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Megan Garber writes the following in the Columbia Journalism Review‘s daily blog:

We currently find ourselves in, to put it mildly, a lull in the 2008 campaign’s primary season. The delegate tallies are in limbo. Parsing them seems to require a postgraduate degree in calculus.

I call mathification! The analogue of linguification, this term refers to statements which, as Isabel Lugo puts it, “clearly intend to get across a true point about the real world by making a false point about mathematics.”

Calculus is not a postgraduate subject. Single- and multi-variable forms of it are taught in the first year of undergraduacy. Here in the U.S. and A., kids these days can take AP Calculus, a course which covers the basics of differentiation and integration. If you take the exam at year’s end and do well enough on it, some colleges will give you credit. In my experience, and that of other pulsating brains, AP classes tended to squeeze out chances to explore and make knowledge one’s own, since given the time constraints the only topics which could be taught are the ones which could easily be tested. Still, high school was basically a horror to be survived, so changing little things like the calculus curriculum might be misplacing one’s priorities. Even if you want to make the case that some people don’t encounter it until after they’ve finished a degree — say, during an MBA program — it’s still going too far to say that calculus is a postgraduate subject.

(The Mortensen Math package, intended for young’uns in elementary school, includes a series of booklets which purport to teach calculus. The upshot is that kids get to mechanically manipulate coefficients and exponents in polynomials, filling in the necessary blanks to compute integrals and derivatives. I don’t know how much insight this actually gets across — I certainly didn’t get any. Doing the arithmetic to turn [tex]x^n[/tex] into [tex]nx^{n-1}[/tex] is easy; understanding what you’re doing and when you’d need to do it is a different business.)

Phrases like “a postgraduate degree in calculus” arise by taking a subject which sounds difficult to the author, and thus probably to the intended audience, and emphasizing it with a modifier which the author judges the audience will understand. The result is a phrase which fails to describe reality.


  1. Well, one can get a postgraduate degree in analysis. And that’s just “calculus for grownups”.

  2. . . . and Cauchy sequences and Lebesgue integration are probably even less relevant to superdelegate vote tallies than are the topics covered in AP Calculus or 18.01. (-;

  3. Hmm, what do Yooler and Dee-bragh-lee have to say about this?


    • Aaron F.
    • Posted Monday, 2 June 2008 at 15:19 pm
    • Permalink

    Calculus is not a postgraduate subject.

    Having just met an elliptical integral in a dark alley, I beg to differ. ;) And I’m content to leave this kind of calculus to the postgraduates!

    The upshot is that kids get to mechanically manipulate coefficients and exponents in polynomials….

    I was pleasantly shocked, while reading George Gamow’s Gravity, when I realized that I’d never actually proven the power rule for differentiation! Fortunately, Gamow gave a pretty proof. ^_^

  4. One of my novels recently received a derisive review that stated:

    You don’t need to have a PhD in Boolean algebra to read this, but it might help.

    On top of the bizarre notion that “Boolean” could make “algebra” scarier and harder, the actual scientific content of the book was … general relativity.

  5. On teaching (pre-university) calculus, I’m a big fan of the Leibniz product rule as the key to everything. It’s so easy to motivate (just draw a rectangle and discuss how the area grows as the sides change length), and it leads pretty easily to most of the other elementary results.

    And years later, students will find that many extensions of the concept of a derivative are defined simply by having an operator satisfy the product rule.

  6. Wow. I regard calculus firmly as a high school subject.

    With good reason: at least in Australia, it is – from the figues I saw, a little over half of students finishing high school will do calculus.

    I did two years of calculus before university.

    There were (and still are, almost 3 decades later) four different “levels” of mathematical study for the examinations that take place at the end of year 12, and calculus is included in three of them (most students do at least the second level subject, called simply “Mathematics”, and almost all students do mathematics in some form – so slightly more than half of all students that complete high school here will do calculus in high school; moreover, judging by the figures I’ve seen, the trend is toward more students doing harder subjects – which means more calculus).

    [The easiest level of mathematics (General Mathematics) focuses on more "practical" themes , but still skirts fairly close to basic calculus; for example, Simpson's rule is covered.]

    If you’re intending doing anything even vaguely numerical at university, you are almost guaranteed to do calculus at high school.

    I’ve just checked the syllabus – the subjects haven’t gotten noticeably easier in the years since I did them either; there’s substantially more statistics (which makes sense), and some of the topics I recall are gone (no proving Euclid’s algorithm produces the gcd for example, and integration by partial fractions seems to have dropped out), but otherwise the difficulty and coverage of the material seems to be pretty close.

  7. Update on that information, for the sake of accuracy:

    I got hold of more recent figures (the previous ones were 2001-2004); the trend in the earlier figures reversed somewhat, and the most recent available figures suggest that now about half of those doing mathmetics do one of the versions that include calculus, and the overall proportion doing mathmatics to the end of year 12 has dropped a bit as well, so the overall proportion completing a subject that includes calculus at the end of year 12 is now somewhat under a half.

    I’d still say it counts as “high school subject”, even so.

  8. I think the overall message of that quote is that numbers=math=scary=I really don’t feel like thinking about it. Leave it for one of them nerds.

  9. Which is, now that I think about it, mildly disturbing in a fairly intellectual circle (writing by and for journalists).

  10. Ditto on Leibniz’ rule. I kind of half-heartedly tried that approach in my calculus section this past semester, and I think I’m going to do it all the way next time. | cialis suppliers in uk | buy levitra uk | levitra generic vs |