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> The mathematical logic, proof, rigor, and how to create a model is what is needed and that is missing. This is interesting to me. My experience was the oppo

> The mathematical logic, proof, rigor, and how to create a model is what is needed and that is missing. This is interesting to me. My experience was the opposite. So much time in my honors math in high school was focused on proofs and deriving them, that developing and intuitive understanding of the material and how to apply the math to solve problems was secondary.

ndriscoll 3y ago
I suppose the commonality is just that primary/secondary math education is often bad, but doing proofs without intuition seems to be completely missing the point. A decent proof should mostly be the intuition. Once you've learned the basic techniques, you just say "by induction X", "evidently X", etc. to wave away routine calculations, and mostly stick to the "meat" of the argument, with explicit calculations for technical steps only if something is tricky.
ChainOfFools 3y ago
> honors math This may or may not be comparable to what is referred to as high school math in the general sense. I don't know how your curriculum worked, but presumably the students who are taking honors math had already demonstrated a capable, if not above average faculty for the minimum level of rote memorization necessary to simply get the basic arithmetic and algebraic symbol manipulation right most of the time. This would leave class time and homework time available to explore the matrix in which these manipulations are grounded, since "how" they work is taken to be table stakes. But the vast majority of students don't have the extra bandwidth available, due to competing pressures in other areas of life, or simply insufficient short-term memory capacity, to get past "how to" with enough time left over for "but why" even if they have a natural curiosity and interest in the question. Beside irony told this is that the more one understands why, the easier how it becomes to memorize. But finding this balance seems to be a very unique mixture for students who are not extraordinarily capable in the ladder, there is a huge advantage to being able to build a working toolchain of mechanical spellcasting to reliably obtain repeatable, testable results so that you can be productive when postulating why the spells work at all. Essentially it helps to be capable.of mimicking an ersatz computer when you need to develop human intuition fpr computation. but computers are getting so good at thinking like a human that humans who best think like computers are going to be less prized than they have been in, say, the 30s, 40s, 50s and so on, when the premises that are still baked into our current pedagogical sensibilities were formed.

ndriscoll 3y ago

I suppose the commonality is just that primary/secondary math education is often bad, but doing proofs without intuition seems to be completely missing the point. A decent proof should mostly be the intuition. Once you've learned the basic techniques, you just say "by induction X", "evidently X", etc. to wave away routine calculations, and mostly stick to the "meat" of the argument, with explicit calculations for technical steps only if something is tricky.

ChainOfFools 3y ago

> honors math This may or may not be comparable to what is referred to as high school math in the general sense. I don't know how your curriculum worked, but presumably the students who are taking honors math had already demonstrated a capable, if not above average faculty for the minimum level of rote memorization necessary to simply get the basic arithmetic and algebraic symbol manipulation right most of the time. This would leave class time and homework time available to explore the matrix in which these manipulations are grounded, since "how" they work is taken to be table stakes. But the vast majority of students don't have the extra bandwidth available, due to competing pressures in other areas of life, or simply insufficient short-term memory capacity, to get past "how to" with enough time left over for "but why" even if they have a natural curiosity and interest in the question. Beside irony told this is that the more one understands why, the easier how it becomes to memorize. But finding this balance seems to be a very unique mixture for students who are not extraordinarily capable in the ladder, there is a huge advantage to being able to build a working toolchain of mechanical spellcasting to reliably obtain repeatable, testable results so that you can be productive when postulating why the spells work at all. Essentially it helps to be capable.of mimicking an ersatz computer when you need to develop human intuition fpr computation. but computers are getting so good at thinking like a human that humans who best think like computers are going to be less prized than they have been in, say, the 30s, 40s, 50s and so on, when the premises that are still baked into our current pedagogical sensibilities were formed.