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This sounds like a response from a humanities or business major.

If you've never felt utterly defeated practicing a difficult passage in music or pulling an all-nighter on a problem set, then I question the extent of learning.

I've learned more from the chess and go games I've lost (leaving me in tears) than the ones I won.

Bandying opinions with one's peers is a form of learning, yes, but it's a nonrigorous one that I wouldn't pay tuition for.




My experience is in the context of teaching mathematics in particular.

Mainly calculus because that is be there level at which pedagogy theories are typically experimented with most. In upper level classes are typically straight lectures.

Edit: I meant "opinion" in the sense that you don't really have much to say to your partner about a technical topic you don't understand yet. And in much of math you don't have intuition you can verbalize until you've worked many problems, which means the time to have conversations with your peers about it is probably not the same time you're learning it for the first time. That may explain why in practice the students who read the book before hand are often really just instructing the other students when they are having discussions.


I've learned the most from struggling through the end problems in a PhD textbook; where when I go to sleep I feel so stupid and defeated that I wonder why I bother. Somehow doing this long enough you actually learn things...




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