Difference between school mathematics and university (real) mathematics Several people I know were good in mathematics when they were in high school and they loved it but when they joined a university (specializing in mathematics) they felt mathematics is hard and that they were somewhat deceived because this wasn't the type of mathematics they loved and joined the university to learn. How can we overcome this problem in contemporary curricula? and why there isn't a universal mathematics curriculum? (I mean mathematics is not country-dependent like languages or history)
 A: To my experience the main difficulty is that at university mathematics mainly consists of proofs rather than simply calculate something. Proofs are much more difficult because good ideas are required. Unfortunately, the interesing part of mathematics is often too difficult to be handled in school, but some nice proofs could be made also in schools. Unfortunately, this is the case very rarely.
A: That it a very interesting question. I am teaching in a University, almost exclusively to math majors, and often I hear such complaints.
I believe, if students have not learned some proofs, and they have not proved something by themselves, they have not felt that great feeling after proving something by yourself, then they do not know what Mathematics is all about. There are of course mathematical subjects (for example Scientific Computing) where proofs are less important, but no one can call himself/herself a mathematician without the knowledge of proofs. 
Today, a kid can be the best in his/her class in math (and thus be encouraged to study math) if his/she can solve computational problems faster than all the other kids. Then the same kids gets disappointed if he/she chooses to become a math major, as computational skills are not enough and all the hard courses require proofs and theoretical thinking.
I strongly believe in the teaching of proofs in high schools, and I am campaigning for the return of proofs in high schools. And not only the return of proofs, but of theorems, axioms, and mathematical foundations. All these help kids organise their thinking, not only the mathematical thinking, and in this way kids learn what Mathematics is all about, and if they really want to study math in College. 
A: Schools need to get students through mathematics courses.  Including the ones who don't want to learn mathematics.  The way to get students through successfully wen they don't want to learn the subject is to teach phony courses.  Students who don't want to learn math do not complain about the phoniness of the courses.  Students who do want to learn math should sue for malpractice.  I intend to encourage such lawsuits.
(I didn't have fake math courses in high school, but I encounter undergraduates who did.)
