An Op-Ed titled ‘Is Algebra necessary’ is bound to provoke reaction. So, here I am, reacting to Andrew Hacker’s anti-algebra screed (New York Times, July 29th, 2012). It is a strange argument, one unsure of what it is attacking–mandatory math education, elementary algebra, higher algebra?–and one founded on an extremely dubious premise: that the way to carry out educational reform is to cherry pick your way through a curriculum, questioning the ‘utility’ of a particular component in case there are no jobs that require an exact application of its material. Hacker makes things worse by leaning on statistics that cry out for alternative explanations and pedagogical reform, rather than the ‘lets drop the subject students seem to have difficulty with’ approach that he favors. If American students are struggling with algebra, it might be time to inquire into how it is taught, to show students how abstraction and symbolic representation are key to understanding a modern world underwritten by science and technology. Dropping algebra seems like a profoundly misguided overreaction.

The ‘surrender in the face of poor test scores’ approach results in a series of bizarre statements of which the following are merely representative samples:

It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.

Certification programs for veterinary technicians require algebra, although none of the graduates I’ve met have ever used it in diagnosing or treating their patients. Medical schools like Harvard and Johns Hopkins demand calculus of all their applicants, even if it doesn’t figure in the clinical curriculum, let alone in subsequent practice.

I have news for Hacker. There is little evidence that being able to leads to ‘more credible political opinions or social analysis’ either. Furthermore, if job skills are examined as superficially as Hacker does in his examples then it becomes all too easy to dismiss large parts of one’s educational background as being irrelevant. Hacker would be alarmed, I presume, to find out that even though modern physicists hardly ever roll balls down inclined planes, freshman physicists are still required to spend a semester solving problems that are full of problems that stress just that. Hacker dismisses the argument for a general education in mathematics with the alarmingly glib ‘It’s true that mathematics requires mental exertion’ without stopping to inquire what that ‘mental exertion’ might consist of and what it might engender in turn. This is hardly an attitude toward pedagogical reform that breeds confidence.

It is a consequence of Hacker’s argument that the only students who should receive an education in algebra are those preparing for careers that require them to apply algebraic techniques and concepts in their jobs. Everyone else can be spared its ‘difficulties, ‘ like the above-mentioned abstraction and symbolic representation. How would an extension of this argument work in, say, fields like history or literature? A relentless whittling down of the curriculum would result, leaving us with a list of subjects read off the Help Wanted Ads section.

This is an impoverished, grimly utilitarian, and ultimately soulless view of education.

In the age of teach-to-the-test and “no child left behind,” any legitimate concern about algebra is so profoundly outweighed by all the other nonsense that goes on that I think you’re right to flag his column as essentially about provoking a reaction.

Well put, Samir.

I can’t imagine what he’d have to say about Latin, a subject that is currently undergoing quite the boom in city public and charter schools. Not to mention the fact that people have built careers around the quantitative analysis of human interactions. Math certainly can teach us a lot about how we interact with one another.

More generally on the idea of “teach them what they’ll use:”

What I’ve realized in my three years of teaching Latin and my summer course on the history of the universe is that students are inspired in the most fascinating ways by all sorts of subject matter, and that they are often wrestling not only with the content but also with the larger implications of their work. (Often, this has something to do with personal growth.) For example, my school wants its students to learn about and appreciate the value of cooperation. So our lessons in Latin class on the friendship of Cicero and Atticus and those from the biology teacher lecturing on species that cooperate via symbiogenesis serve a double purpose. Hacker’s proposals are all the more shameful because they would severely inhibit a school’s opportunity to help students’ build character, instead of merely a set of “marketable” skills.

Samir, you point out well some of the problems with Hacker’s piece. In particular, singling out is a bit bizarre. However, one fo the things that I might take out of his article is that he’s suggesting that it (and some other mathematics) are already inappropriately singled out – I’m not at all familar with American education, so I’m not sure how much this reflects reality. The question of what should be required for any particular purpose, rather than simply valued as helpful education is a real one. As you say, this op-ed doesn’t exactly breed confidence regarding academic reform, but I don’t doubt that adjusting these requirements could make a positive difference if done sensibly.

(I also think he’s seriously underestimating the direct relevance some basic school algebra, but that’s probably less important than your comments.)

Well, I have to say, I found the article neither a “screed” nor “anti-algebra.” Indeed, I think I agree with much if not most of what Hacker had to say. His argument, primarily, is that while we should require that everyone study the sorts of mathematics that are necessary for daily and professional life, it is not obvious what purpose is served by making the study of algebra ubiquitous.

Unfortunately, though Hacker gives any number of reasons why we ought *not* to require across-the-board study of algebra, you have not provided any reasons *to* require it. As for the one remark you *do* make in this direction–“to show students how abstraction and symbolic representation are key to understanding a modern world underwritten by science and technology”–this strikes me as one of those things that Hacker described as “sounding good” at first, but which becomes rather wispy, once you start trying to figure out what it actually means. (What does it mean, by the way?)

So, chalk this reader up as completely unconvinced by your criticism (in good part, because there really isn’t one) and quite persuaded by the article itself.