Simple City  

If you haven’t read A Mathematician’s Lament, Paul Lockhart’s gloriously polemical assault on

the confused heap of destructive disinformation known as “the mathematics curriculum”

then I strongly encourage you to put that right.

The focus of Lockhart’s ire is mathematics in the US school system, but it translates without difficulty to the UK and probably a great many other places.

Lockhart doesn’t diagnose the cause of this mathematical malady, but I will offer one thought: the take-over of exam results as the be-all and end-all of educational attainment.

If you fancy discussing this issue further, there’s a webinar on the topic over at MathFuture this evening, hosted by David Wees and Richard DeMerchant.

Everyone is familiar with George Bernard Shaw’s line: “He who can, does. He who cannot, teaches.”

Apparently it isn’t universally popular in educational circles.

But what did Shaw actually mean? I’d always taken it in the same way as everyone else: as a nasty swipe at the teaching profession. But my contact in the Shaw Society suggested an alternative explanation.

The quote comes from Shaw’s slightly odd 1903 work Maxims for Revolutionists: just a categorised list of aphorisms, which includes others of his most famous lines^[1].

Interpreted as such a maxim, the quote takes on another meaning altogether: it’s a description of how revolutionary societies should organise themselves. Everyone who can should get involved in the fighting, cooking, carrying, building, etc: doing. And those who cannot (on account of being too old, wounded, or whatever) should teach the others.

So, I believed this interpretation for a little while. But now I’m not so, erm, sure.

If you look at Maxims for Revolutionists, it’s quite short on practical advice for organising uprisings, and despite its title it does seem like a depository for his thoughts on various topics. Advice on “How to Beat Children”, for example, strikes me as being of limited use to people actively preparing for revolution. In particular the section on Education (line 31) does contain general snarking at teachers, or at least teachers of certain types: “When a man teaches something he does not know to somebody else who has no aptitude for it, and gives him a certificate of proficiency, the latter has completed the education of a gentleman.”

So now I don’t know. At any rate it doesn’t seem plausible that Shaw would have failed to notice the more obvious reading, and that interpretation doesn’t exactly run contrary to his attitude to the education system of his time (I’m told he described his own school in Dublin as a “futile boy prison” where he learnt “dishonourable submission to tyranny”). So it’s difficult to conclude that he didn’t intend it, at least as an overtone.

In any case, we can perhaps agree that teaching, as it should happen, was better summed up by Aristotle: “Those that know, do. Those that understand, teach.”

Sorry for the feeble pun in the title, by the way, but it’s a sort of unwritten rule when discussing Shaw.

[1] Though not my favourite: “I like flowers, I also like children, but I do not chop their heads and keep them in bowls of water around the house.”