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>, and you were teaching 16 year olds, it would be not hard to cover the up-to-3rd-grade curriculum In this conversation of hypotheticals, I don't see why we h

by jasode 7y ago

>, and you were teaching 16 year olds, it would be not hard to cover the up-to-3rd-grade curriculum In this conversation of hypotheticals, I don't see why we have to dumb down the goal from 7-year olds learning advanced math like calculus to the easier goal of 16-year olds learning 3rd-grade arithmetic. Let's recap the discussion up to this point: - You contend that some people don't improve at math 10x than others. (The 10x can be explained away by mostly fear, grades anxiety, culture, teaching, 1-on-1 teaching, fostering curiosity, etc) - I mention 2 examples of different math ability: (1) lower math ability (maybe ~0.1x math progress) and (2) high math ability like Terence Tao (maybe 10x math progress) Based on your comments [0], I think you believe my examples of varying math learning speed is invalid and that TT is an "average math brain" that benefited from great teaching. Ok, if that is true, why can't we make breakthrough math course that can teach 7-year olds to master calculus? Not just simple 3rd-grade arithmetic but advanced calculus. If a math teacher believes strongly in the thesis that people like TT just have an average math learning speed (which means the general population is equal to TT in math learning ability), he could make a "Calculus for 7-year olds" course that could make more money than the "Baby Einstein" DVDs. Instead of graduates with math degrees accepting low-paying adjunct professor contracts for $30k/year, they can charge $50k to tutor/mentor the children of millionaires/billionaires and guarantee they can get a SAT MATH 760 score like 9-year old Terrence Tao. Those breakthrough teaching courses haven't happened which means we still have a misunderstanding/overestimation about math pedagogy that doesn't explain TT's advanced math skills at his young age. Also as a side note about fear and anxiety in math teaching... there are lots of horror stories from China, Japan, S Korea of kids getting physically punished (both by teachers and parents) for getting wrong math answers and yet they still become very good at math. [0] >I also dispute that with all else held equal, certain people are inherently “10 times faster” at “improving” at mathematics.

jacobolus 7y ago
Terry Tao was passionately interested in mathematics starting from an early age, had extreme amounts of support from experts, and spent incredible amounts of time and focused effort on it. There are vanishingly few people in the world who spent as much time or had as much guidance at a similar age. It’s basically impossible to find a reasonable comparison vs. Tao of someone who had similar amounts of support and spent a similar amount of time and yet was never able to learn anything. Humans (including young kids) are incredibly capable if they consistently practice something every day over the course of years, with useful feedback along the way. Take for example the Polgar sisters, who became 3 of the strongest female chess players of all time because their family made chess success a long-term full-time family project. There is no particular reason to believe that any average baby adopted into the same family at birth would not also have become a skilled chess player.
- solveit 7y ago
  Talking about passionate interest just passes the buck. Sure Tao was, but why was he passionately interested and can we replicate it in an average person? >There are vanishingly few people in the world who spent as much time or had as much guidance at a similar age. It’s basically impossible to find a reasonable comparison vs. Tao of someone who had similar amounts of support and spent a similar amount of time and yet was never able to learn anything. Sure. But do you think you (or someone with suitable skills) can replicate Tao's success? I don't think you can. >There is no particular reason to believe that any average baby adopted into the same family at birth would not also have become a skilled chess player. No reason, except that this sort of thing is very very rarely done despite the obvious rewards. Maybe most people wouldn't be inclined to go through such an arduous project, but authoritarian governments certainly will (and the Olympics prove that they do, and that this works to some extent, although not as spectacularly as you're selling it, for some sports). Where is the horde of Soviet Nobel laureates? Where are the North Korean Fields medalists?
  - jacobolus 7y ago
    > why was he passionately interested and can we replicate it in an average person? That is a very good question. I would imagine there been a lot written about this, but I’m not sure how systematically it has been studied. One thing that definitely does not work for the general student is typical classrooms with scores, grades, a fixed pace, and tons of bureaucratic overhead. > this sort of thing [the Polgar experiment] is very very rarely done despite the obvious rewards The “reward” to being a child prodigy isn’t that great. If the cost is most of the parents’ full-time attention, then most families can’t afford it. This doesn’t scale.
    - solveit 7y ago
      It does if you're a totalitarian state that really really wants to win an ideological battle by producing Olympic medals and Nobel prizes. Only one of those were produced.
      - 7y ago

by jasode 7y ago

jacobolus 7y ago

Terry Tao was passionately interested in mathematics starting from an early age, had extreme amounts of support from experts, and spent incredible amounts of time and focused effort on it. There are vanishingly few people in the world who spent as much time or had as much guidance at a similar age. It’s basically impossible to find a reasonable comparison vs. Tao of someone who had similar amounts of support and spent a similar amount of time and yet was never able to learn anything. Humans (including young kids) are incredibly capable if they consistently practice something every day over the course of years, with useful feedback along the way. Take for example the Polgar sisters, who became 3 of the strongest female chess players of all time because their family made chess success a long-term full-time family project. There is no particular reason to believe that any average baby adopted into the same family at birth would not also have become a skilled chess player.

solveit 7y ago
Talking about passionate interest just passes the buck. Sure Tao was, but why was he passionately interested and can we replicate it in an average person? >There are vanishingly few people in the world who spent as much time or had as much guidance at a similar age. It’s basically impossible to find a reasonable comparison vs. Tao of someone who had similar amounts of support and spent a similar amount of time and yet was never able to learn anything. Sure. But do you think you (or someone with suitable skills) can replicate Tao's success? I don't think you can. >There is no particular reason to believe that any average baby adopted into the same family at birth would not also have become a skilled chess player. No reason, except that this sort of thing is very very rarely done despite the obvious rewards. Maybe most people wouldn't be inclined to go through such an arduous project, but authoritarian governments certainly will (and the Olympics prove that they do, and that this works to some extent, although not as spectacularly as you're selling it, for some sports). Where is the horde of Soviet Nobel laureates? Where are the North Korean Fields medalists?
- jacobolus 7y ago
  > why was he passionately interested and can we replicate it in an average person? That is a very good question. I would imagine there been a lot written about this, but I’m not sure how systematically it has been studied. One thing that definitely does not work for the general student is typical classrooms with scores, grades, a fixed pace, and tons of bureaucratic overhead. > this sort of thing [the Polgar experiment] is very very rarely done despite the obvious rewards The “reward” to being a child prodigy isn’t that great. If the cost is most of the parents’ full-time attention, then most families can’t afford it. This doesn’t scale.
  - solveit 7y ago
    It does if you're a totalitarian state that really really wants to win an ideological battle by producing Olympic medals and Nobel prizes. Only one of those were produced.
    - 7y ago