You're basing this off the premise that the typical calculus and college algebra classes test for a good understanding of math. How could this possibly be the case when the foundations of both are almost completely ignored? Also, don't think that A's in those classes mean you know the subject...
I'm going to sound like a bit of a twat below. Just know that I'm not trying to make math out to be some sort of secret club whose members are the only ones having the "right" interpretation of it. I have a tendency to sound as if I am, though, and I'm sorry about this.
I think it depends on...
I think by following these three "guidelines" you would come away from a mathematical "concept" with only a superficial understanding of it. You've not included the question of why it is, which is of far greater importance. There also needs to be motivation for the concept. There are many...