When Andrew Hacker wrote his “Is Algebra Necessary” article I was basically like

But at least it was well written and brought up some good points about math instruction, many of which math instructors actually agree with. Hacker had a fresh opinion and voiced it in the Grey Lady, which generated a nice back and forth between educational philosophers and math teachers.

Then yesterday, Valerie Strauss decided that Roger C. Shank should throw in a few hundred words in her column space that basically amounted to “ditto, Andrew!” in maybe the most mailed-in piece of writing I’ve seen since that NY Times piece where Tom Friedman rides with a cabbie and learns things. However, being so terrible and so mailed-in, it’s not really worthy of a proper rebuttal. It is definitely worthy of a Fire Joe Morgan style treatment, though.


No, algebra isn’t necessary — and yes, STEM is overrated

This was written by Roger C. Schank, a cognitive scientist, artificial intelligence theorist, and education reformer.

Thank God. For a moment I thought we’d have some math education expertise added to the conversation. And I’m not totally sure any of these things are actual disciplines. Do I have to include the “C” in Roger C. Schank? So many questions.

Schank wrote this in response to a recent post I published by University of Virginia cognitive scientist Daniel Willingham entitled, “Yes, algebra is necessary.” Willingham was himself writing in response to a New York Times op-ed, “Is Algebra Necessary?” by Andrew Hacker. 

Does that make this a response to the response to the response? I’m getting confused. I bet cognitive science can save me from my confusion.

Whenever I meet anyone who wants to talk about education, I immediately ask them to tell me the quadratic equation.

You are a liar. Either that or the Worst Party Guest in History. I’m picturing that conversation.

Party-goer: Hello. My daughter just started fourth grade.


Party-goer: /checks to see if there’s a clear path to the exit.

I wonder if Roger also quizzes people he just met on other, cherry-picked singular content topics at parties.


Almost no one ever can.

So some can? Yay! 😀

(Even the former chairman of the College Board doesn’t know it). Yet, we all seem to believe that everyone must learn algebra.

Roger’s party friends and a guy who used to be at the College Board can’t name the Quadratic Equation when quizzed, therefore we must rid Algebra from our society. That’s some rock solid logic there. I can see why Roger has so many more degrees than I do. I would also like to propose to make several other eliminations from our society, based on things I don’t remember:

  • Traffic Lights, because I don’t know the difference between a red-with-a-green-arrow and a green-with-a-green-arrow.
  • Cats, because I can only name, like, three breeds.
  • Magnets, because, well, you know.

Why this religious zeal over algebra? It helps students learn how to think, people claim. Really? Are mathematicians the best thinkers you know? I know plenty of them who can’t handle their own lives very well.

Meanwhile, every liberal arts major Roger has met all live in houses with three-car garages and summer in the Hamptons. Also, at this point I’d like to remind you that according to Roger’s bio, he’s an expert on artificial intelligence. I’m going to go ahead and throw out that that might not be the most well-assimilated community.

Reasoning mathematically is a nice skill but one that is not relevant to most of life. We reason about many things: parenting, marriage, careers, finances, business, politics. Do we learn how to reason about these things by learning algebra? The idea is absurd.

LOL if you think finances don’t include math. Or than you can get a job in business without knowing math.

Yet, we hear argument after argument about the need for more STEM education (pretending we don’t have lots of unemployed science PhDs).

Ha ha. Who’s pretending that? Roger might be the first person ever to lose an argument with a straw man that he created. Oh, and here’s an interview on NPR’s Marketplace where they discuss how business and science PhDs are having a much easier time finding a job than history PhDs. But, as you were saying.

Everyone must study chemistry, memorize plant phylla and do lots of trigonometry.

Gross! That stuff sounds TERRIBLE. “Do lots of trigonometry”! Ugh. So much trigonometry-doing!

The argument for algebra rests on the transfer from math to other areas of life, something that has never been proven despite the claims of people such as University of Virginia cognitive scientist Daniel Willingham.

Wait, we’re back on algebra now? I thought we were riffing on trigonometry. And phylla.

The defenders of the existing system love mathematics because it is easy to test and there can be test prep courses and state-wide tests and national tests and tests comparing us to other countries, all signifying nothing.

My God, I’m starting to think this entire article is a piece of performance art on how to build consistently more ridiculously straw man arguments one after another. Roger is building a Burning Man of straw man arguments, except instead of burning it to the ground at the end, he’ll quiz you on the periodic table to prove that Science is dumb. Who the hell loves mathematics because it yields more tests and test prep and makes the U.S. look like imbeciles? Who loves mathematics for that? (Answer: Roger’s straw man, that’s who).

It isn’t just mathematics that is the problem, of course. Why do we all learn to balance chemical equations or memorize homilies about U.S. history? Because back in 1892, the president of Harvard University designed curriculum and said that those subjects should be the basis for high school classes.

Any cognitive scientist worth his salt knows that it isn’t subjects like algebra or chemistry that matter. It is cognitive abilities that are important.

