Algebra: It’s More Than Just Parabolas

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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.

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2 Responses to Algebra: It’s More Than Just Parabolas

  1. Prof. David A. Edwards says:

    I’m working on documenting the following:

    Math Myth Conjecture: If one restricts one’s attention to the hardest cases, namely, graduates of top engineering schools such as MIT, RPI, Cal. Tech., Georgia Tech., etc., then the percent of such individuals holding engineering as opposed to management, financial or other positions, and using more than Excel and eighth grade level mathematics (arithmetic, a little bit of algebra, a little bit of statistics, and a little bit of programming) is less than 25% and possibly less than 10%.

    This is a conjecture that desperately needs resolving with solid statistics and in-depth interviews.

    (see: http://www.ams.org/notices/201007/rtx100700822p.pdf).

  2. Jacob Koczwara says:

    I think Andrew Hacker is just straight off wrong. First of all a Political Science professor should not be talking about the validity and necessity of any form of mathematics. He lacks the professional understanding any mathematician or anyone studying mathematics has. Second of all, the fact that he calls the necessity of algebra into question is an automatic red flag that he has no idea what he is talking about. Algebra is one of the fundamental building blocks that all higher level mathematics are based on. It teaches problem solving skills, helps students form a mathematical framework for thinking, and is absolutely necessary to be taught in middle and high school. While Calculus is a major part of any higher level mathematics learning, there also exists a fundamental and critical field of mathematics called Linear Algebra that is important in many professions, for example coding, statistics, engineering, theoretical physics and chemistry, and theoretical mathematics. The fact that he actually rose to academic and popular fame from this sheer heresy is absolutely mind boggling. It shows just how backwards and stupid Americans are and it makes me honestly ashamed to be one. As a mathematics student I stress the critical nature of teaching algebra and I believe it should be mandatory in any students pre-college experience. So I thank you for writing this article and explaining why he is wrong. The fact that he is even allowed to publish these things in the first place is astounding and in my opinion Andrew Hacker should stick to what he knows and not make conjectures about things he fails to understand.

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