[U]nderstanding and mastery are tightly linked. Curricula like Everyday Math try their best to unlink them. They think that understanding concepts with just a little bit of practice is all that you need. This conveniently fits their dislike of drill and kill and how they believe that there is no one way to solve a problem.
Mastery is not just about speed. It's directly related to understanding.
My friend K. came up with an apt definition just the other day.
She said that understanding without mastery is a case of "That makes sense."
It's grasping the logic.
Being able to grasp the logic in a number of different realms is an important goal of a liberal education; it's my liberal education that allows me to read articles about the economic crisis and follow the argument reasonably well.
But following the logic of an article about the economy is completely different from understanding economics with any degree of sophistication.
It was for this reason that, a few years ago, I stopped reading books explaining "math for non-mathematicians" and started working my way through math textbooks.