Most students typically do not understand what mathematics is about until their sophomore year in college when they take linear algebra. The educational system basically lies to to them. Mathematics is presented as formal manipulation of symbols and math is an seemingly endless set of problems to do. Proof, examples, counterexamples, application of theory basically anything a working mathematician might do is ignored. While there are some exceptions, once the student gets to linear (or abstract) algebra or an upper division mathematics course and finds out it mostly is about proof and structure they realize they have been duped.
Similarly. it is now formally coming down the pike with computer science.