17+: go deep on whatever you like
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Alexey Guzey je proslijedio/a tweet korisnika/ceAlexey Guzey
Alexey Guzey je dodan/na,
1 reply 0 proslijeđenih tweetova 18 korisnika označava da im se sviđaPrikaži ovu nit -
no math before ~11yo because math that is taught in the first several grades is trivial and, instead of spending years on it, the children should do something they are good at (learning languages) and then learn it all in like 2 weeks when they're ready
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Odgovor korisniku/ci @alexeyguzey
i like your overall sense of things, but this seems a big mistake. i think higher-math-type thought (not necessarily actual higher math) is very important, difficult, and i assume the earlier the better. bottleneck might be subtle mentoring issues / posing through-provocations
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Odgovor korisniku/ci @argletargle
why do you think the earlier the better?
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Odgovor korisniku/ci @alexeyguzey
lots of stuff has serial depth required to learn, but math has maybe the most serial depth in some sense, like longest chains of master this; only then, master that; only then, master the next; etc.; and has increasing returns afaict.
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Odgovor korisnicima @argletargle @alexeyguzey
(contrast with language, where there's certainly serial depth, but also very high parallelism in some sense: there lots of stuff you can and do learn in whatever order, like you can always just learn any given word)
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Odgovor korisnicima @argletargle @alexeyguzey
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)
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Odgovor korisnicima @argletargle @alexeyguzey
third thing: math (talking about "higher" math here, i.e. [all the intuitive ideas lying behind] college and graduate level math / physics / CS) is heavily loaded on "conceptual flexibility / original seeing / generating de-novo models", which stereotypically kids are better at
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Odgovor korisnicima @argletargle @alexeyguzey
4th: math is a "highly reactive" species of idea, so you get more returns starting earlier. like, you learn about multiplication and division, and meditate on intuitions about flows; then when you play with a hose and put your thumb over the output --> fast spurt --> recognition.
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i really think it's quite a shame that there aren't more people who are both "mathematically mature", and also try to teach young kids "real math", and collaborate to figure out what works. like, keeping eyes on the ball of real math, here.
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Odgovor korisniku/ci @argletargle
i think a lot of your arguments make sense if you want your child to be a mathematician but i don't see how any of these will be material if they just need to learn calculus/linear algebra and move on to other things (which i think won't be affected by learning math)
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Odgovor korisniku/ci @alexeyguzey
hm.. this isn't coming from gearing toward them being a mathematician, but it is coming from gearing toward them being able to "theorize seriously" in some general sense, like be able to see deeper into things than the intuitions we develop naturally. maybe we differ in that goal
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