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So you propose to teach them different methods of solving. I think, while your mapping from solution methods to professions makes sense, the act of solving sho

So you propose to teach them different methods of solving. I think, while your mapping from solution methods to professions makes sense, the act of solving should be taught as an afterthought. The goal should be to build a robust mental model. Personally i find playing around with computer visualisations helps a lot with that. The same is even more important for differential equations, imo. I wish i would have spent less time studying algorithmic DE solving techniques in my school days. The beauty and power of expression of these has nothing to do with the way you solve them, if you ask me.

GistNoesis 2y ago
The whole education can be seen as a sieving process routing people towards their natural abilities as needed by the economy. It starts very early with things like mental calculus, where you try to get kids to compute things like 99 times 101, 98 times 102, finding tricks and rules to make the computation "easier". We could instead teach them to follow mentally some multiplication algorithm, but instead we try to promote some exploration and looking for pattern. In chess, similarly you can train for puzzle to develop some vision without having to calculate, like multiplication table. The education system must also take care not to prevent it from adapting to further changes by being too rigid. If the cat can't get out of the box, the box won't ever grow bigger. But you can't have too many cats getting out, or you'll soon have an empty box and hangry cats. I don't know what the goals should be, far from me the idea of proposing to teach, I only show paths that can be taken.
- lagrange77 2y ago
  I'm not sure i understand your answer, to be honest, especially the cat fable. > as needed by the economy Even if that is the purpose of education, a mathematician, engineer or physicist who has a deep understanding is worth more to the economy, than one who can remember and perform algorithms and computations, isn't he?
  - GistNoesis 2y ago
    From the individual intellectual point of view it's better to have a better education, but from the collective point of view having too many wild cards is not good for anyone. If there are too many physicists, they won't earn enough to justify the cost of the studies, and won't be happy in a menial job after spending years learning advanced mathematics. If anybody can do everything interchangeably, it also tends to create a monoculture which is a more fragile system. Often it's better not knowing how the sausage is made, and trusting that people who have specialized know what they are doing. Wild cats ("overeducated population") are dangerous.
    - lagrange77 2y ago
      Interesting point of view. I have to think about it.

GistNoesis 2y ago

The whole education can be seen as a sieving process routing people towards their natural abilities as needed by the economy. It starts very early with things like mental calculus, where you try to get kids to compute things like 99 times 101, 98 times 102, finding tricks and rules to make the computation "easier". We could instead teach them to follow mentally some multiplication algorithm, but instead we try to promote some exploration and looking for pattern. In chess, similarly you can train for puzzle to develop some vision without having to calculate, like multiplication table. The education system must also take care not to prevent it from adapting to further changes by being too rigid. If the cat can't get out of the box, the box won't ever grow bigger. But you can't have too many cats getting out, or you'll soon have an empty box and hangry cats. I don't know what the goals should be, far from me the idea of proposing to teach, I only show paths that can be taken.

lagrange77 2y ago
I'm not sure i understand your answer, to be honest, especially the cat fable. > as needed by the economy Even if that is the purpose of education, a mathematician, engineer or physicist who has a deep understanding is worth more to the economy, than one who can remember and perform algorithms and computations, isn't he?
- GistNoesis 2y ago
  From the individual intellectual point of view it's better to have a better education, but from the collective point of view having too many wild cards is not good for anyone. If there are too many physicists, they won't earn enough to justify the cost of the studies, and won't be happy in a menial job after spending years learning advanced mathematics. If anybody can do everything interchangeably, it also tends to create a monoculture which is a more fragile system. Often it's better not knowing how the sausage is made, and trusting that people who have specialized know what they are doing. Wild cats ("overeducated population") are dangerous.
  - lagrange77 2y ago
    Interesting point of view. I have to think about it.