> 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/
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/