When we look at something like math and we don't see what we remember from school, we wonder about its validity. Did it really get "watered down" like all the news reports have been saying. Are modern kids being asked to do anything like the rigorous curriculum we used to work through?  

One precept of modern math instruction is that conceptual understanding not only supports math methods, but also should be the precursor much in the way understanding a cat from a holistic standpoint is the important first step before understanding it from a genetic perspective. 

Modern mathematics is always looking for the next conceptual model to study, so we are emulating that by focussing so much on modeling concepts like subtraction, fractions or quadratic equations. If we look at this from another point of view, human intellectual development follows a similar pathway from young child to adult.