THE MALEVOLENT TYRANNY OF ALGEBRA

Gerald W. Bracey

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 May 15,
1992. The story described how parents
in Fairfax County were rushing home from work, bolting down dinner, and going
to school to learn…algebra. "They
came not for their benefit. 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 them 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 Montgomery County (MD) Superintendent Jerry Weast fret over the
failure rate on his algebra test? Why
did Lee Stith, the president of the National Council of Teachers of Mathematics
recently tell *Post *reporter Brigid
Schulte that "Algebra is the civil rights issue of the new millennium,
because it is that critical?"

Because virtually the whole nation has been
algebra-scammed. Said 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 Schulte fell for it and wrote "Algebra is the gateway to
college and higher-paying careers in a new technical world."

Nonsense. Balderdash.

How did we come to think that algebra is important in kid's 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 times over which humans infer causality as with sex and the
appearance of infants or, for some on the Right, the Sixties 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 8^{th} or 9^{th} 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 8^{th}
grade, those that have some talent, in 9^{th} 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 Mr. Stith casts algebra as a civil rights
issue is that minority students are underrepresented in algebra classes in the
8^{th} and 9^{th} 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.

But is forcing everyone to take algebra the answer? Of course not. This will probably turn kids off math and even off school altogether more than it identifies hidden talent. If I were a school official in Virginia or Montgomery County, 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 60% of
Milwaukee 9^{th} graders fail algebra and that 9^{th} graders
constitute over 40% of Milwaukee's dropouts.
According to Redovich, the 9^{th} 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 9^{th} grade contained
9,340 students, but the 10^{th} grade only 6,048 and the 12^{th}
grade only 3,874.

Says Redovich, "Only 60% of the students who take
algebra pass it. The kids fail algebra,
sit around in 9^{th} grade until they're sixteen or seventeen and then
just disappear. Some will hang on until
they reach 18, the legal age for dropping out." Some of the data seems to corroborate Redovich's contentions: If
one subtracts the number of total dropouts from the 9^{th} grade
enrollment, almost 30% of the 9^{th} graders are simply unaccounted for
by 12^{th} grade. The sound I
hear of doors opening, alright, but not doors of opportunity, exits for
students flee through.

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 as all students run a four-minute mile.

We can do better, no doubt.
The place to start is elementary school, not 8^{th} or 9^{th}
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. Neither you, your parents nor your teachers can 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% 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.