Steven gave a very good talk about the multiplication principle as might be given in a finite math course. Following his talk, there was a brief discussion, during which time the following points were brought up:

• It is generally a good idea to give examples or analogies up front (before the general theory) so that the students have a frame of reference for the theory.
• It's a good idea to have fun examples that pertain to real life, if possible. That will keep the students interested and hopefully help them to appreciate the applicability of math.

Annette Pilkington

Professor Pilkington spoke about a course that she teaches frequently - basic finite math. Many of the students for that course are liberal arts students that are busy with their own work and interests and may not be so interested in math. She said that you sometimes have to work hard to get their attention, but they are generally excellent students once you get their attention. The course focuses on chance and strategy since those topics apply easily to life outside of math.

She points out that it is important to convince the students that math is natural and important to use. In particular, it is good to show them how well math describes what they already know or suspect and how it sharpens their intellect. Once there, the next step is to push their intuition to the limit. Annette recommends the books "Why do Buses Come in Threes" and "How Long is a Piece of String?" as good sources for examples.

It is important to be very hands on with the students. For example, she brings decks of cards, coins (to be flipped), an urn full of marbles, and many other props to class. It is important to build on the intuition that the students already have - that will help them to internalize the material. It is also good to use humor and make a very flexible structure. She also recommends creating handouts if there are long definitions or statements so that they don't spend all day blindly copying (i.e., not paying attention).