We are teaching a real analysis course each week for two hours one day and one hour another day. We use a blackboard and we upload most of the class notes to encourage students to participate instead of furiously taking notes.
We are trying to figure out a good way to gauge how much time a given proof or example will take to present in real class time (including time for student questions).
- of course, one can just spend an additional three hours teaching the material to an empty classroom, but we are trying to find more time efficient ways.
- keep a list of how much proving some theorems took in actual class time. Then use that list to help decide how much time to devote for the current proof, if it is similar to any of the listed ones.
- Split the lecture into time blocks and add as much material as possible to each of these blocks. For example, we can split a two hour class into 30 minute blocks and then devote each block to some theme/topic/theorem. When we hit the 30 minute mark, we must stop and move to the next topic. The price of this is that you might have rush the proof, which is bad, so we might have to slip into the next block.