

What maths A-level doesn't necessarily give you - alter8
http://gowers.wordpress.com/2012/11/20/what-maths-a-level-doesnt-necessarily-give-you/

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tokenadult
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.S. The comments on the submitted post are very interesting, and include a
comment by Fields medalist Terence Tao.

