Jon gave a very good talk about the definition of antiderivatives. Following his talk, there was a brief discussion, during which time the following points were brought up:

• Motivation for your lectures is important. The idea that antiderivatives undo derivatives is interesting intellectually, but what good do they do?
• Jon presented a proof that the constant functions are the only antiderivatives of the 0 function (via the mean value theorem). There was some question about whether that is appropriate at Notre Dame - proofs are rarely presented in the calculus sequence. Although proofs can be enlightening and useful for some types of homework problems, the focus at Notre Dame (at least the focus of the students) appears to be on learning how to do the problems.

Professor Himonas

Professor Himonas spoke a bit about 10250 and 10260 (business calculus). The former is for business students as well as arts and letters students, so it tends to be fairly gentle. 10260, however, is for business students only, so it has a much faster pace and tends to be more difficult.

Most of Professor Himonas' presentation centered around a set of discussion questions that he passed out. The first question regarded preparation for the first class of the semester, which is very important. The first day sets the tone - if it goes poorly, you will spend the remainder of the semester trying to get your class on the right page. If you spend time leading up to the first day of the class, the course should run smoothly. It is essential that you give yourself several weeks to prepare and that you have well-defined course goals.

We also discussed what it means to be an effective teacher. Of course, a big part of this is to teach the students so that they know what they are supposed to know at the end of the semester. A good way to make sure that they are on the same page during a lecture is to have them work out an example themselves. If they seem to have trouble, they need help. It is also good to try to anticipate where they might have problems and to keep an eye on them during class to see if they look confused. Be careful about using the students' answers to questions during class as an indicator of their understanding - some students won't answer even if they understand. Also, just because a couple students know the answer to some question doesn't mean that the whole class understands!