High and middle schools of the US do not encourage enough critical thinking among our students.
Everything is being done with guidance of a teacher going through steps of a procedure - and this is where the problem is.
For example, in Math: Teachers provide step-by-step instructions how to solve an equation, how to divide, how to... This does not teach students how to think about math individually. It teaches them to follow the procedure, and maybe get the answer right - but it does not teach how it works, and it does not teach how to think beyond that point.
Our education system cannot produce great mathematicians, because too many people are taught to follow procedures and instructions.