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— James Key"Two contrasting attitudes: non-math person: "Math is so abstract." i.e. "hard to understand" math person: We abstract *in order to understand.* Part of our job is to teach people this latter mentality."
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Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.
— Richard Askey
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And so on, until you arrive at the other side, among the purely abstract self-harming: the grinding over your failures, the refusal to remember anything good, the determination to ensure - if anyone falls into the mistake of making it clear they actually like you - that the next time round they change their opinion pronto. Emotional self-cannibalism, in other words, like those tessellated pictures of a person grappling with a mirror image of himself.
— Alexander Masters
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