Ah, topology. When I was in graduate school I took a topology class where the professor used the Moore Method. No textbook. For each unit there was a handout with a bunch of definitions and a few examples. Then a list of theorems. Prove the true ones, find counterexamples (or proofs of falseness) for the false ones. Class time was students at the board going through their results. If no one had a result, a random student was put at the board while everyone gave suggestions.
I was amazed that there were smart people who had that many years of school behind them and didn't understand the basic management skill for that sort of class. If I had a proof for #3, and nothing for #4 or #5, I was already on the way to the board before the professor could finish asking, "Does anyone want to take a crack at #3?"
Ah, topology. When I was in graduate school I took a topology class where the professor used the Moore Method. No textbook. For each unit there was a handout with a bunch of definitions and a few examples. Then a list of theorems. Prove the true ones, find counterexamples (or proofs of falseness) for the false ones. Class time was students at the board going through their results. If no one had a result, a random student was put at the board while everyone gave suggestions.
I was amazed that there were smart people who had that many years of school behind them and didn't understand the basic management skill for that sort of class. If I had a proof for #3, and nothing for #4 or #5, I was already on the way to the board before the professor could finish asking, "Does anyone want to take a crack at #3?"