Teachings of Old & New

While reading through a discussion board post from a Liberal Studies course that I am taking, I came across the quote "Are textbooks printed in order to teach children, or are the contents of these textbooks to be controlled by the Southern oligarchy and the commercial health of publishing houses?" from Report From Occupied Territory, page 733. This excerpt is found in a book of Collected Essays by James Baldwin. This brought me to thinking about how students were taught previously and how they are being taught today. As per most of my homework experience from elementary school, my parents could help me if it was something they learned. That is, if it followed an algorithm that they learned from their schooling, they could show me how to do it. Now, however, students are not encouraged to memorize a formula or algorithm, but rather understand how the formula works and where it comes from. Students are still (normally) taught the algorithm in the end, but work through it to understand. Mathematics seems to have transitioned from just doing a problem to get an answer to understanding how to solve a problem. More than likely those who only learned the algorithm at one time knew the underlying mechanics, but that part doesn't stick with you very easily. Now students are even more encouraged to understand those mechanics so that they can apply that knowledge to a problem that may look slightly different.