A college math professor who taught calculus told me that on the first day of class he gave students a quiz on basic arithmetic. The questions were easy enough that most students could score 100%. But he found that the speed with which students completed the quiz was a reliable predictor of their final course grade. Rote memorization of basic concepts does have some value in reducing the mental load and making it easier to focus on more complex concepts.
As a practical matter though, I think that most people working in STEM fields — including engineers — would benefit more from learning statistics instead of calculus.
> But he found that the speed with which students completed the quiz was a reliable predictor of their final course grade. Rote memorization of basic concepts does have some value in reducing the mental load and making it easier to focus on more complex concepts.
Maybe. Or maybe it's useless but skill at it is a good measure of how conscientious those students were in high school (e.g. the extent to which they bothered to do their homework). Or any number of other possible explanations.
> But he found that the speed with which students completed the quiz was a reliable predictor of their final course grade
Funnily all my college math professors and their TAs were notoriously bad at arithmetic. They regularly joked that arithmetic isn’t real math so not a big deal.
My physics professor was an arithmetic magician though. The way he could take a ridiculously complex equation covering the whole blackboard and guesstimate the solution in his head was a marvel to behold.
You can have either calculus or arithmetic in your head. But, it sounds like it's good to have arithmetic in your head before you replace it with calculus.
As a practical matter though, I think that most people working in STEM fields — including engineers — would benefit more from learning statistics instead of calculus.