reporter, that “algebra is the civil rights issue of the new millennium, because it is that critical?”
Why? Because virtually the whole nation has been algebra-scammed. Said Mr. Weast: “No algebra means no SAT test. No SAT test means limited college choice” (never mind that even the most selective colleges admit a wide range of SAT scores, and never mind that, in terms of later earnings, it doesn’t matter what college you go to). Even the reporter fell for it and wrote, “Algebra is the gateway to college and higher-paying careers in a new technical world.”
Nonsense. Balderdash.
No algebra means no SAT test. No SAT test means limited college choice.
How did we come to think that algebra is important in kids’ high school careers? Because of a foible of the human brain. Our brains appear to be hard-wired to make causal inferences from mere correlations. No doubt from an evolutionary perspective, this is generally a good thing, because it allows us to see patterns in our lives and in nature. But, as psychologists early demonstrated, we often see causes when they don’t inhere. We infer causes where only correlations exist.
Psychologists demonstrated this many years ago. They showed a circle of light, call it A, moving across a screen and touching a second circle of light, call it B. If circle B then moved within a certain period of time, people watching the lights said that A caused B to move. If there was a delay of some seconds, then people said that B moved independently of A. We are especially wont to infer causality if event A is always followed by event B, and if B never occurs unless A does first. Actually, all this was worked out over two centuries ago by the British philosopher David Hume, but he didn’t have the technology to demonstrate it. He probably also didn’t realize the long periods over which humans infer causality, as with sex and the appearance of infants or, for some on the Right, the ‘60s and the appearance of all current problems.
So it was that a few years ago, the College Board noticed that kids who take algebra (circle of light A), especially kids who take algebra in the 8th or 9th grade, also tended to take rigorous high school curricula and to go to college (circle of light B). Aha! said the board. They saw a correlation between algebra and later attainment. They then leapt to a causal conclusion: Algebra is a “gateway” course. Having observed the correlation between taking algebra and going on to college, the board inferred that there was a causal relationship.
Nonsense. Balderdash.
What happens is this: Schools, whether we like it or not, are sorting machines. Jefferson proposed them as such, and they will function that way until some magical elixir can tune up the neurons in everyone’s heads. Schools identify academic talent in kids. Children that teachers think are talented get algebra in the 8th grade, those that have some talent, in the 9th grade. Those the school thinks have less ability tangle with quadratics in a later grade or not at all.
Is the school’s ability to identify talent flawless? Of course not. Indeed, the reason that the NCTM’s Mr. Stith casts algebra as a civil rights issue is that minority students are underrepresented in algebra classes in the 8th and 9th grades. And some kids, of any ethnicity, who are quiet and shy, might get overlooked because they have not shown their teachers all they’ve got.
Thinking that cramming algebra into all kids' heads is the means to a better life is making a bad causal inference from mere correlation.
But is forcing everyone to take algebra the answer? Of course not. It is more likely to turn kids off math, and even off school altogether, than to identify hidden talent. If I were a school official in Virginia or Montgomery County, Md., I’d start looking for a correlation between forcing kids to take algebra and increased dropout rates.
Already, we have some suggestive evidence from Milwaukee, which has had an algebra-for-all program for six years. Dennis Redovich, a retired educator who runs the Center for the Study of Jobs and Education in Wisconsin, reports that 40 percent of Milwaukee 9th graders fail algebra, and that 9th graders constitute more than 40 percent of Milwaukee’s dropouts. According to Mr. Redovich, the 9th grade in Milwaukee schools has been getting larger each year, largely as a result of students’ failing algebra and lacking enough credits to become 10th graders. For instance, in 1998-99, the 9th grade contained 9,340 students, but the 10th grade only 6,048 and the 12th grade only 3,874.
Says Mr. Redovich, “Only 60 percent of the students who take algebra pass it. The kids fail algebra, sit around in 9th grade until they’re 16 or 17 and then just disappear. Some will hang on until they reach the legal age for dropping out, 18.” Some of the data seem to corroborate his contentions: If one subtracts the number of total dropouts from the 9th grade enrollment, almost 30 percent of the 9th graders are simply unaccounted for by the 12th grade. The sound of opening doors I hear comes not from doors to opportunity, but to the school exits.
The dumbest slogan to come down the educational pike in recent years is “all children can learn.” This meaningless cliché has not been elevated to mean, in the case of algebra, that all students can learn to the same high standard. This will happen about the same time that all students run a four-minute mile.
We can do better, no doubt. The place to start is elementary school, not the 8th or 9th grade. There are also many other reasons for taking algebra that have nothing to do with jobs or college. Taught well (which it often isn’t), algebra can reveal a language of relationships and the beauty and elegance of mathematics. It can actually be an aesthetic experience.
Moreover, learning everything you can about everything you can is a good strategy in school because life after school contains so many uncertainties. You can’t possibly know what you might need one day. I’ve needed some algebra in my field, but haven’t used calculus once in the 39 years since the final exam (jobwise, only 4 percent of the population actually needs advanced mathematics). Had I entered a more quantitative branch of psychology though, calculus would have been integral. French, taken only because that’s what kids in the college track did when I was in school, turned out to be essential when living in France and extremely useful when living in Spain and Italy and learning those languages, because Spanish and Italian closely resemble French. And so forth.
But thinking that cramming algebra into all kids’ heads is the means to a better life is making a bad causal inference from a mere correlation.
