- 15 - 20 minutes long
- focus on a single idea
- forces student involvement. not just by the audience questions, but by assigning actual problems and calculations in the middle of lecture
- makes the student feel like he/she is brilliant, not like the lecturer is
- write big (bigly?)

My quantum mechanics students arrived today (scattering through the open door - no tunneling was required). I walked into our first house meeting alone, began playing the James Bond theme song on my computer (since it's the theme of our dorm decorations), and told the students I was going to deliver a "short lecture, no more than ninety minutes" on the history of the James Bond film series. I talked for about 10 seconds until the other counselors simultaneously burst into the room from all corners, dressed up in Bond-like tuxes, and shot me down with water guns.

But soon I'll get to deliver some real lectures. I enjoy this. I enjoy sitting down and trying to work out the order I want to make all my points. I enjoy trying to simulate what the students would and would not be able to understand. I enjoy being on the stage presenting the material, because I can choose what to talk about and I talk about whatever I think is interesting. But simply lecturing however I feel like it is something of a disservice to the students, because I also need to do everything I can to keep the lecture digestible.

I think I learned the most about this after watching one afternoon while one of the other counselors lectured. He did an excellent job. His delivery was smooth and well planned. Everything was technically correct, even when I asked asinine technical questions from the audience. But the presentation was too long and covered too much material. I realized that I was doing all the same things in my own lectures.

My goal then is to make all my afternoon lectures fit a sort of mold. They should be compact, conceptual, and unified. Each part should be there as a subservient to the goal of the lecture as a whole. No little tangents on things I personally think are interesting, since for the most part these just break the students' concentration. I used to do these starting at 1:00PM, and finishing between 1:15 and 2:00 depending. Now I'm going to start at 2:00 to let them think of the lecture as a short break in their 1:00 - 3:30 study time, to let them work on the problems they're solving first, and to let the food coma that comes on after lunch wear off.

Possibly the most effective lecture I gave was a guided exercise on the binomial theorem. I first asked the students for a crazy number, then told them I would take its square root. I did this using the binomial theorem (to first order, obtaining 3 sig figs). Then I actually wrote problems on the board such as finding the square root of 101 and made the students work through them. After four or five, they had the hang of using the binomial theorem to estimate square roots, so I gave them some cube roots and fourth roots. Then I showed them how to do otherwise difficult division problems with the same theorem and made them work through a few of those. Then finally I gave them an example of how using the binomial theorem to first order fails in some cases, using a series that converges to e.

It was short and interactive. The kids loved it because they were getting results they could understand without using anything very advanced or mystical. It was much better than showing them a proof by induction, or even worse a calculus-based proof of the theorem. And it was relevant, because many times during their three-week course they had to do calculations where the result was a number very close to one, and their calculator would fail them while the binomial theorem would not. So that lecture is a model for what I want to try to do here.

There's no rush to get a certain amount of material covered, because no one's even requiring me to give lectures. I'm doing it just for me own amusement. I can break a difficult concept up over three days if I want. It's a wonderful blank slate. One big challenge is that the students come from a variety of backgrounds, since some do not know calculus and others have taken AP calculus and physics.

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