Tuesday, November 2, 2010

"How much [math, literature, history, politics and music] do we really need?"

Last night I posted a long excerpt from G. V. Ramanathan's op-ed in the Washington Post. Though he made some valid points, I couldn't fully endorse the essay because of paragraphs like this:
Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as "Quantitative Reasoning" improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss. Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.
There are two ways of looking at this, but whichever you pick, this analogy doesn't hold up.

First, we can view that what we learn as transferable. This view is consistent with my experience. I went from a BFA in creative writing to a master's in statistics and found that reading and writing about Shakespeare, Twain and Faulkner was good preparation for classes like experimental design and non-parametric methods. I have also found the reverse true: training as a statistician makes you a better critic.**

If problem solving, pattern recognition, logical thinking and other related skills can be transferred to a non-mathematical context then we can make an excellent for teaching more math (though probably not for the way we've been teaching it). If these skills aren't transferable, we can still make a case for math based on statistics and on spreadsheets (everyone has to deal with statistics as a citizen and consumer and every business I've seen could use at least one person who was good on Excel). We can no longer, however, make any kind of case for literature, history or music.

Let's start with literature. It is true that many people read books for enjoyment, but how much effect do literature classes have on what books people read after graduation? The adult recreational reading experience is largely independent of anything learned in school past eighth grade (working under the assumption that a proficient eighth grade reader should be able to handle most of the books people read for pleasure).

We keep teaching literature through high school and include it in the general ed requirements for college because we believe that what students learn in those classes is, to some degree, transferable. If you honestly believe that reading Macbeth does nothing but make you better at reading Elizabethan dialogue, there is no way to justify the waste of class time covering it.

The situation for history is even worse. You can at least make a reading-and-writing case for literature; barring the writing of erudite-sounding op-eds and blog posts, when's the last time you actually needed a historical fact? A few do occasionally come in handy for understanding current events, but the overwhelming majority have no conceivable value unless we assume that students are capable of transferring what they've learned about the long dead to questions regarding the living.

The case for music and art are strictly based on enrichment.

As for politics, I can't rebut this because I'm not sure what he's talking about. Other than a year of junior high civics, we don't really teach politics. We teach courses that are relevant to politics like history, economics and statistics, but the first one requires the students to generalize what they've learned and the last two require lots of you know what.

Professor Ramanathan makes some great points about the marketing of mathematics (read the whole thing) and I'm glad to see national attention brought to the question of what we should be teaching, but it's a complex and subtle question and the professor's Gordian approach isn't going to cut it.

* Along these lines, I did a couple of posts on economics and popular literature here and here and and a post on economics and film criticism here.


  1. History is massively important for avoiding apocalyptic thinking. If you compare the present to an imaginary past, you become bitter because the present reality doesn't match your idealized version of the past. (Or you become self-congratulatory because the present seems to have better ideas than your simplified version of the past.) When you study history you see that struggle and complexity have always existed.

    Art history is actually a surprisingly useful subject. Art can be used as a lens to examine the past, and it can also be used as a lens to examine the human psyche. Almost all small businesses could benefit from greater design sense, and your designs have more power when you know how to go back to the originals, rather than being inspired by a copy of a copy of a copy. Also, my cousin who went to art school now works as a carpenter.

    Music develops the brain.

    We should teach more civics courses, there might even be a "youth vote" if more youths knew how to vote! Unfortunately it's hard to teach to politics to kids, who aren't allowed to actually pull any of the levers of government, which makes the whole concept of civic engagement sort of theoretical to them.

  2. I was attempting a reductio ad absurdum attack on the "when will the student use this specific fact or skill" approach to education. I'm a cross-disciplinarian by training and temperament. I believe that not only do art, music, history, literature, science and math have value, but that mastering one can give you a deeper understanding and appreciation of the rest.

  3. I think you're mostly talking past Ramathan. I think his claim is simply that taking math courses does not necessarily imply acquiring reasoning ability. By implication, we ought not require everyone to take math. I agree with the motivating skepticism but I'm ambivalent about the policy implication.

    I don't think your reductio strikes more than a glancing blow, if that. At least in my reading, he's not asserting, implicitly or otherwise, that math skills aren't transferable while historiographical or literary-critical skills are, nor that (supposing non-transferability) we only ought to learn what we can be assured we'll directly use in the future, he's just denying the conditional "If A takes calculus, then A will know how to reason." That seems pretty reasonable to me.

