A very interesting post on mathematics education at the secondary school level by Timothy Gowers, a Fields medalist. He writes, "memory works far better when you learn networks of facts rather than facts in isolation. If you don’t really understand what differentiation is all about, then the fact that the derivative of x^3 is 3x^2 is a completely different fact from the fact that the derivative of e^x is e^x. But if you’ve derived them both from first principles (I’ll come back to what I said about e^x in a moment), then they are related: we have a process we do to the functions and and this is what comes out." This is a really good example of mathematician with a deep understanding of mathematics listening carefully to a student to understand how the student thinks, the better to explain mathematics to a struggling learner. "Of course, another reason is that if you forget something, you have a chance of rederiving it, but that’s a slightly different point. Your knowledge of a piece of maths is far more grounded if you know how it is derived, or at least have some memory of the derivation, even if you have no problem remembering the fact in question. Even if you forget the details of the derivations, just having seen them has a major effect on binding together the facts you know." Hear. Hear.<p>P.S. The comments on the submitted post are very interesting, and include a comment by Fields medalist Terence Tao.