Two years ago I taught a topology course in which I never lectured or explained anything at the board. Students did not use any external
resources (no textbooks, no internet, no nothing) and relied entirely on their brains and on each other. I provided them with my own set of notes, which
contained only motivation, basic definitions and axioms, and a sequence of exercises and theorems to prove. Their homework, before coming to class, was to
prove all the theorems. Class time was spent with students presenting their results on the board, criticizing each other's presentations, discussing, and
coming to consensus.
What I just described is known as the Moore Method, a form of Inquiry-Based Learning in mathematics. I will explain why I chose to do it, how I did it,
and how it turned out. I will also survey what the research literature says about it.