As someone who went to Exeter and did higher-level math there, you didn't have to even start calculus in order to graduate. Also, the calculus taught there is roughly the same level as a decent public school. And you can probably get the same level of education at a local college.
After retaking calculus at Berkeley (which I admit is not exactly a local college), IMO they teach it here more rigorously (e.g. they introduce epsilon-delta fairly early, and they are precise about details like domains of functions, etc.)
The real place where Exeter shines is for competition math and for second/third year college math courses. But most of the people who seriously study competition math there have a strong math background to begin with, so I find it unlikely that someone who is inexperienced in math would actually pick up competition math as the culture is intimidating.
Also, very few students take second/third year college math. When I was there, they offered one term of topology and one term of real analysis. Each of these classes had one section of ~10 people. But in all honestly, only a few students in the class actually were mature enough to understand most of that material. Even though I was on the stronger side of students, I don't think I internalized the material at all.
I'm honestly really skeptical of pushing students to learn more and more "advanced" material because getting good at math isn't about being able to memorize mechanical rules for derivatives or integrals. Learning math should be about learning the process of discovery -- playing around with problems until you are able to tease out some insight or a solution. The skill of "distilling" a problem to its essence is one that has served me much more usefully than being able to find an integral.
Agreed. At some point not long after high school, the syllabus explodes and there's just a huge amount of topics to learn. There's no one thing that you must learn, and there's nothing that you won't be able to learn, it's just that you probably won't have time to learn all of math/science/engineering.
The way I'd put it is the kids all need to learn things close to the pace that they can go. If there are kids who can go really fast, let them do that, find a teacher who teaches real analysis or whatever and let them get on with it.
On the other end of the scale, kids with difficulties need help too. Dyslexia needs to be discovered early, and anxieties related to learning need to be resolved.
Whether you think algebra is coming in too late or too early is not really the issue IMO, the idea of one-speed-fits-all is the real problem. I always wondered why education wasn't just a bunch of ladder steps. Pass a given course, get put on the next one asap. For all subjects, without cross-restrictions. For instance I'm still a relative beginner in creative writing, and I'll likely stay there, but I should be able to take some advanced math and coding courses.
I'll probably end up implementing this myself for my older kid via tutors, since he's interested in a lot of things above his year, but I think everyone would benefit if the system worked this way.
After retaking calculus at Berkeley (which I admit is not exactly a local college), IMO they teach it here more rigorously (e.g. they introduce epsilon-delta fairly early, and they are precise about details like domains of functions, etc.)
The real place where Exeter shines is for competition math and for second/third year college math courses. But most of the people who seriously study competition math there have a strong math background to begin with, so I find it unlikely that someone who is inexperienced in math would actually pick up competition math as the culture is intimidating.
Also, very few students take second/third year college math. When I was there, they offered one term of topology and one term of real analysis. Each of these classes had one section of ~10 people. But in all honestly, only a few students in the class actually were mature enough to understand most of that material. Even though I was on the stronger side of students, I don't think I internalized the material at all.
I'm honestly really skeptical of pushing students to learn more and more "advanced" material because getting good at math isn't about being able to memorize mechanical rules for derivatives or integrals. Learning math should be about learning the process of discovery -- playing around with problems until you are able to tease out some insight or a solution. The skill of "distilling" a problem to its essence is one that has served me much more usefully than being able to find an integral.