To the casual observer, it may seem that teaching is a communication from a professor to the students. My own anecdotal experience suggests that this is a misconception and that effective teaching and learning requires mutual communication between teacher and learners. In fact, a professor learns a great deal from the students about how well information is conveyed by observating and querying the students. Perhaps the most revealing method I have found for adapting my teaching methods is to watch a student work a problem in front of me interactively and have the student explain the thought processes used in the solution. Mistakes are in important part of this process, because students learn more from direct participation and observing how and why things don't work than from just watching a professor do it correctly every time.