It is thinking that is important! Finally, we have the answer! We’re not teaching enough Thinking in school. I can’t wait to take Roger’s “Intro to Thinking” course. So much better than my previous course of “Algebra-where-you-don’t-think 101”.

You can live a productive and happy life without knowing anything about macroeconomics

If you read the last sentence of Roger’s blog post, he basically refutes this. Maybe. It’s hard to tell. At this point, I’m not sure if he’s writing it or it’s a computer algorithm spitting out attempts at truisms.

or trigonometry but you can’t function very well at all if you can’t make an accurate prediction or describe situations, or diagnose a problem, or evaluate a situation, person or object.

Oh my God. Please find me the math teacher that doesn’t want to foster those attributes in his or her students, then put me on the panel to help fire them. Because making predictions, describing situations, and problem solving are at the core of what math teachers do. I must admit, these fictional educators Roger creates in his mind DO sound awful.

The ability to reason from evidence really matters in life, the names of famous scientists and their accomplishments do not.

Dang, and I spent my entire teaching career having students memorize George Boole’s pets’ names.

We can teach people the skills they need if we allow them to choose what interests them and then teach them to predict, evaluate, diagnose, etc., within their area of interest. Teaching algebra and then hoping those skills will transfer to other areas of life is simply fantasy, a fantasy that makes our kids bored and miserable in school.

The average person never does abstract reasoning.

Um, Roger, have you met people? I’m starting to think you may not have ever met a person. It’s probably because you scared them off when you asked them to recite the state capitols right after you were introduced. Because I promise you, every person does abstract reasoning. Whether you’re explaining directions, making an argument, writing songs, drawing a schematic, describing a setting, or pretty much communicating with anyone, you’re abstracting. Talking is abstracting.

If abstract reasoning was so important,

It is!

we could teach courses in that.

We do! It’s called algebra! And geometry!

We need to begin teaching people to reason well enough to make sensible political and life choices. This is a very important idea in a democracy.

OK now I’m convinced Roger is just playing around with his artificial intelligence machine. Because this last line sounds like it was written by a computer algorithm.  I figured it out! So it doesn’t pass the Turing testEither that or it was written by a 6th grader trying to pass his end-of-course Geography essay by following the format that his teacher showed him.

[Thesis] [2-3 sentences] [Something about democracy]

It really was this last paragraph (read: two sentences) that was the impetus for this blog post. I mean, it’s one thing to be completely wrong about pretty much everything and to develop entire theses based on cherry-picked and irrelevant anecdotal data (people not being able to answer your Quadratic Equation question). But it’s another thing to just mail it in. I’m willing to bet I put more thought into the first paragraph of this blog post than Roger did for that whole column. I mean, “this [reason well enough to make sensible life choices] is an important idea in democracy”??? At least end it on something other than every middle school paper I ever wrote.

So, just to recap, Roger can’t find many people that remember the Quadratic Equation, and he knows some mathematicians who don’t totally have their lives together, something about abstract reasoning, something about democracy, therefore algebra as it exists in Roger’s head should be done away with. This is a terrible job of abstract reasoning. So congrats on proving that point?



  1. +1 Rant!

    It just makes me sad that Mr. Schank has such a narrow view of math education. Thanks for the laughs. BUT articles like his make me realize what a massive public relations problem math education has. Reminds me of a comment from a neighbor who wondered how math could possibly be different these days, since 2 plus 2 will always equal 4, and triangles will always have 180 degrees.

  2. Wow, remind me never to argue with you! You make some extremely valid and humorous points. I agree with everything you said. I kind of also agree with what these guys said about algebra (ducking head) not because I disagree with your points, but because there are plenty, I mean PLENTY of algebra classrooms out there that do not do what you propose. In fact, if you took your average kid enrolled in algebra, you might find a dearth of problem-solving/thinking skills. You can imagine what his algebra class was like that he would feel so passionately about it. So, win-win, everyone is right!

    I will admit though, that the thing that took the wind out of his sails for me was the bit about the myth of jobs in the science world. We lived in university housing for 5 years and maybe it was a totally unique environment, but EVERY, I mean EVERY hard science Ph.D had a paid degree (major grants available) and jobs aplenty upon graduation. Our friends in the humanities went several years without a single interview and those that got jobs in the middle of nowhere as adjunct faculty were thrilled about it. Maybe Santa Barbara was unique, but I would love to find those places in the country where my husband’s humanities doctorate would do for him what the science folks had. We knew undergrads with jobs lined up around the corner at the pay rate double what the people in humanities who had 7 years of doctoral work could get if they were lucky to even get an interview for such a position. So mythical creature or not, someone should tell the UC system that the money they are getting for STEM research is actually supposed to be in the humanities departments.

    1. As I said, I don’t really have a problem with the Hacker piece because it was well written and well thought out. I don’t mind pieces that disagree with my worldview (and as I said, I actually agree with many pieces of the Hacker – and Schank! – piece that you point out as well – lack of a problem solving atmosphere in most Algebra classrooms in practice). The real sin here is just bad and lazy writing and bad and lazy argumentation. This article added nothing to the discussion and, in fact, subtracted from it.

