can you recommend good books on HOW to develop this thinking process?
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i have never read a book about it! people say good things about polya's "how to solve it":
amazon.com/How-Solve-Math
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short of downloading your knowledge into my brain this is the next best bet
thanks, I'll check it out!
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yeah but it could happen faster if people talked about it more explicitly i think. we sort of expect math students to at some point just osmose this stuff implicitly which is a little unfair
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it's like... there's a few distinct transitions you go through on the way to building up "mathematical maturity," a few really key "developmental milestones" for absorbing how mathematicians think about math that i think could be organized into a rough stage model
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i've def met smart reasonable adults who did well in math classes who later realized they did not understand this and were just manipulating expressions syntactically the whole time
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not at that level but like people who thought of themselves as being good at math in school