Here’s a very dispiriting new blog post by Tim Gowers about the dire state of school maths teaching in the UK. I’m a bit surprised, though, that he’s surprised by what he discovered (but then being in the happy situation of teaching Trinity mathmos is likely to colour your view of the world!). Certainly, my experience teaching Cambridge philosophy students — a very bright lot — about half of whom had done A-level maths and got top grades, was that very few of them really understood any maths. They might have picked up a bag of tricks to apply in response to some formulaic questions. But as for some conceptual understanding of classical analysis or an appreciation of the idea of rigorous proof ‘in the wild’ … Sigh. (No wonder philosophy of mathematics can leave them cold!)
And judging from the many comments to Tim Gowers’s post, the decline in school maths teaching is not confined to this declining off-shore island.
Well, there’s no point in moaning about this, though I hope my local friendly mathematicians are exercising what influences they can to help stop the rot. But it does mean that there’s a real problem for teachers of logic and writers of logic books aimed at students. We tend to be mathematically ept ourselves, and students are good at dissembling — or at least, at remaining silent — so we can so easily fail to realize just how mathematically inept so many of them are (through no fault of theirs, let it be emphasized). What to do? I don’t have the teaching problem any more: but I still do have the writing problem. I guess I’ve fallen over the years into working with the principle if in doubt, go slower and explain even more. But it does make for long books to write and long books to read.