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the math myth
22 september 2018
If you're going to agree with a book that critiques math education in America, you have to come clean about how well you did in math. So here goes: I made As in math, in high school, except for 11th-grade trigonometry, where I think I made a B. Uncoincidentally, I remember absolutely nothing about trigonometry. I know, from the Greek roots in the word, that trigonometry means measuring triangles. I do not remember why anyone would want to do such a thing. I remember the words "sine," "cosine," "tangent," "arctangent" – is "arctangent" real? I am afraid to look it up.
I did go on to 12th-grade calculus, and that was somehow easier. Calculus has a more practical side, the figuring of speed, acceleration, and area. I repeated pretty much the same calculus course as a college freshman, though, made a C, and that was the end of my math education. Like every other college student blocked by calculus, I should probably blame my instructor, who true to stereotype did not speak English very well (he was German). But really it was me: I can go only so far in mathematics, and though I'm in awe of stuff like prime number theory, I can follow it only with painful difficulty, and I need a refresher course every time I return to it.
Andrew Hacker suggests in The Math Myth that I am not alone. The single greatest barrier to academic achievement, Hacker claims, is the presence of mathematics requirements in the secondary and post-secondary systems.
And he means here true mathematics. Hacker is careful to distinguish mathematics from arithmetic. Multiplication and division, figuring percentages, even some very basic algebra in the sense of solving for x when determining how many things of what size to get – these things are undeniably essential. What he's not so sure about is trigonometry, because, as I've just demonstrated, you can have a Ph.D. and review books on the Internet while barely remembering what trigonometry is.
My C in calculus didn't keep me from getting my Ph.D. because I got it in English, but I was perhaps lucky to clear some hurdles that loom long before college calculus: the math requirement that I needed to get into college in the first place, and the ability to make at least plausible scores on the standardized math tests that, inexplicably, I still needed to take in order to apply to Ph.D. programs in English. Millions of kids aren't as lucky. Local curricula, the Common Core, the standardized tests that have American education in their grip, all seem to think that the essence of schooling lies in esoteric mathematica that almost nobody – even engineers and IT experts – ever make use of in their lives or on their jobs.
Hacker spends a good bit of time wondering why this should be. He especially blames professors of mathematics, who sit in their ivory towers doing impenetrable research, insisting that ninth-graders be assessed in terms of their ultimate fitness to tackle that same research; refusing to teach math to the masses, yet insisting that they know how it should best be taught.
One of Hacker's bugbears is that research faculty in universities never even teach Differential Equations to sophomores, let alone remedial algebra to freshmen on the verge of failure. He cites a wealth of data showing that college math is taught by underpaid, stressed, English-challenged grad students and adjuncts. Yet while I'm sure that professorial arrogance is a thing, I am less sure that the low investment in basic college teaching can be traced entirely to that arrogance. It's mostly traceable to the chronic understaffing that proceeds from running schools like for-profit businesses. If universities sought out and tenured good math teachers, then lower-division math would suddenly be taught by tenured faculty. But tenure costs money. You can do the math.
Math, Hacker suggests, may be the Latin of the 21st century. Two hundred years ago, American colleges, such as they were, placed classical languages at the center of their curricula. The languages were good for nothing except reading the ever-less-relevant classical and medieval scholarship written in them, and a few beautiful poems. Latin and Greek placed obstacles in the way of social mobility, surmountable by the very clever and skirtable by those with money for tutors and prep manuals. Sound familiar? It's basically the SAT and its kin, especially the math portions. There is next to no rationale for learning to factor trinomials, any more than there was in 1818 for learning the minutiae of the pluperfect subjunctive.
I think there's an additional political angle that Hacker, woke as he is, doesn't fully explore. American educational policymakers have made math central to all their endeavors – a mania shared by neoconservatives like George W. Bush and neoliberals like Barack Obama. Math is stressed to the detriment of history, civics, literature, and the arts – the only subject nearly on a par with math is abstract linguistic facility, as measured by the verbal portions of the major tests.
Math is in fact stressed to the detriment of science, its acronym-mate in the formula STEM. And you can see why. As Hacker notes, science is always provisional and always contested. Science takes students into the thickets of evolution and climate change. We want our students to demonstrate pure aptitude, freed from the messiness of the arts and sciences. Math truly provides it: you can either recite Euclid's proof of an infinity of prime numbers or you can't, and once you can, you're irrefutable.
Hence we pour more and more money into teaching and assessment that is less and less useful outside of the mathematics classroom. Judging schools and students by math scores obviates the necessity to teach anyone the arithmetic that might make them more competent and critical adults, let alone the scientific method, the historical analysis, and the literary sensibility that might make them critical citizens. It's the one thing left and right can agree on and feel good about. Math will never be touchy-feely. Hacker laments that math will never be of the slightest interest to anyone if we keep pushing it down the road of the surrogate-Latin that it has become, but at least it will be objective and neutral. And it will be colorblind in a way that allows the right to blame minority failures in minority IQ genes, and the left to blame minority failures on racism – all the while ignoring the fact that maybe success at trigonometry is unattainable by a significant majority of all colors (and both genders) – and useless even if attained.
Of course this seems easy for some guy who got a C in calculus to maintain. Many would argue that the discipline of mathematics, its sheer mental-boot-camp properties, is essential for entry to the adult world, long after the specific content of college algebra is forgotten. Didn't my slaving away at arctangents or whatever the hell they were engrave some sort of mental channels in my brain, channels that have turned me into the upper-middle-class nitwit I am today?
They used to say the same of Latin, of course, and they say the same of music and memorizing poetry and diagramming sentences. And it is plausible that for some learners, a truly liberal discipline, abstractly related (if at all) to most of life's pursuits, is a virtue in and of itself. Some of the subjects I remember best from high school and college – choir, geology, lab astronomy – are ones that I barely retain any formal information from, but are reflected, I reckon, in my mental makeup. Choir taught me breath control and performance discipline. Geology taught the long view and the big picture. Astronomy taught me patience as I fiddled with recording my observations, and the sense that literally cosmic phenomena could be grappled with and reduced to a system by the human mind. It may well be that for some people, even the C students, trigonometry and calculus do something analogous.
But of course the liberal-arts and life-of-the-mind rationales for studying math (which Hacker strongly endorses) are usually subordinated to the idea that we have to teach the workforce quadratic equations, or we will lag behind China. But that's just false. Hacker shows that a minuscule portion of even the technical workforce ever needs to use quadratic equations on the job. Yet there they are, blocking students' path to managing medical-records offices or rental-car offices.
Hacker closes by describing a math course that he taught (despite being no mathematician), a course in numbers, reasoning, and critical thinking for life. I would like to teach such a course myself some day, despite my checkered mathematical past. Hacker managed to slip his past the "mandarins" at his college, he says, but warns that it might not be as easy at all institutions. In part such courses, in real-life arithmetic rather than ivory-tower equations, would simply make it easier for people to get degrees in other things, and empower the workforce. But in part they would serve a positive civic function. At my university we have recently moved away from making English a requirement in favor of expressive communication classes and other kinds of "cultural" options that don't involve a lot of reading and writing. Yet math, even if somewhat eroded, remains central. Why not teach arithmetic engagé instead of the asymptotes of functions? If such a suggestion is heresy, you might want to consider why you really want math taught in the first place.
Hacker, Andrew. The Math Myth and other STEM delusions. 2016. New York: The New Press, 2018. QA 11.2 .H35