alt Hacker NewsI’m a physicist, so I’m biased, but my experience of pure maths was about the same. We had to do it, but at no point was any utility actually demonstrated - that was left to the physics professors. It was all just “look at this thing I can do with these symbols” without any actual tangible relationship to anything.
Then again, I remember how we were taught calculus at high school - we were taught how to mechanistically integrate and derive everything under the sun. At no point did anyone think to explain that we were measuring the areas under curves, or their rates of change - it was all just “memorise this operation”. Again it was left to the physics teachers to explain why this was useful, and what we were actually doing.
Poor teaching, if you ask me, and it more often than not left me retrospectively wondering if said mathematicians had actually understood any of what they did, or if they just had little blind symbol manipulation Turing machines in their heads.
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Teaching only the practical side risks not teaching the subject with the appropriate theoretical depth and the ability to generalize it to other applications. Courses for purely applied fields utilize calculus to solve the current problem and then move on without teaching the finer points. Basing a calculus course on physics alone might be preferable in high school, but would be of disservice to students in university.
Well, in at least some cases, they do understand what they're doing, on a deep intuitive level!
Using spaced repetition to see through a piece of mathematics
https://news.ycombinator.com/item?id=18895613
The title is a slight misnomer in my opinion. The author did make heavy use of spaced repetition of course, but deemed it neither necessary nor sufficient for the result he described.
The actual active ingredient is curiosity to the degree of obsession. Actually wanting to understand what's going on.
You can do that with pure math just as much as with applied.
But it may be harder for many people for such a desire to arise if there is no obvious connection to real-world matters. (I certainly had such thoughts, sometimes! What is this for? What's the point?)
>At no point did anyone think to explain that we were measuring the areas under curves, or their rates of change
In my experience you get taught the definition of a derivative of a function at a point is equal to the instantaneous rate of change and that integrals are defined as a Reimann Sum, the sum of the area under the curve. Everything in the class comes from building on top of those definitions.
Re: obvious intuitive explanations are ignored.
I remember squinting at the definitions in my calculus textbook for a full 10 minutes before realizing... oh my God, if this had been a 5 second animation, I would have understood it instantly.
I remember being rather upset! "If it's so obvious and intuitive, why didn't they just say so?"
I want to say, "well, unfortunately you cannot put an animation in a textbook." But that's actually false!
Even as a child I made flip book animations. And there was plenty of room here in the margins for several of those :)