  4. Victor,

    I think Ramanathan has a lot of reasonable things to say (which is why I linked to him), but he spends a large part of the last five paragraphs arguing that other than professional mathematicians and scientists, that no one needs or even comes in regular contact with mathematics. This would certainly seem to suggest a "directly use in the future" standard.

    If 'he's just denying the conditional "If A takes calculus, then A will know how to reason."' I am not sure why he spends so much time hammering away at how irrelevant the math is and I have no idea what to make of this:

    "Unlike literature, history, politics and music, math has little relevance to everyday life."

    This is an explicit distinction and I assume the context is still education (he gives no indication that he's changed the subject). Wouldn't conditionals built around literature, history and music classes be equally absurd?

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  6. I think the discussion hinges on how one glosses 'math' in the clause 'math has little relevance to everyday life'. It's clear Ramathan thinks *some* math is relevant, since he implies everyone does need some 'quantity' of math that can be learned early on (likewise with grammar and composition).

    He does leave the precise quantity of math he has in mind an open question, however. So I'm not sure where he'd draw the line between required and elective -- algebra? calculus? real analysis? Maybe he has an entirely different curriculum in mind. Or maybe he's just attacking 'Math for Poets' courses.

    I think there's a case to be made that knowing how to complete the square or take a derivative is mostly irrelevant to the practice of most people's everyday lives.

    (I absolutely disagree, however, that knowing how to deploy a reductio or modus tollens is irrelevant. More on that below.)

    Conditionals built around literature, history, or music would indeed be equally absurd, but no one (at least in Ramathan's view, I think) is asserting such conditionals, so they needn't be denied. But people do assert as much of math--unjustifiably so.

    I think most lower-level math the way it's taught most places doesn't do much to build reasoning skills. What it does is teach computational algorithms and build computational intuition (though it's mostly unjustified intuition).

    Maybe that has some utility for people in general, but I think it really only has utility sufficient to justify the time-investment, anyway for people for whom such skills are propaedeutic toward skills to be learned in their own disciplines or for people who will eventually continue with higher-level, proof-and-theorem math, which probably has greater impact on overall reasoning ability.

    Justification: whatever critical thinking ability I have has been cultivated more in philosophy courses (specifically, formal logic) than in math courses. Formal logic has much more in common with higher-level than lower-level math, but higher-level math is pretty much inaccessible to most people because of all the preparatory work it requires.

    So I think, if we want 'critical thinking' skills to be widely disseminated, having a universally mandatory, moderately rigorous logic course at some point in the educational system, would do more toward that end than the current math requirements at the college (and perhaps even high school) level do.

    (But that's just me generalizing from one observation! Agh, what do I know.)

  7. Oy. It's hard to proofread in these tiny text boxes. Apologies :)

  8. Victor,

    These are all good points but I'm still getting stuck on this:

    "Unlike literature, history, politics and music, math has little relevance to everyday life."

  9. Right. Like I said, the plausibility of the second clause hinges on how one reads 'math'. He obviously doesn't mean to use the term categorically, so it's ambiguous what he means. And I think it's certainly true, for instance, that for the average person the finer points of topology has little relevance to their everyday life.

    You could argue that by juxtaposing it with 'literature, history, and music' without qualification, he does in fact mean to use 'math' categorically. But that would be uncharitable and it would conflict with his later points about most people being able to learn most of the math necessary for everyday life early on.

    His statement can be paraphrased as "Literature, history, politics, and music have relevance to everyday life. Math does not." If he's not using these terms categorically (and I don't think he is), then all that is required for this to be a valid statement is that some of each of the former terms be relevant to everyday life and some of the latter one not be.

    That it sounds disparaging of math is unfortunate, but I don't think the tenor of the statement should be held against its validity. But maybe I'm misreading it.

    Great blog, by the way!

  10. You know, I was going to preface my comment with "Is this a joke? You are surely joking, but just in case you are not..." But then I decided that "I disagree with you, therefore you must be joking" was a dismissive and elitist attitude to take. So I removed those lines. As it turns out, I should have stuck with my first reaction.

    But now you see that blog posts with poorly thought through arguments, which can be easily contradicted, get the most comments! (You probably knew that already.)