I discovered that when you are teaching something that you know very well, preparation only gets in the way. Improvisation
1. Forces you to develop the ideas from scratch out loud which gives the students a glimpse at how to arrive at those ideas rather than just seeing them fully baked on an overhead.Instead of calling it "improvisation," I call it "teaching from an outline." This approach has pitfalls too. Namely, students who need more structure tend to get lost in the mix. I like to teach from an outline, but when I teach a new course, I combat this weakness by typing a set of notes to help add in the missing structure.
2. Creates an element of danger that you naturally respond to by digging deeper and finding your way through.
3. Gets the students’ attention. They can tell you are doing it without a net and the drama of that hooks them in.
4. Makes it less like a lecture and more like a conversation.