Why not use transparencies or other forms of still graphics? In my opinion, one clear advantage of electronic presentations is interactivity. Apart from what has been said earlier, you can also easily take control of the data flow, highlight important things, and hide statements you want to show later. Electronic software now offers lots of intelligent ways of organizing presentations without going into the necessity of covering part of a transparency with a piece of paper. Do not forget animations, which would be impossible to reproduce in any way other than by use of computer software.

What does it have to do with teaching mathematics? Let me share some of my personal experiences here. I used to do everything on the board with a couple of occasional transparencies. I still dedicate a lot of time to blackboard exercises. However, I found that it really helps to take a little break, switch to the electronic materials I have at hand, review important concepts and get students involved in analysis on an interactive applet. It would take me enormous amount of time to stage a similar experiment without technology. Below is a sample screen capture from such a presentation.

Simulations are not the only purpose I use electronic presentations for. I believe most students learn better by repetition. But how can a teacher organize the material in such a way so as to ensure the students are keeping up with the new topic, dedicating enough time to reviewing old material and still can manage to keep the consistency of the course structure? I guess there is no unique answer. The problem of time is universal for all of us. I must confess this is still a big issue for me, since you can never predict how students will react to this or that concept, and you may end up with spending a week explaining things you thought would fit into one lecture. Since I know by experience that such things do happen, I try to save time whenever I can. One thing I found useful is to do a short review at the end of each chapter to summarize the material and identify potential problems, before moving to the new topic. I would make some Powerpoint slides to complement the material of a chapter and would go over them in class. Since all materials are available in the electronic format, students focus more on the issues being reviewed rather than on copying them to their notebooks. Here are the presentation files in the Powerpoint format: Math22chapt03 and the PDF format: Math22chapt03.

Technology does have its drawbacks. The major trouble for me is the equipment. Some of the rooms I have taught in did not have all necessary equipment installed, so I had to bring missing items with me every time and made sure they were all connected properly before the class started. This can be really frustrating in case something goes wrong. For example, even in fully equipped rooms, there were situations, such as the projector would simply refuse to work. Therefore, you always need a backup plan.

The scheme that works best in my opinion is a combination of different teaching strategies, from traditional lecture style teaching to computer-based presentations. In my opinion, good use of technology is a moderate use of technology. So, I alternate all these techniques in order to maximize the efficiency of the overall presentation and to minimize the risk each one of them carries.