As an undergrad math major, I've just recently run into this problem as I begin to take graduate level math courses. In the past (i.e. through high school math and basic calculus) I have always had a deeper understanding of the math going on such that I didn't really need to memorize many formulas or rules because I could always "reinvent" them (at least the simpler ones such as cos^2(x) + sin^2(x)=1) if I needed them.
I have found this level of understanding far more difficult to attain recently. For example, this past semester I took a linear algebra course. Whenever I am given a definition or property, I typically try to prove/justify it to myself or at least figure out why it is interesting. I found in my linear algebra course that this was very difficult to do, since there were so many definitions that just seemed to be "dropped in", unexplained by the professor. Thus, I found myself memorizing formulas and theorems instead of having the deep understanding of them I was used to.
I may have gone off on a little bit of a tangent, seeing as this article relates more to basic mathematics, but I think the underlying problem is the same. I'm not really sure what the solution is in my case, but I would guess that if my professor were to devote more time to explaining the usefulness of some of the more abstract concepts (such as eigenvalues) I would probably feel more comfortable with the subject.
I have found this level of understanding far more difficult to attain recently. For example, this past semester I took a linear algebra course. Whenever I am given a definition or property, I typically try to prove/justify it to myself or at least figure out why it is interesting. I found in my linear algebra course that this was very difficult to do, since there were so many definitions that just seemed to be "dropped in", unexplained by the professor. Thus, I found myself memorizing formulas and theorems instead of having the deep understanding of them I was used to.
I may have gone off on a little bit of a tangent, seeing as this article relates more to basic mathematics, but I think the underlying problem is the same. I'm not really sure what the solution is in my case, but I would guess that if my professor were to devote more time to explaining the usefulness of some of the more abstract concepts (such as eigenvalues) I would probably feel more comfortable with the subject.