The Sublimity of Quadratic Equations

In today’s New York Times, Andrew Hacker asks whether algebra should be necessary for higher education. Hacker, a political scientist who has written extensively on race relations, argues, first, that algebra is, for many, a useless qualification that serves as a barrier to higher education, —“In the interest of maintaining rigor, we’re actually depleting our pool of brainpower.” He argues, further, that it is not required for “quantitative reasoning,” and does not contribute to “more credible political opinions or social analysis.” “It’s not easy to see why potential poets and philosophers face a lofty mathematics bar,” he writes. In place of algebra, Hacker proposes, the universal mathematics background should be something more practical, like “citizen statistics.”

Both of Hacker’s arguments bother me, though I can’t say that I have the kind of evidence that would make me confident in rejecting them.

The first is that he seems to think that a universal math requirement is pedagogically defensible only if it serves to advance quantitative reasoning. Algebra (and mathematical logic) is a branch of abstract thinking, and is meant precisely to abstract away from the details of quantitative analysis. The question is: is it good to require of all university students that they develop skills in abstract mathematical thinking? Is this a transferrable intellectual skill that ought to be part of every educated person’s repertoire? Or should it be reserved for specialists?

It also bothers me that Hacker wants to abolish the algebra requirement because it is difficult for many. High prestige colleges “look for 700 on the math section of the SAT, a height attained in 2009 by only 9 percent of men and 4 percent of women.” Yet “a mere 5 percent of entry-level workers will need to be proficient in algebra.” “I’ll grant that with an outpouring of resources, we could reclaim many dropouts and help them get through quadratic equations. But that would misuse teaching talent and student effort.”

Higher education seeks not only to provide skills training, but also to nurture the intellect. It is, perhaps, not for all. In wealthy, diversified economies, a Bachelor’s degree is available to 50% (or perhaps slightly more) of the population. That is approaching a natural maximum. To increase this proportion a great deal benefits neither society nor those who get in, over and above the 50% or so. If this is right, then one should not get rid of algebra because it is a barrier to a larger proportion of baccalaureates. Rather, one should argue against it because it is the wrong kind of qualification. Assuming that higher education is for the improvement of the intellect, the argument for it being the wrong kind of qualification cannot rest on it being unnecessary in the workplace.

Art and literature are not necessary in the workplace. Yet very few deny that they are integral parts of higher education, even for doctors and scientists. Is algebra similar? Is a mind that has never tackled quadratic equations as deprived as one that has never pondered high art? I don’t know, but I know which way my instincts go. In the comments section, one K. Shankar of Chennai India moans: “This is the strangest article that I have ever read.” S/he has evidently led a very sheltered life. Nevertheless, I see what s/he means.