The necessity of algebra

Recently Andrew Hacker published an op-ed in the New York Times about Algebra. It’s extremely hard for many people, and it’s of dubious practical value, he says. We should de-emphasize it.

I’m entirely sympathetic to this point of view, even though in general, I support the agenda of the traditional liberal arts. I’m one of those people for whom math of all kinds was always exceedingly difficult–painfully, excruciatingly, humiliatingly difficult. I have no idea why this is. It could be some kind of psychological tic or block; it could be some kind of genetic inability; it could be the fault of nuns in first grade. I really don’t know, and I’m still actually slightly ashamed to admit that I never passed algebra in high school, and that my high school cobbled together some kind of individual remedial studies thing for me so I could graduate and supposedly go to college.

Ironically, by that point I could not imagine ever going to college, because the experience of constantly being made to enact my own math incapacities had made me bitterly hate and detest the entire apparatus of education. Imagine being brought to the roof of a building, day after day, and being told to jump off and fly. You fail every time. Soon it becomes clear to you that you will always fail, and that you are enmeshed in a bizarre and authoritarian form of sadism. It’s Kafka-esque, something I came to recognize partly because I was a voracious and precocious reader who took comfort in Kafka among many others. Education was like the punishment machine in Kafka’s Penal colony. If I could fly as low on the school’s radar as possible, I could avoid having the punishment of algebra endlessly re-inscribed. So I sat in the back of the slow classes and read Keroauc, and thought of ways to undermine the punishment regime.

Critics of Hacker will mock him for suggesting that he wants students to have it easy, to preserve some lazy idea and cheap notion of  “self esteem.” My self esteem is perfectly robust, thank you, despite my encounters with algebra: sometimes, a person forced to fail develops a sense of critical rage or contempt which is exactly the opposite of low self esteem, and not in a good way. If you keep forcing a one-armed man to play the guitar, he will either come to hate himself or come to hate you and everything you stand for. That’s latter is not an example of low self-esteem; it’s an example of alienation.

Predictably, I have never had any need for algebra in my adult life, ever, even though I like to build things and work with my hands. But the experience of mindless compulsory coerced failure has never left me. It made me cynical, skeptical, and untrusting, stubborn and truculent. These can be good qualities, in balance with others. But I agree with Hacker: it’s time to de-emphasize algebra in the curriculum. By all means teach it, maybe even make everyone take a crack at it. But let it go: not everyone can do it, and there’s nothing at all wrong with that.


UPDATE: I want to make it clear I have no objection  to algebra per se: I wish I understood it, wish I had access to that kind of thinking. Nor do I think pure utility is a good index of a subject’s worthiness. I agree with Hacker’s argument in the sense that compelling algebra is a bad idea. I assume–and Hacker doe sno offer good evidence–that there are many people for whom algebra is at best a chore akin to memorizing the Presidents in succession, and others like myself for whom it’s an exercise in futility.


As a side note, it’s interesting that I have a brother who is my obverse–terrible at reading and writing, startlingly, embarrassingly so, but good enough at math to hold degrees in both mechanical and civil engineering, and work for more than a decade as city engineer of a major western resort town. He was always bad at reading, from a very young age, in exactly the same way I was bad at math. He’s a smart, personable, capable guy who still gets little pleasure from reading. I’m not at all sure what to make of that. It could be nothing more than coincidence.




  • Or maybe your experience had something to do with the teaching and not you? The Catch-22 with any requirements is that it can punish the student for the faults of the school… but by not having any requirements, a school would also not hold expectations of teachers. We could strike every subject based on the experience of some portion of students, but I think that way leads to the type of class-, race-, and gender-based tracking we had in the first half of the 20th century.

  • It’s possible it was the fault of teachers, though I’m hesitant to blame them: everybody does, and as I recall they tried hard. I think Algebra should be taught, maybe even required, but maybe I’d say “lightly required.” I completely agree with you about the general value of both knowledge and training in thinking, but my experience is that some things just don’t work for some people

  • it's not that hard wrote:

    If you can’t solve for x to a basic linear equation, your opinions don’t count for much in the 21st century and you only have a job through the surplus labor of others.

  • And yet here you are, reading and responding to this blog

  • Why are we just hating on math here? I liked algebra in high school – it was like a fun puzzle – but I hated science. I’m pretty sure my one teacher went out of his way to make us feel like dumbasses, and actually called me stupid on several occasions because I didn’t know what was boiling away in some beaker. I actually purposely stopped trying in science classes because I wanted to be put in easier classes and left alone. Fortunately no one has given me a beaker of sludge and asked me to determine what is in it; but at the same time, I haven’t had to do much algebra lately either!

  • No hat­ing, I don’t hate alge­bra, I wish I could do it. I hate being forced to fail.

  • I understand that, certainly. Perhaps math is the best example because it’s what most people struggle with. It’s just that everyone has their weaknesses and are forced to fail in some way. So I’m saying it’s not just math.

  • But there are people who were forced to fail writing or history or other subjects. Fewer, perhaps–that’s one of the few points that Hacker managed to assemble a credible argument on, that algebra is the Waterloo of many K-12 students. No one likes that experience, that sense of repeated humiliation and inadequacy. But if you say, “Anything that people are forced to fail is a thing they shouldn’t have to do”, you’re really criticizing the idea of a mandatory benchmark for a given level of education, not a specific subject.

