second thing: "half" of math is heavily visualization-loaded, and children are, stereotypically anyway, better at visualization (would love to see confirmations and denials of various possible empirical cashing-outs of this generalization)
but, you aren't by default led to think about things **more deeply in some general sense** than you've ever thought about things before. (i'm groping for my point here...) in other words: math is about investing heavily in generalization.
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perhaps this is why i feel that math is unnecessary because i definitely am by default led to think about such things
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i'm not saying, train on some skill of theorizing that's supposed to generalize from learning math to... theorizing. i'm saying math *is* (a lot of the hard part of) theorizing. so you want to get good at it. maybe you disagree that math is a key element of theorizing
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not talking about the often-bad kind of generalization, where you drop important aspects of some phenomenon and then call it "more general" because your thoughts depend on less detail. talking about the good kind.
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the good kind is where you explain all the data better / unify all the skills more elegantly. real math is about doing that iteratively, each time re-including your new understanding into the pool of data to be explained / understood.
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