LogFAQs > #977228333

Yellow posted...

I think most people could learn advanced calculus... Given enough time.

I've never seen this formally recognized, but I generally get the impression that everybody has a certain point in math after which it stops coming naturally to them and they have to start taking it seriously and actually practicing to push further than that. For some people, that's basic addition. For me, it was intermediate calculus. For some, their limit hasn't actually been invented yet. I fully expect that that point can be shifted with teaching that better aligns with a given individual's optimal learning style, but there's still going to be a soft cap somewhere.

Part of the issue, then, is that school doesn't necessarily give everyone the tools and opportunities they need to put in the extra effort to move past their soft cap, including failing to recognize that those people are soft capped and insisting on grading them in a way that compares them to people who aren't, but another big part is that there just often isn't much point in putting that effort in. If I'd applied myself, I could have done a math degree and taken my math ability much further than I did. I just didn't want to. My major was Biology; even the basic calculus I took was just to satisfy the math credit requirement in a way that wouldn't bore me as deeply as the actual "get your math credit requirement even if you suck at math" class would have. I took intermediate calculus mostly for fun, then when it turned out to be something I had to work hard at, I chose not to go further in math because it wasn't fun anymore.

If we're framing math's primary value for most people as a sort of mental exercise (which I think is quite valid), I think it's important to recognize that while everybody can benefit from exercise, not everybody needs to push themselves to exercise at a high level. Analogously, you can be in perfectly healthy physical shape but never even consider getting to the level of being able to run a marathon. Casual exercise is still beneficial, whether it's physical or mental. In cases where gym is graded, a lot of times it's a matter of grading whether or not people put effort in rather than whether or not people excel the the activity by some arbitrary metric, and I think that philosophy has more merit in math than most curricula recognize.