Which would you recommend in general? (1) Doing mathematics research with a professor more or less one-on-one over a summer or (2) doing a traditional mathematics REU, of which I've already done one. I ask because my favorite teacher at my school has been giving me some research-level problems to work on over the semester, and it has occurred to me that he may accept a request to mentor me over next summer provided he doesn't leave the country. I know there are lots of details missing. I'm just hoping to get a general impression of what's thought about this, and it may be an interesting question for others as well for whom the details differ but the general question is the same.