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Comment by saghm | Hacker News Reader

In my freshman E&M physics course, there was no calculus prerequisite, so when we had to answer a question on a quiz or test that would be solved with an integral, the professor said we could just put the integral without needing to evaluate it and he'd mark it as correct. I think this approach makes a lot of sense; understanding the concept of "summing" the value of an expression across a range by using an integral is much more important than being able to do the actual calculation.

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That's ridiculous. When I took the entire undergrad physics series for scientists and engineers, it absolutely required calculus, vector math, and diff eqs.

Why is it ridiculous for an intro-level course to not require people to manually compute integrals? I'm open to the idea that maybe I'm wrong about this being reasonable, but "I had to do it so everyone else should have to too" is not a very convincing argument.

To be clear, I had already placed out of the calculus course that would have taught how to evaluate these integrals, so I wouldn't have been disadvantaged by it being required. There definitely weren't any differential equations in the course though; it seems like you might be overestimating the intensity a 100-level physics course required for people like me who never did physics again after.

For the same reason not grinding out the code by hand and copying from your LLM is going to result in you being a less competent programmer in the long run.

I really believe there is something to be said for putting yourself through the mental strain of evaluating the integrals (or code) and that doing so contributes to you having a better feel for how it works on a conceptual level as well, you don't just get better at calculating by doing things the hard way.

If you can easily see the solutions and manipulations you can make to an integral by hand, then you are more able to quickly get a feel for what it represents just by looking at it. If you are not as experienced doing them by hand, just reading them is going to sap some of your brain power and energy, and you will be less able to reason about them abstractly as a result.

I think the whole "just learn the concepts" approach to almost anything is fundamentally misguided and not at all how representative of how humans really learn.

I guess I just fundamentally disagree with you on this one. To me, spending time manually calculating integrals in a timed exam is less similar to copying code from an LLM and more similar to manually translating the source code you write into machine code instead of using a compiler; it might have value, but the amount of work it would take a student in an intro class to do that would drown out their ability to retain anything else.

I think in Asia though it's expected of highschool students to evaluate the integral without a calculator. Education in the US should at least match what they do in Asia to stay competitive.

There is a lot of rote in Asia, and an over emphasis on classic geometric proofs that have little relevance in today’s world. Yes, we should try as hard as Asia in math, but blindly copying Indian or Chinese education practices isn’t the right way forward.

Well, with the current state of mathematics in the US education system... blindly following Asia is a step up.

I do agree with you that in theory we can do better than asia, but that is too high of a milestone given that we are basically currently significantly worse than Asia on all fronts.

NCLB was as disastrous as throwing away phonics.

Adopting elements of the Finnish model would probably be an improvement.

The goal of learning should be mastery, not memorization of specific cases.

With geometry, the style I was taught emphasized explanation of complex problems using proofs but building from first principles.

You are almost guaranteed never to have to another Euclidean geometric proof again after you take the gaokao. It’s like the LeetCode for chinese college admissions.

(Shrug) It depends on what you "master." Mastering symbolic integration isn't going to do much for your career or your country's industrial prospects. Life is short, and there are too many more-useful things to learn.

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