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I'm not saying that problem solving and understanding aren't important (see Bloom's taxonomy). I'm saying that you still need memory to justify whatever domain

I'm not saying that problem solving and understanding aren't important (see Bloom's taxonomy). I'm saying that you still need memory to justify whatever domain your knowledge is in, and that memory seems to be the bedrock of further knowledge (understanding, creativity, problem solving etc.). Am I missing something here? Do you not need some element of memory to explain things from first principles, and to have an understanding of something? edit: I've just realized from reading wtallis' comment that I might be confusing two different forms of knowledge: memory and reasoning, insofar as reasoning can produce further truths. Is that what you are getting at?

Retric 16y ago
You can easily manipulate symbols without understanding what's happening. The problem is it's hard to progress significantly past your understanding using this approach. Not that Math really has levels as such, but if you don't get Calculus at a fairly deep level DiffEQ ends up being fairly meaningless. PS: It's a common thing for most calculus classes to redirive old formulas. Not because they stoped working, but rather because you really should understand why it's 4/3 pi * r^3.
Someone 16y ago
It is similar to the difference between say svn and got: you should not remember the various revisions, but how to get there, because that will knowledge will be reusable in different branches. As an example, I had a maths professor who derived the formula for solving a quadratic equation in class (in 30 seconds or so) because he did not remember it.