Optimal for the majority of people is what I believe the parent was arguing. The vast majority of people are not self motivated and forward thinking enough to learn calculus all by themselves.
1. Make it possible for HS students who are interested in Calculus to take the course under the instruction from a college profess on the high school campus. That way it would be set up for students to get college credit for the class and they would not need to travel to a college campus or deal with the AP exam system.
2. Make it possible for HS students who are not interested (Yet) or at all to graduate with out taking the class. Lots of student are ready for Calculus until college anyway. No need to force them on a single path IMO.
>The other half of USA high schools? They don't even offer a Calculus course of any kind [1]
That's a bit misleading. There are many districts where one school serves as a magnet school where anyone interested in taking more advanced classes can go. So yes while it may be true that half of all schools don't offer calculus--far less than half of all students can't readily take calculus.
I've seen very, very few people able to learn calculus outside of a school system. Most will just go to elaborate lengths to avoid using calculus and justify why they don't need to learn it.
Calculus is really simple. The part some people have trouble with is that they're forced to remember all the other math they've learned to that point. Others struggle with it because the concepts are new.
There are successful studies teaching 12 year olds calculus, using software that helps them with the computational side (they don't have to remember all their trig rules or how to factor but they need to know when to apply the core ideas). These arguments that people shouldn't learn calculus (or should because they need some rigor) are all wrong. A small number of people should learn to do by hand, all the non-calculus computation they'll run into in calculus. Most people should probably just be taught the main concepts and how to apply them using readily available software that can help them with the calculation part.
My high school don't go beyond Calculus 1 (edit to add: this was two semesters and covered differentiation and integration).
That was years ago (pre-internet) and if a student wanted to take other college-level math they were released to take it at the local university campus. Today, I guess online classes are an option.
> "Yet we regularly teach smart high school students and first-year undergraduates calculus..."
High school students are taught plug-and-chug calculus where one uses rules and formulae without any real understanding of the underlying subtleties that make calculus work.
Except the kids taking high school calculus likely ARE going to do those things one day. Maybe not all of them, but some.
Heck, I don’t use calculus directly in my daily life. But I’m glad I took it because I recognize where it is used, and how, and that helps me understand my world better then without.
Maybe they don't, in a way, but are you sure they still don't benefit from it, even if they find it hard and even if they only reach a pre-calculus level?
b) High-school is a terrible place to learn calculus (or anything). Online resources are often far better.
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