[jimmaswell]

It depends. I tend to remember a fair amount of material in math classes from just paying attention. I rarely explicitly study at all for math classes and when I do the results are mixed. Example: In calculus 2 there were all those annoying weird trig integral forms. I couldn't remember them all because it was like a new one arrived daily for a while. I set out to do practice problems with them but still didn't remember much and did poorly on parts of tests that required them. Other things like arc length, double integrals, integration by parts or integrating vertically instead of horizontally, all were just intuitive to me and I remembered them without trying to. I'm not sure how typical or not my results are but in general throughout school if I felt the need to study something and practice it, it was bad news, but if something made sense to me it stuck without much further effort.

[pyromine]

I'll add on my own anecdote here, I'm a stats major and I've found that in my stats (as opposed to pure math) classes, I find the learning is very much done just by reading the book because every new concept is just an intuitive application of earlier ones, once introduced to the concept I can understand it even without working through the excercises.

In my more pure math classes (and admittedly in some topics like counting problems) I have to spend a lore more time doing exercises to actually have a grasp of the material. It's frustrating but that's just how life goes.