Question

I believe the basic notions of abstract algebra like groups and rings can be given at the high school taking the Integers as prototype. And since the students at high learn about the equations of geometric objects like line, circle, ellipse, etc., I am sure with utmost care the seed of Algebraic Geometry can also be sown. Other than that, I think we need to put more emphasis on theory of functions and calculus (including some proofs,if possible) and geometric insights.