Mathematics is not a spectator sport

Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics. Sometimes this means doing even more than the assigned problems. (See ``time committment'' above.) This is how to avoid the common pitfall of ``understanding everything in class but blanking out on the exams.''

I realize this isn't welcome advice, and I admit that I haven't always followed it myself. But in years of teaching (and 20+ years of learning) mathematics I haven't found any shortcut.