In a perfect world, preservice teachers (PSTs) in my mathematics methods course would leave each class session with 8-10 important ideas that I have tried to cleverly squeeze into a 150-minute session. By the end of the semester, then, they might have 120 or more important ideas about teaching mathematics -- barely enough to get started.
Woven in and out of each assignment and field experience is a much smaller list of significant ideas about effective teaching. I try to connect these overarching ideas each week so that PSTs can see what they look like, for example, in a second grade math lesson or on an algebra test. At the end of the semester, I ask my students to tell me three important ideas they want to always remember about teaching (mathematics) effectively.