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Comment by brnaftr361 | Hacker News Reader

Can you define what you mean by abstract thinking skills?

Everything else you've listed can be acquired as a dishwasher or a line cook.

Anyways, the classes always seemed to me to tend more towards shut up and calculate than they did building a robust understanding and perhaps most important of it all: a mathematical intuition. I always found it profoundly stupid that there were never any essay questions in math, I expect those who elect to teach the subject are often wont to expediency (which would explain the number of coaches in the department) rather than an inclination towards the subject itself.

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I grew up in the midwest US, and what we called "word problems" were a pretty common component to learning (classes), practicing (homework) and verification (testing). The one that stuck with me is the explanation of how speedometers and police radars actually calculate speed using derivatives in pre/entry calculus. We also learned to write very basic proofs. I would consider both of these to be the essay equivalent of mathematics.

Students who didn't show an interest in higher maths courses either took slower versions of the earlier courses where they could get more time with the material, or more business oriented maths such as basic statistics and accounting.

AP Calculus was the closest I experienced to "shut up and calculate", if only because our teacher somehow managed to get behind the lesson plan in our first week and we ended up doing homework for lessons the night before the class where she would actually explain it. That was the second most brutal experience of my academic career, only after the semester in college where I was taking a macro economics course taught by a Polish grad student and a micro econ course taught by a Greek grad student; neither of them pronounced things (especially, and perhaps obviously, the greek letters in equations) the same way, and it turned into a nightmare keeping things straight.

When did you receive your education? I, too, grew up in the Midwest but my experience has always been "shut up and calculate" rife with mostly process-learning and unrelatable problem sets. Certainly important, yes, but also boring. Nothing creative, nothing playful, just very mechanical, very dull. Word problems were infrequent, and anything with real world application was jammed into the margins and given only the most cursory glance. Not to mention doing the online homework was awful.

During graduate school I interacted with academics working in math education who felt similarly, that math should be taught through essay questions, e.g. "explain the concept of a limit", and the like. I've always felt it was a deeply misguided pedagogy and I hope it does not become popular. Solving well crafted exercises requires a deep understanding of the material, it's unnecessary to check understanding in some other way.

Well for one it's prompting you to make a meaningful linguistic exercise of the matter, which is at once a creative task and secondly it enforces a more dynamic approach to whatever problem is presented.

I wonder if you could get a professor to do anything more than plug and chug, and that's a skill we've long ago delegated to glass. Not only do I want to explain these things in my mother tongue, I expect to know why some variable is in some such place, and how a cube of some other variable is related to the problem at hand. Calculation is banal.

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