      This is a very important idea in a democracy.


  3. I just thought that wrestling with the pig made the pig happy. Or, arguing an illogical way that students should/should not have to take algebra is an example that it didn’t work.
    I read Lewis Carroll’s biography. When he was an undergrad at Oxford, he was learning/tutoring Geometry as we now have it in high school. I cannot buy the argument that we as a species have evolved mental powers so much beyond where they were 200 years ago. However, I do understand that we have the little blighters in school, otherwise they are unemployed, and we have to entertain them with something. I just don’t expect it to “take.”

  4. I’m actually really surprised by your response to Schank’s piece. I thought it would be interesting for math teachers to get some ideas on how to take what’s really been a failing effort and improve it for everyone. There’s no way to conclude that high school math has been a success, as it’s done today. There are just too many people ending up “hating math” and too many people who, even if they don’t fail, don’t “get it.” And it’s not because you math teachers are bad people, it’s a structural problem. (Although going after Schank with a bunch of ad hominem and otherwise fallacious attacks is making me rethink that last point.)

    And speaking of logical fallacies, the Willingham piece was ridiculous. For example, he says “The inability to cope with math is not the main reason that students drop out of high school. Yes, a low grade in math predicts dropping out, but no more so than a low grade in English.” Even assuming the assertion in the second sentence is true, which I must grant as I don’t have evidence against it although it seems intuitively problematic, there are fundamental logical fallacies to using that assertion to suggest that means math is important. It is just as correct to conclude that we need to rethink both math AND English as they are taught. And since students typically take more than twice as many English classes as math classes, it’s still very possible that low grades in math are twice as likely to predict dropping out. Another important point – dropping out is not necessarily the metric we want to use for failure – perhaps we should use the metric “hates math” instead. The rate of *that* metric is a lot higher than the dropout rate. As someone who loves math, loved it in high school (but I was self-taught), and loved it in college where I majored in it, that’s very disappointing.

    Getting back to the Schank piece, I think it read very clearly as a thought piece. I did not literally think that every person Schank encountered at a party got the “quadratic equation” question – I interpreted that, because I have flexible cognitive skills, as a rhetorical flourish or poetic license. As a rhetorical figure, it was very effective – it very clearly brought to mind any number of situations where someone might be expressing an opinion about the importance of X, Y, or Z course, but who, when challenged, can’t actually remember what happened in that course. As Schank points out, this suggests several questions: Is there a reason for everyone to learn the quadratic equation and be able to find roots of second degree polynomials? And is there a better way to teach kids the abstract thinking skills, logical skills, cognitive skills, etc. that we are hoping they learn when we teach them the quadratic equation, a way that will not lead them to say “I hate math?”

    As an example of an alternative, I would suggest something like what Dan Myers has come up with in his What Could You Do With This series (here’s one http://blog.mrmeyer.com/?p=8483). It’s still in the context of a math class (so still about a subject) but he’s engaging a lot of cognitive skills that most math classes just don’t touch. I’m not sure Schank would approve or not, or what Dan thinks about Schank’s opinions, but it’s clear that Dan has managed to get kids a bit more interested in what he’s selling in math class than most teachers have. And implicitly, I’d say, he’s doing it by being much more cognizant of tickling the cognition of his students.

    1. You don’t have to tell me how much kids hate math and how we’ve dreadfully failed at teaching math thus far. No one is arguing for the status quo (except for the fictional math teachers in Shank’s head). I’m trying to do my small part to change that.

      Feel free to criticize my tone all you’d like – I may be a bad person, but not all math teachers are! – but that Shank piece was so dreadfully mailed in, it deserves nothing more than outright mockery. I’d point you to Kate’s blog post (above) for a more professional criticism. But again, for me it would have taken more time to rebut the post than Shank spent writing it.

      – Geoff

  5. Roger’s arguments, if you can call them arguments, are ridiculous. However, I’m going to shoot for the middle ground. My best math teachers were my doctorate professors in applied courses in economics and finance. “We will examine the theorems, without worrying about proving each point.” This gave me courage to look at the Black-Scholes Option Pricing Model (partial differential equations) and other things. I now enjoy reading about Banach and Hilbert spaces and all the applications. Too many of my bachelor degree math professors had their heads in the clouds. I doubt if they knew any applications. However, the other side of the coin (no pun intended) is that when I teach coins, cards, and dice in elementary probability (business undergraduate level), I’m often accused of not teaching the “real world.” “Teach business applications!” I do, but after the coins. But if Roger believes in the Socratic method of questioning and guiding, I’m with him. May I add that I cannot be responsible for what a student remembers after they leave my charge. I can be held to many things like, “being prepared,” “showing up on time” etc. But I cannot guarantee outcomes.

  6. Amazed that pulling to pieces in such a disrespectful fashion is considered okay in your culture. So many “put downs” . You guys deserve your Donald Trumps.

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