I work as a private tutor for proof-based math, and I have a lot of students who've spent some time self-studying before coming to me. The comment by godelski matches my experience: the biggest obstacle seems to be the fact that it's hard to learn how to check your own proofs if no one has ever taught you how. I see a lot of variation in how well people have managed to develop that skill on their own.
Having more textbooks with solutions to the exercises would probably help a lot with this, especially if you used the solutions judiciously. I think the fact that this isn't more common sadly has a lot to do with their role in undergraduate teaching: every exercise that has a solution in the back of the book is one that college students can very easily cheat on. I definitely agree that it's frustrating that the product has to be made worse for everyone else just because some people would misuse the better version. Far from the only such case in the world!
Yeah it’s a catch-22. I’m in grad school and occasionally I get to be instructor. When I am I focus far less on tests and more on homeworks and projects (I do ML so it’s well suited for that style). The homeworks are made to be “play around” and the project is to be very self driven (with plenty of help, but they are juniors or seniors so they be fairly self reliant) and to find passion.
The reason I do this is because grades matter so much to students that even if they care to learn material they are incentivized to cheat (and subsequently cheat themselves). I think a lot of academics still don’t get this and are resistant to change (it is a lot of work to create a class but not to much once you worked everything out).
I think this confidence thing is also something that needs to be learned in every subject. Even in CS the compiler, type checking, and even unit tests aren’t enough (though they are extremely useful).
I should also say, one unfortunate thing I find in academic teaching of coding is we often don’t look at code. There’s not enough time. But to me this feels like trying to grade a math proof by looking only at the first and last lines. I think this builds lots of bad habits and over confidence
Having more textbooks with solutions to the exercises would probably help a lot with this, especially if you used the solutions judiciously. I think the fact that this isn't more common sadly has a lot to do with their role in undergraduate teaching: every exercise that has a solution in the back of the book is one that college students can very easily cheat on. I definitely agree that it's frustrating that the product has to be made worse for everyone else just because some people would misuse the better version. Far from the only such case in the world!