I think this article - "A Mathematician's Lament" by Paul Lockhart - is something everyone should read Not exactly an answer to your questions and not exactly aimed at math beginners, unfortunately, but it's a really engaging rant about this topic https://www.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf …https://twitter.com/graciegcunning/status/1298804338727489536 …
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A *lot* like if we taught music and art by saying "This is what a painting is supposed to look like! We discovered that in 1519!" "This is what jazz is supposed to sound like! We discovered that in 1943!" and then just made you carefully copy someone else's work
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The actual answers to your questions take a long time to learn, in the same way that a musician explaining in words "What makes this chord the right one to play at this point in the song?" would take a while But it's a very worthy question, it's the whole point
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And I think Lockhart does a really good job of at least getting across to non-math people - like me - how the way he thinks about math is all about those questions and it's night and day from the stuff bad math classes make you think math is about
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(Kind of like how you'll find a lot of professional authors, including really famous ones whose books are taught in school, who don't have much nice to say about their 7th grade English lit classes)
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End of conversation
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