There is without a doubt an aesthetic appeal to mathematics which resonates as surely as it does with literature and music. On the other hand, just as The Violin Concerto and The Canterbury Tales aren’t everybody’s piece of cake, so is the case with complicated mathematical topics like trigonometry and algebra.
A typical school day finds millions of high school students and college freshmen struggling with algebra. In both senior school and college, all too many students are expected to fail. Why do we subject students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.
My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and cubic equations.
There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic.
This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.
It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, which fits them for demanding jobs.
A skeptic might argue that, even if our current mathematics education discourages large numbers of students, math itself isn’t to blame. Isn’t this discipline a critical part of education, providing quantitative tools and honing conceptual abilities that are indispensable — especially in our high tech age?
Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic. Quantitative literacy clearly is useful in weighing all manner of public policies, from the Jan Lokpal Bill, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What’s needed isn’t textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x + y) ² = (x² + y²) + (2xy) leads to more credible political opinions or social analysis.
Many of those who struggled through a traditional math regimen feel that doing so toughened their character. This clearly supports the fact that institutions and occupations often install prerequisites just to seem rigorous — hardly a justification for maintaining so many mathematics mandates. Certification programs for veterinarians require algebra, although none of the graduates ever use it in diagnosing or treating their patients. Medical schools like Harvard demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice. Mathematics is used as a hoop, a badge to impress outsiders and elevate a profession’s status.
It’s not hard to understand why IIT’s want everyone to be proficient in mathematics. But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar.