As part of class assignments I've given in class presentations, most of which usually included a power point presentation. I knew teaching a small class of first semester calculus students the mean value theorem wouldn't exactly merit the same type of preparation as I had done previously for class presentations. And so with some experienced guidance from Barry I began to prepare. I started to prepare almost a week before the day of the lecture. For a while I thought I might be going overboard by giving myself that much time to prepare, however, I found that plenty of time to think about the mean value theorem beneficial. I found myself explaining to a fictional audience related theorems, such as Fermat's theorem, and thought about how clear my thoughts would have been had they been vocalized to a real audience. Eventually I started to plan what exactly I wanted to say in class with the hope that the evolution of the lecture would give way to a clear understanding.
After deciding on what I wanted to say and what examples I wanted to mention, I only needed to internalize the order in which I would present the ideas and the formal statement of the mean value theorem. I wrote down in a spare notebook the things I write on the board. All the details of what I would say to clarify the intuition behind the theorem had already been established from my pseudo-lectures in front of the fictional audience I had been practicing in front of for the past week.
When it came time to lecture I hardly needed my notebook, except occasionally to verify what I was writing on the board agreed with what I had in my notebook. I definitely had things I could improve on, such as my use of the whiteboard. While I enjoyed explaining the ideas behind the mean value theorem, Barry informed me that a bit more enthusiasm would improve the overall presentation.
Hopefully when I give the next lecture on the substitution rule for integration I can come through with a bit more charm and organization on the whiteboard. We'll see how it goes the second time around...