Assembling a Lecture
 
   There are some general guidelines for any lecture. 1) Every lecture should have a beginning, a middle, and an end. The lecture should follow the rule, "Tell them what you're going to say, say it, and tell them what you've said." Note that a lecture can be longer than a single class period, but if it must be broken up over several periods, at the end of each one, there should be a running summary that sums up the day's talk, and a fairly extensive recapitulation at the beginning of the next period. 2) Attention span limitations say break the lecture every 15-20 minutes with a 1-5 minute activity. This can be a simple "What are the three most important things you've heard in the last 15 minutes?" to a mini-discussion of some question you have thrown out. 3) Listener fatigue says introduce your most complex ideas at the beginning of the period. After 40 minutes of even the most brilliant exposition, ideas tend to run into each other in the listener's head. Where feasible, complicated ideas should be introduced as early as possible in the lecture, then developed fully before moving on. If you present a complex new idea toward the end of the period, you won't have time to explore it properly, and for all practical purposes, you'll have to present it from scratch at the next period. 4) It takes at least 15-20 minutes to present a genuinely new idea. It takes quite a while to present the idea, give a couple of examples, try to connect it in some way to something they already know, give another example or two, present it from a different viewpoint, and summarize. At most, you can only offer about three brand-new ideas per period, if you want to have any hope that they will actually understand what you said. You can present a lot more new ideas than this during one period, but most of the students will then simply be overloaded transcribers---.