Sounds like you had poor teachers. Mathematics should always be about problem formulation and understanding which methods are appropriate and how they fit toget

Sounds like you had poor teachers. Mathematics should always be about problem formulation and understanding which methods are appropriate and how they fit together. Memorizing formulas is not mathematics at any level. Here is a very good, albeit rather long, piece on the subject. ftp://math.stanford.edu/pub/papers/milgram/milgram-msri.pdf