The Math Myth, in italics, that is: the title of a new book by Andrew Hacker, whose last name is not eponymous as he’s a professor (emeritus) in political science. This is that sort of book that has one solid point and then pushes that point too far: we have elevated the place of mathematics too far, with the consequence that good kids, deserving kids, can’t get college degrees because they can’t meet the math requirements that exist even for non-technical degrees, and the reason for this is that it’s mathematics professors at universities who set these standards, for no good reason, but are indifferent to helping students achieve them.
Now, he has a point that not every student can reasonably be expected to do well in an Algebra II-level math class, and to the extent that this is a roadblock in some cases, to getting degrees, well, by all means, let’s discuss this — though he doesn’t provide concrete details on what, exactly, is required for, say, humanities majors, at typical universities. And he suggests that a solid knowledge of arithmetic — the four basic operations, fractions, percents, etc. — is really quite enough for just about everyone, by coming up with nonsensical straw men examples of rather more complex material. In fact, the basic concept of algebra — manipulatng an equation to solve for a variable — is important, as is a general notion of trig and geometry. And, beyond this, all students, even those who are convinced they’ll never use it, should learn math to the greatest degree their innate capabilities enable them to, rather than, as Hacker suggests, discarding math as useless unless there’s a specific need.
Hacker also raises the issue of whether there’s a shortage of tech-trained graduates; it’s the same stories we’ve read before, that tech companies whine about the lack of US graduates, then run off to hire Indians, while firing their US staff, and, lo and behold, paying those Indians wages that are far below what an American could expect. He also notes that large numbers of STEM-trained graduates are not doing STEM work because they’ve discovered that other jobs are more profitable, and pulls out the list of projected-to-grow occupations, which are low in math needs.
And, yes, Hacker has a good point that universities who create math requirements have an ethical obligation to create the right set of conditions so that students can meet those requirements, rather than leaving the teaching of those courses to graduate students who may or may not be able to even communicate in English effectively. And the very notion, which still, he says, exists, of first-level math courses as “weeder” courses, is highly unethical, to create a class (and ask students to pay for it) with the very intention that a large number of students will fail.
What does Hacker want? Classes which emphasize “hands on” math and, it turns out, story problems which call on students to think politically about math-related issues. One bizarre example is a standard early-grades question: “I have X students, and cans of pop come in cases of Y each. How many cases do I need?” He envisions students coming up with answers like: “not everyone will drink a whole can of pop, so let’s pour the pop into paper cups instead, so it stretches farther.” He then describes an idealized college math-for-nonmajors class in which they learn about gerrymandering or looking at the CPI, the “basket of goods,” and spending in income tiers to think about income inequality.He also questions the very idea that learning math creates “thinking skills” which transfer to other fields of study, but he’s really determined enough to prove this notion wrong that he doesn’t really give the thesis a fair shake, but rather creates a straw man that studying math will make you better at everything, then demolishes this.
But here’s the most interesting claim in the book: he rejects the idea that boys’ consistently higher test score in math sections of tests such as the SAT demonstrate that boys are in some way better at math than girls. (Here’s an article that just popped up in my twitter feed yesterday, “2016 SAT test results confirm pattern that’s persisted for 45 years — high school boys are better at math than girls.“) After all, he notes, as does the linked article, that in classroom performance, girls do better, and what others attribute to girls’ better ability to stay on task and “behave” that gets them better grades and more academic success than boys, in general, and increasingly so lately, he attributes to girls’ inherent ability. Why, then, do boys do better on the SAT? He attributes this to the fact that the SAT is a timed test, and that boys’ propensity to rush through and be aggressive rewards them in the case of a timed test.
Here’s a full paragraph:
Given their affinity for speed, boys start by sizing up multiple-choice questions with a quick glance. The Educational Testing Service, which runs the SAT, found that boys save time by mental strategies “that enable them to see the solution without actually working out the problem.” As a result, they show less hesitation about racing ahead. And this usually pays off, since the SAT format doesn’t ask or care how you got to your answer. Another tactic that comes more readily to boys is to eliminate, say, three of the options as plainly wrong, and then guess between the remaining two. This willingness to gamble shaves the odds in their favor. Another ETS study was even more revealing. It found that because girls spend much more time pondering, they are measurably more likely than boys to leave some questions blank, and hence fail to reach the end. In all instances, girls’ greater penchant for reflection undercuts their scores. (p. 67)
Which is all very interesting, and deserve more attention than one paragraph — though in a different book than this one, because it’s a whole ‘nother topic. And, after all, these same test-taking strategies ought to work just as well for the verbal section of the SAT, but there the boys do not perform as well.
(Full disclosure: I do really well on exams. In fact, my life might have turned out quite differently if I hadn’t had the opportunities exam success brought me.)
At any rate, this is mostly a tangent in his book, and the ultimate aim of this section of his material is to say that it’s unfair that the most highly-selective schools demand high SAT scores in both the verbal and math areas, because this penalizes plenty of otherwise smart people. But if this is the new direction that schools are scholars are taking — that girls are better than boys at everything that counts, and pfffbth to those dumb boys! — then that’ll make the already serious problem of young male drop-outs (e.g., playing video games instead and especially high numbers among young black men) even worse.
And, by the way, we were at the National Honor Society induction at my son’s high school Monday night (ended just before the debate!). I didn’t tally the ratios, but there were a lot, lot more girls than boys, and all of the officers on stage were girls.
Image from flickr: https://www.flickr.com/photos/wwworks/15344079560; by woodleywonderworks