In Defense of Teaching Algebra

Over at HuffPo, my colleague Nick Warner has posted a piece about why we teach algebra to people who supposedly “won’t need it”, and he makes some excellent points. (Recall the silly New York Times piece by Andrew Hacker entitled “Is Algebra Necessary?” that I mentioned a few posts ago.)

I recommend Nick’s piece.

-cvj

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7 Responses to In Defense of Teaching Algebra

  1. robert says:

    Ah HuffPo – I remember Arriana as an undergraduate, even before she met Bernard Levin. And it was a very silly, and annoying, article.

    Yours, showing ones (and Arriana’s) age

    Robert

  2. anonymous says:

    I understand that Michael Faraday, one of the 100 most influential scientists, knew only basic algebra. How do you reconcile that fact with the fact that he contributed a hell of a lot more than more mathematically sophisticated physicists of his time? His achievement seems to give the lie to your colleague’s claims. If Nick Warner is correct Faraday should have been less able to think abstractly then his better educated peers and contributed less than they did, which is clearly not the case.

  3. Clifford says:

    Hi anonymous,

    With all due respect, that’s a stunningly faulty argument. For a start, it is analogous to the claim that some people make that smoking is not bad for you because their uncle Al smoked 3 packs a day and lived to age 100. Concepts from basic statistics and population sampling (all often underpinned in early studies of basic algebra, ironically) should immediately come into play here to show why this makes no sense at all.

    Several more points spring to mind:

    (1) What are you calling the “basic algebra” that Michael Faraday only knew? Are you sure it is comparable to what we’re talking about in basic education in school?

    (2) Regardless of the answer to (1), the main point is this: Algebra is known to prepare you for learning how to do abstract reasoning, logic, and so forth. (And, crucially, for teaching the appreciation of the value of such reasoning too.) Nobody is saying that not having had algebra means that you definitely won’t learn those skills in other endeavours. But if you are building an education system for your society, why would you deliberately leave out the structures that you know are predictably of high value in that regard ? Being (wrongly) perceived as “difficult” is certainly not reason enough, and catastrophically flawed black-swan-type arguments don’t help either.

    Best,

    -cvj

  4. Anonymous says:

    Hi Clifford,

    According to Wikipedia: “The young Michael Faraday, who was the third of four children, having only the most basic school education, had to educate himself.[12]… Faraday was an excellent experimentalist who conveyed his ideas in clear and simple language; his mathematical abilities, however, did not extend as far as trigonometry or any but the simplest algebra. James Clerk Maxwell took the work of Faraday and others, and summarized it in a set of equations that is accepted as the basis of all modern theories of electromagnetic phenomena. On Faraday’s uses of the lines of force, Maxwell wrote that they show Faraday “to have been in reality a mathematician of a very high order – one from whom the mathematicians of the future may derive valuable and fertile methods.”[6] ” . I don’t disagree with you or Warner on the importance of mathematics. How would you evaluate a person like Faraday assuming that the Wikipedia article is correct on his lack of mathematical ability? I think that Hacker’s point that the entire set of skills a person has should be taken into consideration is correct. I don’t doubt that Faraday was unusual, but would science have benefited if he hadn’t been given a chance despite his lack of sophistication math wise?

  5. Clifford says:

    Hi,

    Faraday and Maxwell are scientific heroes of mine, by the way, so thanks for picking this example.

    But the answer is in your question… in the quotes you gave. We don’t need to evaluate Faraday, since according to your quote, Maxwell already has. He was “in reality a mathematician of a very high order”… so by that measure, he is hardly the counterexample you seek to what Warner, myself, and others are saying about the value of learning mathematics. While he may have started out with a “basic” education, he learned what he needed in order to do the science that he did.

    If your point is that based on this example people should not get an education in topic X because if they need it we will just pick up topic X on their own, I think that the evidence does not bear that out. (And X need not be algebra here, it can, by your reasoning, be anything else, like, say reading and writing). I see all around me countless examples of people not fulfilling their potential because the education system (and more broadly, the larger culture) failed to expose them properly to various ideas early in their lives.

    Bottom line*: We cannot run a functioning society by expecting that everyone is going to have the opportunity, motivation, or resources to just “pick it up” along the way. Some notable examples of this happening with spectacular results does not mean it is going to work for a planet of 7 billion (plus) people. (I refer you to the smoking argument of before.)

    Best,

    -cvj

    *Sticking to your initial point about Faraday being somehow (!) an argument for not teaching algebra. – The other point about valuing broader skill sets, and so forth, is a different point and fairly obviously correct and not controversial at all.

  6. Anonymous says:

    Hi Clifford,
    N. Warner begins his article with the following story: “An apocryphal joke has a medical student failing physics and questioning why he should ever have to solve useless mechanics problems that he will never again see in his life. The physics professor reassures the hapless student. “These problems are terribly important: They save lives.” “How?” cries the student.”They keep thousands of idiots like you out of medical school.” ” Your reply to my last comment claims that you don’t need to evaluate Faraday since Maxwell has done so and found him to be a superior mathematician. Maxwell was talking about the mature Faraday not the Faraday about to start his brilliant career. I fear that the young Faraday, judged solely on his grasp of math, would have been put in the same bag as the hapless student. I’m a little offended that you should ascribe to me a view that I do not hold. I never claimed that algebra or any other math was unnecessary and should not be taught in school. As members of the math/physics guild you guys are overzealous in your defense of the tradition. Hacker’s point of view is more realistic than that of Warner’s apocryphal physics professor. You and Warner are looking at the issue from a bureaucratic perspective, you have hundreds of students to evaluate and don’t have time to look for black swans. How is your graphics novel progressing.

  7. Clifford says:

    Hi,

    You say:

    I’m a little offended that you should ascribe to me a view that I do not hold.

    Well, I was responding to what you wrote. I refer you to your own comment here. You seem to be now arguing a different point. I was answering the point you started with, not the point you changed tack to.

    As for the story that Warner chooses to quote at the start of his piece, I find it entirely irrelevant to the core issue. Take his story up with him.

    The graphic novel is going ok thanks. See the occasional post for updates.

    Best,

    -cvj