Mathematics: discipline of pedagogically impared idiot savants.

Today in calculus just reiterated to me the things I hate about the discipline of mathematics (as percieved by someone being taught it). First, they obligate me to get a hundred-dollar graphing calculator, which is not optional. Although I will never use this for anything other than my classes, nonetheless I will not be able to use it on my first test. This leaves me wide open for simple errors that, although they are completely irrelevant to whether I understand the subject material, will nonetheless count against my grade. This will undoubtably be useful for me when I am attempting to calculate the instantaneous velocity of a falling coconut while trapped on a desert island.

Secondly, the pedagogy sucks crap. While I mean no offence to my specific teacher, calculus is a subject that is all about motion and curves and movement and limits. For instance, today he ‘explained’ how to calculate the average and instantaneous velocity of a curve. This is exactly the sort of thing that would be much clearer with an animation or two.

Thirdly, the notation is a baroque cluster fuck.

  • They are perpetually re-using the same symbolism to mean entirely different things. For instance, the notation for a function that is the inverse of a one-to-one function, i.e. f(x), is f-1(x). Which of course doesn’t mean 1/f(x), like it does every other goddamn place you see something to the -1 power. Another example is the “left and right hand limit” notation – where right hand limit means “from the right” (i.e., decreasing values of x) and left hand limit means “from the left”, (i.e. increasing values of x). Which of course couldn’t possibly be expressed by some human language word for “left” and “right” or even the existing mathematical notation for “greater than” and “less than”.
  • They constantly re-use the same one letter variables to describe different things. As illustrated by the naming section of “How to Write Unmaintainable Code”, this is one of the cardinal ways to make sure you don’t get your point across. Is paper really so damn precious that we can’t use multi-letter variables? Or even – gasp – variable names that have something to do with whatever the fuck you’re talking about? While we’re at it, take the “function called f”. Please. Preferably out back and beat it senseless. I’ll refer you again to the naming section of “HtWUC”, this time to Item 3: Be abstract. You would think that you could use some letter other than f to talk about your fucking function. The coup de grace of this bullshit is the fact that they can’t even be arsed to use all the letters in the alphabet – normally they’re stuck with x and y.
  • The corrolary to the bullshit one-letter variables that are constantly meaning different things, is all the one letter variables you’re just supposed to know always mean something else. Take e, for example. Just another variable? No, it’s a constant. This crap has thoroughly infected physics, too, and if you don’t believe me you can take your mass and convert it into energy – e = mc2 – but, of course, you need to keep in mind that in that case, e is not the e we were talking about one sentance previously.
  • Of course, the converse of all this reuse is the fact that for every new idea they have to introduce a new notation. Instead of saying something like limit(x,a): function(x) they have to invent limit example . And the list goes on and on. If you think you’re too special to use a latin character for your new special constant, evidently you raid greek. And if you’re really bloody happy with your work, make the character three times as big as the rest of the problem (vis Σ ). Or, just make up something that looks kinda like another letter but isn’t really (see integrals). I got Maple the other day, and looking through all the symbols it’s like bloody Chinese or something.

6 thoughts on “Mathematics: discipline of pedagogically impared idiot savants.

  1. Heh, thanks… I am glad my ranting was pleasant; I tried for an amusing vibe. I swear, I’ve never met a culture so beholden to the fashions of 17th-century auteurs.

  2. It almost hurt my feelings but I actually agree with much of what you had to say. My personal rants would include ripping up how we’re taught arithmetic in grade school (for how many years?) and how calculus is taught to everyone more out of dogma than any real usefulness. (Well I guess there’s money to be made selling those atroicious 1000+ page piece of crap textbooks. Apparently James Stewart has 80% of the market share.) Terrible shame that we can’t do something more interesting, more useful, or more beautiful.

    It’s actually really sad that it’s taught the way it is, since mathematics at its best is thought provoking, inexhaustible and gorgeous. And it saddens those of us with passion for the subject to see idiot pedagogy earn its almost universal distrust and even contempt.

    -M@

  3. I’m sorry, Matt – I was really pissed at my Calculus class and I should have constrained my critique to that. Certainly all mathematics isn’t this bad, and all professional disciplines have their own jargon.

    The thing that gets me is most of the disciplines I’m interested in have rapidly changed their terminology and verbiage to suit the demand – not always to good effect (viz 10k inscrutable names for genes). Calculus is like legacy memeware in math – it’s been around so long people have just gotten used to how wierd it is.

    My hope is that Divine Proportions rekindles my interest in calculus, and that my teaching continues to show me how hard it is to talk to people in their ‘native’ tongue.

    In the meantime, I’m pursuing a graph-theory directed study, on account of needing to know more about the properties of dynamic graphs.

  4. Hey, you may or may not use this “crap”, but you can say that you know how to do it. It makes you a more rounded person and a step ahead of all those people who think they are to good to learn somthing they may not use. Your a better person for taking calculus. Calculus is a must in physics, chemistry and other areas of the world. Thats where you make the big bucks.

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