[wageslave99]

> Can you imagine a hypothetical education system where students leave secondary school with an advanced-undergraduate level of mathematical maturity?

That would have been my dream.

> Why or why not?

Mathematics is the foundation of science, so that would have been helpful for my (then) future studies.

> What would such a system have to look like?

Not teaching algorithms to resolve problems, teaching from the source of the mathematical principles, I mean the practical issues that caused scientist to develop Math. I suppose that the Russian School of Mathematics[1] teaches Math that way, like in some Soviet books that were mainly practical.

Also, it is needed to have 5 hours per week of Math, to not have a fast pace when teaching kids. Math needs some time to "assimilate", and IMHO, 3 hours/week was not enough.

In this system, once you get out high school you could pursue the proofs of each theorem or a more inner and rigorous approach to learning Math.

[1] https://www.mathschool.com/

[pl922]

I'm a big fan of the Soviet-era books, though they often require a degree of independence to fully appreciate. Perhaps schools should focus more on developing students' ability to self-teach.