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I actually do a lot of discrete math (numerical analysis) and statistical analysis for work, and completely agree that there is too much emphasis on symbolic ma

by nickff 4y ago

I actually do a lot of discrete math (numerical analysis) and statistical analysis for work, and completely agree that there is too much emphasis on symbolic manipulation in school-math. That said, I’m trying to address the reality of what exists in high schools, and the current reality is that a little extra discrete statistics, and a lot less continuous calculus seems like a good trade-off to me.

noobermin 4y ago
Alright, sorry to assume less of you. It is a sentiment across the thread but you do know that it's analysis and that calculus is just analysis. Really, calculus of continuous smooth functions is a special subset of calculus. The thing I remember vaguely is when I was taught calculus first, we "took limits" by hand, including derivatives, numerically, and then we did the formulae and spent the rest of the time doing nonsense like difficult trigonometric integrals and integration by parts. The thing is as you go onto proofy classes including real analysis and such, you go back to the original concept and learn that that was the important bit and actually useful piece after all, as most of life's data cannot be well modeled by analytic solutions you can write down. I think this is what I contend the problem is. Unfortunately, I don't have much contact with people who actually teach students high school calculus, but almost every mathematician and physicist I know (apart from the theorists may be) agrees with me, that at the end of the day, there is a lot of value to the concepts underlying calculus because they are general and help both naive models of data in your head and eventually statistical and numerical (read computational) models that vastly more people use, while the trigonometric substitutions are much less useful, and are really only useful if you're going to go on to being a theoretical physicist (or at least get a degree in physics where you'll need to do derivations).

by nickff 4y ago

noobermin 4y ago

Alright, sorry to assume less of you. It is a sentiment across the thread but you do know that it's analysis and that calculus is just analysis. Really, calculus of continuous smooth functions is a special subset of calculus. The thing I remember vaguely is when I was taught calculus first, we "took limits" by hand, including derivatives, numerically, and then we did the formulae and spent the rest of the time doing nonsense like difficult trigonometric integrals and integration by parts. The thing is as you go onto proofy classes including real analysis and such, you go back to the original concept and learn that that was the important bit and actually useful piece after all, as most of life's data cannot be well modeled by analytic solutions you can write down. I think this is what I contend the problem is. Unfortunately, I don't have much contact with people who actually teach students high school calculus, but almost every mathematician and physicist I know (apart from the theorists may be) agrees with me, that at the end of the day, there is a lot of value to the concepts underlying calculus because they are general and help both naive models of data in your head and eventually statistical and numerical (read computational) models that vastly more people use, while the trigonometric substitutions are much less useful, and are really only useful if you're going to go on to being a theoretical physicist (or at least get a degree in physics where you'll need to do derivations).