The Necessity of Algebra

Although a number of people have already commented on Andrew Hacker’s July 29th article in the New York Times (“Is Algebra Necessary?”), I feel compelled to add my views to the mix. Mr. Hacker makes some strong points. I do not dispute the depressing dropout statistics that he cites, nor even the notion that algebra may contribute substantially to those statistics. And, indeed, Mr. Hacker is correct in some of the prescriptions he offers; but as for the notion that algebra should be dropped wholesale as an educational requirement, he is, I’m afraid, deeply misguided.

Mr. Hacker calls for the study of quantitative reasoning, the history and philosophy of mathematics, and mathematics in art and music as part of the mathematics curriculum. He is absolutely right, and especially right with respect to math in the elementary and middle grades, where I happen to teach. It is our responsibility to teach not just the “bare bones” of mathematical literacy (if those bones can really ever be bare) but to imbed that teaching in an understanding of math as a human enterprise, to expose the connections between math and literature, math and art, to teach math as a lens through which the universe can be seen and better comprehended. The failure of most math programs, I’m sad to say as a teacher, lies not in the intrinsic difficulty or abstruseness of the subject matter, but in the way that it is often taught: as something desiccated, disconnected, and lifeless. However, algebra, properly understood and properly taught, is not the problem – rather, it is the very key to the sort of rich mathematical understanding that every child deserves and every child can achieve. Algebra is the mathematical art of abstraction; it is that which allows a student to move from the particular to the general – surely just the sort of thinking that Mr. Hacker would hope for on the part of an informed citizen. I will grant that some of the more esoteric subjects that Mr. Hacker mentions as part of the algebra curriculum – “vectorial angles,” say – need not be mastered by every student (I teach algebra to sixth-, seventh-, and eighth-graders and manage to avoid the subject of vectorial angles), but a strong and thorough grounding in basic algebra is a fundamental part of mathematical literacy. Mr. Hacker’s vision of courses in practical mathematics would be very difficult to realize without some algebraic facility on his students’ part; in particular, I would defy anyone to develop a robust understanding of the Consumer Price Index without basic algebra skills.

But the flaw in Mr. Hacker’s thinking runs much deeper than this. As Rob Knop, for instance, suggested in his blog on the subject, Mr Hacker’s view is, at its heart, depressingly utilitarian. Mr. Knop was speaking largely of higher education when he wrote that, “A liberal arts education is all about expanding your mind, all about being able to think,” but I would suggest that the statement is perhaps even more true of elementary education. Yes, to some extent it is our duty as teachers to train future workers, at least in the sense that we should strive to inculcate in our students the habits of discipline, the ability to work both independently and collaboratively, and the skills to think critically. And yes, we certainly bear the responsibility for educating future citizens: people who can reason clearly, who have a sense of civic duty. But even this is too limited a description of a teacher’s job. Because our responsibility is also to the individual student: we should be concerned not simply with imparting skills or knowledge, but with lifting the spirit, with lighting the flame of intellectual curiosity, with opening young eyes to both the wonder and the problems of their world. Algebra – sadly so often regarded as drudgery – is a key element in this kind of genuine education. To give just one example, we can say a great deal about gravity, but Newton’s Universal Law of Gravitation is one of the clearest, truest, most succinct, and – yes – most beautiful statements that has been made on the subject; without a genuine understanding of algebra, that statement is meaningless. Our real duty as teachers is not merely to prepare our students for some “real world,” and certainly not merely to prepare them for the workplace. If we deny them access to algebra, we deny them access to an entire intellectual universe.

Math is certainly hard to learn, and in my judgment much harder to teach. But most things that are worth doing are hard in one way or another. I am all for rethinking the way that math is taught in order to make it “as accessible and welcoming as sculpture and ballet.” But really appreciating either of those disciplines takes genuine work; and I doubt that there are many sculptors or ballet dancers who describe their jobs as “easy.” Mr Hacker is to be commended for proposing a bold solution to what is quite clearly a genuine problem. However, it would be sad indeed were his proposals actually to be adopted.

Linus Rollman
Math and Humanities Teacher
Arbor School or Arts and Sciences, Tualatin Oregon