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.

  • 1
    $\begingroup$ You could offer yourself as a case study to a researcher in the field. $\endgroup$
    – Tommi
    Dec 5, 2022 at 8:30

1 Answer 1


I recommend a science citation search for papers on mathematics correspondence courses. Perhaps restrict it to last century, to eliminate online courses, as being a little extra scaffolding. Old style correspondence courses are a little more scaffolding than just having a book. But a decent proxy. In particular, look at dropout and pass rates.

I think the biggest hurdle is dropout. Look at the massive drops in moocs. Anything you can do to minimize that, the better. Easier texts. Auditing. Feedback loops. Making a promise to a friend. Having an external objective like a validation or AP test. Paying a tutor. Etc. This is more serious than the learning, or not, from question answering sites.

If you don't master one tricky homework problem, but get through Stewart calculus front to back, you have outperformed the kid who drops out in chapter 2 of Spivak. And you can always do the Spivak later.


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