My motivation for this question is personal. I'm a software engineer and I study mathematical logic as a hobby. Subjectively, it feels like I make the most progress after asking a question on the Math Stack Exchange or with friends and getting some kind of feedback on it. Also, I seem to get some benefit from preparing a question even if I later discard it. I don't know much about the effectiveness of various kinds of self-learning though (and receiving feedback from other people might not qualify as self-learning), and I have no non-anecdotal knowledge.
I'm wondering if any research has been done on acquisition of undergraduate and post-undergraduate-level math outside of classroom settings and what kinds of strategies yield what kinds of results.
It seems like research on this would be hard to do: you'd have to pick a subject, pick a book or a paper, send it to people, give different groups different instructions, and then compare results after a while. I'm not sure what you'd test: maybe test the effect of doing exercises in a textbook versus not on student performance on an exam.
So I'm curious if any kind of study has been done on this before.