I was put through all the way to Calculus in High School. Didn't do much for me, I didn't really ever end up using high level analysis in college. The math I di

I was put through all the way to Calculus in High School. Didn't do much for me, I didn't really ever end up using high level analysis in college. The math I did become interested in was set-theory, topology, logic, those sorts of things. I feel like its more important to teach kids those latter topics than analysis, since almost nobody uses analysis in their day to day lives, but operations of logic and abstract algebra and the like can always apply and also help you think about the world differently. I would say: logic, set theory, algebra through elementary/middle school. Then introduce maybe some geometry and basic trigonometry in late middle early highschool. Then you can have different tracks for different areas of math: kids who really love analysis can do an analysis track, kids who think set theory is the shit can continue with advanced logic (maybe some philosophy of math?), geometry as well. And for Juniors and Seniors who are really, really into math, you can introduce advanced topics like analytical geometry or algebraic topology and the like (although I think those topics are probably more appropriate for a college level class).