Algebra Matters, But Not for the Reason You Think
People who work with numbers, a group that includes a substantial share of the tech world, were understandably outraged by political scientist Andrew Hacker’s lead piece in The New York Times Sunday Review, ”Is Algebra Necessary?“ The odd thing is that Hacker’s central point, that hardly anyone needs the math taught in high school and beyond in their lives or jobs, was quite correct. But both his arguments and, more important, his conclusion, were totally wrong.
Two years ago, mathematician Underwood Dudley wrote a provocative article titled “What Is Mathematics For?” in which he questioned the increasingly common assertion, promoted mainly by teachers of mathematics, that a wide variety of jobs requires skills in algebra and maybe calculus. If Hacker had been serious about engaging in the debate, he surely would have encountered Dudley’s widely read and easily accessible piece.
That he apparently did not is a shame, for Dudley not only made the argument against the necessity of algebra with far more wit and cogency than Hacker, he came to the opposite conclusion. While higher math is actually used only in very, very few jobs, learning it is nonetheless a vital component of any decent education.
Dudley demolishes the arguments for job-related math by pointing out that just about any problem that anyone might encounter has been solved and converted into a readily available formula. All that most people, even engineers, have to do most of the time to get the results they need, is to plug in the numbers. Rarely are math skills required beyond those you learned before reaching middle school. For example, I know how to compute the discounted present value of annuity using algebra, but if I need to do it, I’m going to plug an income stream and a discount rate into Excel or an HP12C calculator.
Dudley decries “the error of supposing that problems once solved must be solved anew every time they are encountered. House builders have handbooks and tables, and use them. Indeed, houses as well as pyramids and cathedrals, were being built long before algebra was taught in the schools and, in fact, before algebra.”
So why do algebra and other higher math disciplines belong in the curriculum? Dudley argues that it teaches reasoning better than any other subject: “Reasoning needs to be learned, and mathematics is the best way to learn it.”
I’ll go a step further and make explicit an argument that Dudley makes only implicitly. Mathematics at its core is about abstraction, about drawing the essential facts out of a situation, analyzing them, and rationally applying general principles to find the correct solution for a specific case. This is a high-order thinking skill that really is needed for a wide variety of jobs, not to mention the challenges of daily life, and the only place most students will ever be exposed to it in a rigorous and formal way is in algebra and beyond.
Even the tech industry doesn’t require a lot of day-to-day math from most of its engineers. Coders don’t really need calculus, but they do use a lot of discrete math. But engineers and programmers definitely need strong and deep abstract thinking abilities, and math class is where they are going to acquire them.
There is another importance to math education that mathematicians don’t much talk about. Math courses are useful gatekeepers. We want college-bound students to take four years of high school math because we want them to prove they have the cognitive skills and reasoning ability to do college-level work.
(There are some students who, for poorly understood reasons, struggle mightily in mathematics while excelling in other areas. There may well be a neurological basis for this, but the area has been much less studied than learning disparities involving reading or writing. It should be possible to make accommodations for their deficits, as we do for dyslexia.)
I was particularly disturbed by Hacker’s criticism of medical schools for requiring undergraduate calculus. “Mathematics is used as a hoop, a badge, a totem to impress outsiders and elevate a profession’s status,” he writes. It’s trues that doctors don’t use calculus much if at all. But to be honest, I really don’t want a doctor who lacks the analytic skill and reasoning ability to get through first- and second-year calculus.
Hacker is an emeritus professor at the City College of New York, but he seems unaware of the fact that his own field had become increasingly quantitative. Economics papers look like they belong in math journals. And questioning why “philosophers face a lofty mathematical bar” ignores the fact that philosophy has become a highly technical field that operates at a level of abstraction that baffles many mathematicians.
I’ll freely admit to a bias. I’m writing this at Math Fest, the summer meeting of the Mathematical Association of America, in Madison, Wis. (Both my math teacher wife and math professor son are active participants.) I hang a lot with mathematicians, who are not only, as widely believed, extremely intelligent but, in contrast to the stereotype, extremely interesting people who care deeply about many things other than mathematics.
The MAA is concerned primarily with undergraduate mathematics education. It shares a good bit of the blame for promoting the vocational necessity of high school and college math. Fewer math students mean fewer jobs for math professors, a subject that concerns them deeply. But a major concern of the participants and the sessions is improving the abstract, high-order thinking skills that make math education valuable. Andrew Hacker should have stopped by.