[stordoff]

> Unfortunately, we tend to teach mathematics by rote

This is one of the reasons I never felt it valuable to memorise times-tables (literally chanting them in classes). IMO, it's much more useful, and generalises better, to be comfortable taking, say, 9x8 and saying "OK, it's 10x8 - 8 = 72" (instead of just memorising 9x8=72).

It may be a fraction faster, but being comfortable in those manipulations still helps when tackling something more complex (e.g. 99x89) whereas mere memorisation doesn't.