    “I’ve never had to use it” is also not a good way to distinguish what’s mandatory and not mandatory. There are people who can quite legitimately say that they’ve never needed to write beyond the 8th grade level or so, or that they rarely if ever read literature or any kind. Almost no one “needs” history or historical knowledge in the strict sense. And so on.

  • No one needs history or literature–that’s manifestly true. Both are extremely useful in some realms, that’s also. Should everyone know everything? Yes, absolutely. My experience was that algebra was simply impossible.

    I have a brother with two engineering degrees, who had severe difficulty with reading and whose writing is bizarrely inept. He rarely reads but he’s accomplished at his job, city engineer for a major tourist destination in the west. His experience mirrors mine: school is about meeting impossible standards and being humiliated.

    I’ve never had to use it is a good a way as any to distinguish whats mandatory and what’s not. It was clear to me in fourth grade that Math was a world I’d never comfortably inhabit. And yet on and on the machine went.

  • Right, but then Hacker is the wrong guy to follow, because his point of entry is a misfire. The real question is why we don’t design education to scale to a wide variety of learning styles and habits of mind. There are plausible ways to do just that, but we don’t both because public education in the US began as a project skewed towards creating a mass society and stnardized vocational inputs and because it would take resources and creativity to retool education in this way.

  • The deeper question really is: who decides the “standard” curriculum and what (and whose) purposes does it serve? Two centuries ago all educated people needed to know Latin and Greek. Now, that’s not the case. But school systems–and teachers and parents–need to be more self-reflective about what they teach and why. And somehow there needs to be more willingness to allow for a variation in learning purposes/learning styles.

  • Well and also the balance between being made to try to learn something hard, which I very much believe in, and being made to re-enact an inevitable failure because of some kind of generalized standard. We obviously need some form of standardization, but not all forms of thinking are equally accessible to all people. I can’t accept the argument that I should have been denied the chance at a college education because of inability to pass algebra, even though I accept the argument that I fall short of the ideal of the liberal arts.

  • Dear Mike,

    The Hacker piece had already caught my attention. You are not entirely fair to the essay. He is anti-algebra but not anti-math. I agree that algebra is not useful for most people except as an introduction to puzzle solving. But, if one reason for an education is to produce discerning citizens, then no one should be allowed to graduate from HS without an introduction to statistics. Much more valuable today than algebra. Hecker suggests some sort of instruction in “quantitative reasoning.” I am currently reading Kahneman’s “Thinking Fast and Slow” and some simplified version of that should be required reading for HS students. Just as everyone should be required to take a course in advertising so they know how they are being manipulated. So chucking algebra does not imply innumeracy. Finally, he does not address the problem that math in general is taught appallingly poorly in most cases. Indeed, that is such a deep problem it may be impossible to fix.


  • I don’t think anyone can hate algebra. Anyone who’s calculated how much change they should get or what the tip is on a bill is doing basic algebra. Just because not everyone (including me) can do it to the penny in their head doesn’t mean they shouldn’t understand the concept of knowing some things (average miles per hour and distance) and figuring out something else from them (travel time). If you’re resisting advanced algebra, it may be that some people are better at it than others — but the ones who are have the potential to be math, science, and engineering majors (including me). Why shouldn’t they be able to identify those potential skills in high school? Maybe Algebra II doesn’t have to be a required course — I hate graphs as much as the next person — but even supply and demand curves in economics make more sense if you understand what they’re based on. In my high school we had “pre-calculus” for those who weren’t ready for calculus — maybe we need a version of “pre-algebra II” that would expose people to concepts without putting them off all math ever.

    The same is true with statistics — how can you be an informed person in the world if you don’t understand that if the margin of error on the election poll is higher than the difference between the candidates’ numbers, the poll isn’t really telling you much? (And many people who “can’t do” statistics can still tell you the batting average and on base percentage of their favorite ball player and know what that means for the likelihood their team will win tomorrow.)

    Reexamine the way we teach things, maybe — connect them better to the real world — but don’t throw the life skills (or potential future engineer or scientist) out with the bath water.

  • I struggled with Algebra in High school. It took me four years and one summer school session to pass two years of Algebra. Yet, I was an A/B student in all my other classes. It amazed me when some of math proficient friends could not understand how I could remember all that History stuff–dates, places, names, events-but not be able to work an Algebra formula. I wondered how that could make sense of something that was nonsensical to me. I did manage to get a degree and make a decent living. Part of my job involved gathering and analysis of statistics, which I did very well without understanding the value of X. Also, I got to tell one of my Math teachers at a class reunion that I was not digging ditches for a living as he predicted that I would. he had interpreted my math struggles as a lack of caring, trying, motivation or possibly intelligence but I assure you none of this is true. Algebra was as mystifying to me as if you had placed Chinese writing in front of me and asked me to translate it. Algebra should be a part of the curriculum in high school, but nor for everyone because not everyone needs it. Those who plan to go into engineering or scientific fields surely need it, and so do those who might teach math some day. However, for me and others like me courses in business math, accounting or statistics would be far more feasible for what we do with our lives. I know that high school would have not been the daily torture and embarrassment that I endured because of Algebra had I been given other options. For those of you who were good with and “got it” with Algebra and higher forms of Math, good for you. However, please understand that there were those of us who never did “get it” and never will. You saw my comment about remembering stuff for History. Well, why can’t you remember? It’s easy.

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