Worst thing about teaching mathystuff (I'm including eg semantics) is showing defs up front rather than _designing_ them.
Imre Lakatos's "Proofs and Refutations" is a wonderful book-length discussion of this and related points.https://twitter.com/AnalysisFact/status/752888067455852544 …
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It's often possible to teach in such a way as to discover them. Slower, but deeper.
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if Lakatos is the discussion, Polya's "Mathematics and Plausible Reasoning" is the manual, "How to Solve It" the TL;DR
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love that book
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he also died in poverty, almost willingly so! https://en.wikipedia.org/wiki/Oliver_Heaviside …
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