I was given the opportunity to give our calculus class a lecture on the mean value theorem. I'd like to share the process of preparing this lecture.

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...

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...

David, you did a good job with that Mean Value Theorem lecture! Enthusiasm is a tough nut to crack--am I a teacher or an entertainer? Well, both, and we just need to embrace that. For a freshman calculus class the instructor definitely needs to focus on keeping the class moving with varied instruction. UMM is a bit weird in that classes are 65 minutes long, so that's a long time to keep everyone engaged--class can grind to a halt pretty easily if the instructor becomes disengaged!

I'm looking forward to your lecture on substitution. You've been helping students with homework all semester, and they respond well to your instruction.

Things I think about when preparing a lecture:

Have I taught this material before? What worked before and what didn't work?

What's the point? What should students learn from the lecture?

How can I connect what I am doing today, to what we did yesterday, and what we will do tomorrow? These connections are critical to assist student learning.

What activities can I use to help them learn whatever it is? Is there the possibility of some self discovery (hopefully) or is it complicated enough that I need to show them the result?

Should we use Mathematica for something?

Can I have some problems for them to work on together (bit of group work)?

Ideally, the lecture will end up consisting of a variety of activities, all designed to help the students discover concepts and build their mathematical skills.