Timeo Danaos…

They were the first, and they are the greatest multinational. Their dust has settled evenly over the orb.

Every university is one of their foundations. In every corner of the world eyes clamber over alphas and betas, zeta and etas; everywhere scientists reach for psis and omegas.

No imbecile, no mugger, no doctor, no politician anywhere in the world can open their mouth without uttering some pidgin Greek.

Tibor Fischer, The Thought Gang: “Slaves”.

Our resident Malvolio has become concerned about the problematic transition from school to university mathematics. Following the combustion of an unknown quantity of midnight oil, our department was presented with the solution: apparently we should remove all Greek letters from first-year maths.

At one level this recommendation is purely and simply daft, though I don’t envy the colleague whose job is to explain this to Malvolio while maintaining a professional demeanour and avoiding a summons for assault. It’s such a dense nugget of stupidity, though, that it repays a little examination.

At least he had an excuse for seeing things that way.

At least he had some reason not to trust them.

The immediate cause of the recommendation, I suspect, is that Malvolio, looking at first-year mathematics education with the eye of an MBA rather than of anyone with a background in mathematics or education, has identified the funny squiggly letters as the disturbingly alien element. (I don’t know for sure, but I’d be surprised if Malvolio realises that symbols such as \displaystyle\int, \forall and \exists are about as Greek as I am.) Leave alone the fact that one can learn the Greek alphabet with about an hour’s study of the relevant page of the Ladybird Book of Tables and Other Measures: that which is unfamiliar to an MBA has no place in the modern university. In that respect, Malvolio is merely reflecting a heresy very popular among business leaders and education ministers — albeit with unusual, er, literalism.

More basically, though, I suspect that Malvolio’s recommendation is rooted in two common misconceptions: the misconception that higher education should be an imperceptible continuation of secondary education, and the misconception that it is possible and desirable to reinvent a discipline in order to make it easier to teach.

Let’s take the second misconception first. Mathematics, as a global discipline, is held together by a dense fabric of conventions, of which the notational conventions are simultaneously among the most arbitary and among the most powerful. Fluency in the (mathematical) Greek alphabet, from \pi upward, is assumed by these conventions, and a maths student who can’t handle it is in a similar position to an English student who hasn’t heard of capital letters or punctuation — in principle one could cope without them, but only by reducing one’s output to a kind of baby-talk.

In fact, some students seem to prefer baby-talk: I do encounter some who try to convert every Greek letter into a vaguely similar Roman letter, and who convert every upper-case letter into lower case. The third-year exam I once set which, following perfectly standard notation, employed k, K and \kappa in a single question, presented these students with some entirely self-inflicted problems. (I’ve also lost count of the number of times I’ve had to inform students, including postgraduate tutors, that “to times” is not a verb. This usage may not be ambiguous, but it’s like hearing people in a vet school talking about “the cluck-clucks” or “the woof-woofs”: it doesn’t exactly breed confidence.)

One could, of course, develop a lobotomised version of mathematical notation that avoided these complications — at the expense, presumably, of lengthier expressions and probably a loss of precision — but it would cut students off so completely from the rest of the discipline that it’s questionable whether we’d really be introducing them to mathematics. I’m reminded of the well-meaning attempts to teach children to read using artificial spelling systems such as the Initial Teaching Alphabet, leaving them unable to cope with a linguistic world that wasn’t going to rearrange itself to accommodate the fads of their parents and teachers. There is a reason why wholesale spelling reforms tend to appeal most to absolutist regimes, unconcerned about isolating their citizens from the past and from the outside world.

Now onto the really big misconception, which crops up in many forms. At the more benign end it’s presented as “easing the transition to higher education” by shielding students from teaching methods or demands with which they’re unfamiliar. This shades through various species of “student-led” or “student-centred” education, which often boil down to the belief that students learn best when in their personally-defined comfort zones, until it reaches the idiocy of the students who insist that anything at university that differs from what they did in school must necessarily be wrong. The same students who transliterate \theta into Q and \Sigma into E typically give the impression in many other ways that they expected to spend four years sitting Higher Maths six times annually before emerging with an Honours degree. Why, as I try to encourage them to ask, should it work like that? University education is pitched at an entirely different level from school: it is more intense and specialised; it is shaped by the requirements of a global discipline or profession rather than the priorities of a local or national examination board; it operates under completely different assumptions about the resources available and the responsibilities of both learners and teachers. It’s not at all clear to me that trying to conceal these differences from learners, and thus encouraging them to delay any real engagement with the requirements of higher education, will do them any favours at all.

I recently came across a cracking little paper [M. Clark & M. Lovric, Maths Ed. Res. J. 20(2): 25–37, 2008] which makes this point at greater length and more thoughtfully than I can. Looking at transition through the lens of “rite of passage” theory, the authors argue that

there is no such thing as a smooth transition, and that this is not even necessarily desirable. Shock is inevitable, we must acknowledge it and deal with it. We must tell our students, in no uncertain terms, that (for most, if not for all) the first semester… will be a stressful, demanding, life-changing experience, requiring many changes and adjustments, and it will be painful in many ways. But, we should also convince our students that all this, in the end, will be worth it.

This “stressful, demanding, life-changing experience” seems to be what I recall from my own first term at college, and it was indescribably difficult and rewarding. I’m sure you can look at it, if you will, in terms of thresholds or in terms of the struggle to unlearn junk thought of many kinds; but however you do so, it’s a model of transition completely opposed to the one that Malvolio would have us adopt. I know which sounds more like education to me.

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One Response to Timeo Danaos…

  1. Pingback: More educational unspeak | New-cleckit dominie

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