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I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I

I wonder if there’s a way to teach Calculus in a more practical way. I use the principles of Calculus constantly in many aspects of my job, but I don’t think I’ve ever done say, integration by parts professionally. Understanding deeply what an integral and a derivative are is a very useful skill though.

bee_rider 3y ago
As an undergrad I tutored folks in a sort of “calculus for non-STEM students” class that focused more on practical stuff and applications… and TBH I think trying to shield them from the complexity didn’t really do them any favors. I often found that they had some practical algorithm memorized step-by-step and some graphical or conceptual intuition, but when the steps and intuition betrayed them we’d end up spending a while backtracking to find where they lost track of the concrete rules, and then we could work our way forward to catch up to their intuition. Practical results are good guideposts but don’t replace full understanding I think. That’s just my perspective, though, I have a pretty simplistic, algebraic way of looking at math. I could never be a mathematician or see true beauty in math, it is just a bunch of little rules to me. IMO calculus class is fundamentally just relatively abstract compared to the stuff before it. But once you’ve finished it, your engineering and science classes should be full of practical, reinforcing applications, right?
- rocqua 3y ago
  Isn't the actual calculations of e.g. integrals the least useful part of calculus for non-stem students? Instead the basic concepts are where the easily accessible value lies. Teaching tricks without teaching the concepts not only fails in the way you describe (it prevents building ideas further). It also fails to teach anything useful at all. Because barely anyone outside of STEM wil ever have to solve any kind of integral or derivative in their life.
rocqua 3y ago
The valuable part of calculus to me was understanding the concepts of limits, differentiation, integration, and a tiny bit of differential equations. Learning how to actually solve integrals or differential equations was useless other than it teaching me more about calculus and how it is useful. For calculations in practice I will turn to wolfram alpha, but it has some value to understand what wolfram alpha is doing under the hood. I think a calculus course whose tests defocusses calculations might be very valuable for practically minded people. Knowing to think about derivatives is much more useful in practice than actually being able to calculate a derivative.

bee_rider 3y ago

As an undergrad I tutored folks in a sort of “calculus for non-STEM students” class that focused more on practical stuff and applications… and TBH I think trying to shield them from the complexity didn’t really do them any favors. I often found that they had some practical algorithm memorized step-by-step and some graphical or conceptual intuition, but when the steps and intuition betrayed them we’d end up spending a while backtracking to find where they lost track of the concrete rules, and then we could work our way forward to catch up to their intuition. Practical results are good guideposts but don’t replace full understanding I think. That’s just my perspective, though, I have a pretty simplistic, algebraic way of looking at math. I could never be a mathematician or see true beauty in math, it is just a bunch of little rules to me. IMO calculus class is fundamentally just relatively abstract compared to the stuff before it. But once you’ve finished it, your engineering and science classes should be full of practical, reinforcing applications, right?

rocqua 3y ago
Isn't the actual calculations of e.g. integrals the least useful part of calculus for non-stem students? Instead the basic concepts are where the easily accessible value lies. Teaching tricks without teaching the concepts not only fails in the way you describe (it prevents building ideas further). It also fails to teach anything useful at all. Because barely anyone outside of STEM wil ever have to solve any kind of integral or derivative in their life.

rocqua 3y ago

The valuable part of calculus to me was understanding the concepts of limits, differentiation, integration, and a tiny bit of differential equations. Learning how to actually solve integrals or differential equations was useless other than it teaching me more about calculus and how it is useful. For calculations in practice I will turn to wolfram alpha, but it has some value to understand what wolfram alpha is doing under the hood. I think a calculus course whose tests defocusses calculations might be very valuable for practically minded people. Knowing to think about derivatives is much more useful in practice than actually being able to calculate a derivative.