You've accessed another part of you mind, the part that doesn't need a process to get the answers. Process being step-by-step thinking or memorization of facts.
I can't say that I've had experiences like yours in class, but when I was working as a programmer I would get the solution to my problem in a flash of insight quite often. One day the whole object model for a new project I was working on popped into my head. I mean it went on forever. I wrote down the base objects and associations before it faded from view. That was a couple days work right there.