• My own experience both as student and as teacher is completely different. As a student I was expected to produce proofs of results that I’d not previously seen. My first topology course was even taught modified Moore method: we were proving things on our own almost from Day $1$. As a teacher I expected my students to do so in such courses as real analysis and abstract algebra. Of course the results that I asked them to prove were simpler than some of what we covered in class, or I broke them into manageable pieces, but I expected them to do math. – Brian M. Scott Dec 15 '13 at 23:28