Preparation enables the teacher to cover all the salient points, yet allow student questions to drive the direction of the lecture. This gives the students the feeling they have participated in a remarkably coherent yet spontaneous lecture. I prepare classes quite differently for undergraduates and graduate students. Many undergrads have a thirst for good grades rather than a thirst for new knowledge, so my challenge is to harness the former to achieve the latter. I try to take advantage of the time outside of the classroom with interesting homework assignments, trying desperately to balance what is learned versus the time needed to complete the assignment.
Graduate students do have that thirst for new knowledge.
I treat them as young colleagues, intellectual equals who just need some experience before they become my betters. Graduate students are weakest at selecting problems and at time management, so I help them with a list of suggested research problems and then meet with them every few weeks to monitor progress and suggest midcourse corrections. In the last week of classes each group gives me and the teaching assistant a formal half-hour presentation outside of class, with term reports due a week later. I then pick a sampling of the best projects for students to present to their classmates. This allowed students to wander about the room and teach each other what they had learned.