> He said "a derivative of a function is the rate of change of that function."
I'm confused by this comment. That's the intuition that you see in just about every introductory calculus textbook: that the derivative is the instantaneous rate of change.
This was back in the late 1990s and early 2000s. I hope things have improved.
My conclusion is different though. I think there are different types of thinkers and different teaching styles and when the subject becomes very complex the disparity between the two is exacerbated. And luck plays the role in matching up with the right teacher/professor for you.
I was taught calculus in high school, well before university, in Australia in the late 1970s.
Visual analogies such derivatives being tangential rates of change and 2nd derivatives being local curvatures were taught and drawn on the board in the first week of two years of Calc I and Calc II classes that came before leaving high school to attend university.
Nearly all math textbooks and lectures mention practical applications. The problem rather seems to be that you have/had a different understanding of "practical" than your math professor.
I always had the benefit of being the tutor, though. I have to imagine that teaching a calculus one course is near impossible with 30 students on 30 different levels of experience and aptitude.
That said, I think that first year of calculus is often taught valuing mechanics over concepts.
I like to imagine what 12 years of math would look like if people weren't chained to a timeline. Here's khanacademy, go!
Chances are your teachers said almost, if not exactly, the same, but it didn’t stick yet.
In my first analysis class, the professor said we shouldn’t worry if we couldn’t complete any of the exercises, adding something along the lines of “If, during the course, you look back at the exercises from four weeks ago, you will find you can easily do them, and won’t even understand why anybody could have trouble doing them”. That turned out to be o so true.
https://betterexplained.com/articles/colorized-math-equation...
Even worse the language of math was never adequately explained. You were expected to learn the meaning of some new squiggle or greek letter by... its context? Symbols and terms you'd never seen before were just thrown at you without explanation. Definitions when given sounded circular or were given in terms of other things that had never been defined clearly.
I had one professor who just turned his back to the class and wrote things on the board. Students were meant to just magically understand.
I'll never forget in year one of college being absolutely stuck in calculus. I called up my dad and he tried to help me a bit, then he stopped and said: "you know what a derivative is, right?" I said no, not really. They tried to explain in class but it didn't click. He said "a derivative of a function is the rate of change of that function." I thought for a second and then said "thanks, now I understand calculus." I was un-stuck instantly. My professors never explained it that clearly.
Later on I took classes in things like population genetics and evolutionary dynamics. The professors of those classes explained the relevant math better than my math professors did to the point that if I'd taken those classes first I would have done better in the math classes that were their prerequisites.