What kind of maths should be taught in high-schools?

This is an apparently simple question, but the answer is not always obvious.

BUT there are things a teacher (or a problem books writer, etc.) should not ask 16 years old kids in regular schools to solve. One example is Exercise 28, on page 55 from the book by Burtea et al. “Matematica: Culegere de probleme, Clasa X, Trunchi comun si diferentiat”, Ed. Carminis, Pitesti, 2005. The exercise asks: “Show that there are no surjective functions between a set A and the set of all its subsets (ususally denoted by P(A)). ” This exercise is nothing else than what 1st year (university) students in mathematics meet in their mathematical analysis course as “Cantor Theorem”, whose proof is based on a not really intuitive contradiction argument. Kids and trainers preparing themselves for the mathematics olympiad may want to prove Cantor’s result by themselves, but all the others should pick other nicer and more accessible math exercises involving surjective functions…

Author: multiscale
