How should we teach Maths

I came across this new feature in the NYT via Science Blogs by Steven Strogatz. You may remember him from his paper with Duncan Watts on small-worlds that arguably kick started modern network theory. It looks like it's going to be a regular series so I highly recommend adding the feed to your rss reader.

The article that first caught my eye was called Rock Groups. It starts by differentiating between the serious side of arithmetic and the playful side. This is something I've long gone on about but never quite had the nice way of putting it like these guys do. Maths teaching for kids is like torture. I was having a discussion a while ago where I questioned whether we really needed to recite endless times tables aged 10 years old. A suggestion that drew scorn from my opposite number. But really, why?

The book that is heavily quoted in the article, "A Mathematician's Lament" by Paul Lockhart. It starts with a musician having a nightmare that children are not allowed to touch an instrument until they have mastered the theory of music and how to read a score. Only after many painful years are they allowed to lay their hands on an instrument.

This is a powerful analogy. You don't have to learn all the nuts and bolts of mathematics before you can start playing with numbers. Back in the Strogatz article he shows how much you can discover without being able to do any addition at all, just by grouping rocks. I wish I could quickly multiply two large numbers in my head but it wouldn't make me a better mathematician. It's like arguing that the best playwright should be able to spell every word in the dictionary.

The beautiful thing about the rocks is that it shows how much you can learn about number by pushing things around with your hands and being creative. Perhaps all those people who complain to me that "oo I could never do maths me" would have enjoyed it more if it was based on this rather than being expected to master "a complex set of algorithms for manipulating Hindi symbols".

Make sure you keep up with the Strogatz series. I found a pdf of the essay that inspired the Lockhart book. If I ever get through my Christmas backlog I might get around the getting the book.