I try to keep my students thinking. I find that "doing" is much more effective than passively listening. In my calculus classes, I often have students work in small groups at the end of the period. The emphasis is on understanding, not just following steps. To help keep the minds engaged, I typically lecture by asking questions. In the advanced classes, the goal is to help students become self-sufficient researchers in mathematics. This is accomplished through reading assignments and a progression of carefully chosen exercises consisting of theorems to be proven.
Professor of Mathematics