Algebra: It’s More Than Just Parabolas

Our old pal Andrew Hacker is back at it again. With the publication of his new book and a spate of recent media appearances, he is a man on a mission. A professor emeritus in the Department of Political Science at Queens College, Hacker first rose to fame notoriety when he called for an end to high school algebra requirements in his 2012 op-ed, “Is Algebra Necessary?” This year, he’s doubled down on that demand in his book “The Math Myth and other STEM delusions.”

Naturally, mathematicians and educators have had a lot to say about this. Hacker’s main thesis is that we need to get away from this idea of teaching the arcane rules and formulas of algebra, and instead, replace it with something more intuitive and relatable which he calls “numeracy.” In an excerpt from his book, Hacker says, “Calculus and higher math have a place, of course, but it’s not in most people’s everyday lives. What citizens do need is to be comfortable reading graphs and charts and adept at calculating simple figures in their heads.” Numeracy, he explains, entails a broader sense of quantitative literacy and ability to interpret numerical information without all that rote memorization and jargon.

Hacker is right, cramming rules and pointless seeming equations into the brains of young people is painful for everyone and it totally misses the point of math, which contains so much beauty, utility, and historical context — or ideally at least two of those three. Instead, says Simon Jenkins in The Guardian, “the prominence of maths in the curriculum is education’s version of Orwell’s imaginary boot, ‘stamping on your face … forever’.” Sounds pretty grim. In a post on Math With Bad Drawings, Ben Orlin claims, “Andrew Hacker has a coherent and lovely vision for how to teach mathematics. But to treat his work as a blueprint for all of mathematics education is to make a category error.” Orlin points out that there’s a looming backstory to why we teach the math that we do, competing interests from teachers, future employers, governing bodies, administrators, you name it. To malign the subject of algebra is to ignore the fact that the way we teach those rules and equations is actually more relevant than the rules and equations themselves.

And this is why I will now point out that Hacker is wrong. And the basis of his wrongness, as Keith Devlin breaks down in a post on Devlin’s Angle, seems to stem from the fact that he doesn’t really know what algebra is. Algebra, according to the Khan Academy, is simply “the language through which we describe patterns…Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it’s impossible to move forward.” Algebra is not, as Hacker tries to claim, the inane study of parametric equations, polynomial functions, and vectorial angles. Algebra is the way that we learn to wrangle not just numbers, but concepts and unknowns. It is an ancient art form that allows us to frame questions about numerical things we don’t totally understand and march slowly towards an answer using a systematized approach. For example, suppose that a movie studio earned $15 million with 2 million total transactions. Part of that coming from $6 video rentals, and the other part from $15 video sales. How could you find out how many videos were rented versus sold? Algebra! It is incredibly powerful and as far as gaining a sense of numeracy and quantitative literacy, it can’t be beat.

Personally, I think the part that really sticks in my craw is that Algebra, when taught properly, is just not that hard. I am totally on board with toppling calculus from its place of prominence in the high school math echelon. Because it’s true, not all people need calculus. In fact, most people don’t. But Algebra? I think it’s ok to suffer through a year of Algebra I just to be aware of the fact that we can talk about the general behavior of math using equations and unknowns. To me, that’s the mathematical equivalent of learning how to read a chapter book. If we were willing to accept an equivalently low bar for literacy, then most of our nation’s high schoolers wouldn’t even be able to read Hacker’s book. Or any grown-up book for that matter. And what a scary world that would be.