In my opinion, the biggest problem is the focus on learning math subjects as dependencies for learning the next math subjects. This problem is exasperated by tying a subject to semester or school year.

If I'm not supposed to learn Calculus until I learn Algebra, that must mean I can't learn Calculus until I learn Algebra.

If my Algebra class lasts for a year, that means it must take an entire year to learn Algebra.

If I am supposed to learn Algebra first, then I must not be able to sufficiently wrap my head around anything related to Calculus.

That means that whenever I hear about "limits", "d/dx", I should immediately lose attention; after all, those are Calculus-related things, and my underdeveloped brain will not be able to comprehend such subjects for another year, and I shouldn't even try.

Of course, none of those are true. If I wanted, I could

* learn at my own pace * learn in the wrong order * wrap my head around limits, d/dx, L'Hopital's rule, etc. before understanding factoring, trigonometric functions, etc.

In fact, any of these would have put me far ahead in my education.

"Traditional" education requires a student to be lazy, or hold [him/her]self behind academically. To make matters worse, it requires that student to be a specific, quantified amount of lazy/held back.

For me personally, I struggled to keep up with the obscene amount of expected rote homework, while also feeling miles ahead of lectures, even though the homework and lectures were from the same class.

When I started learning about programming on my own, I suddenly had the freedom to do all of the things I mentioned above. Programming, as a subject, is especially applicable: There are abstractions, paradigms, languages, etc. You can jump into any aspect headfirst, and still get your bearings.