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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