And there was much rejoicing
When I took my undergraduate math courses, almost everything was done on the blackboard. When I took my graduate math courses, almost everything was done on the blackboard. Almost every seminar presentation I've seen has been done on the blackboard.
Sometimes overheads were used in my lectures, but their purpose was used to illustrate the main subject matter, and not to present it. There was one exception to this in a second year calculus course. It was a one term course created by merging two other one term courses, so there was a lot of material to be covered. Even then, it wasn't until the end of the course that the professor made use of overheads to present the main subject matter. In that case, though, we were being taught something that was a straightforward generalization of a concept that we had learned in first year, so even though it was impossible follow the details of the argument, it was possible to understand, if not to predict, the overall structure of the argument.
At some point in my undergrad, professors started wheeling laptops with projectors into classrooms, and by the time I was done, most of the larger classrooms had been equipped with their own permanent projectors. There were a number of courses that I took in my first year or second year whose classroom technology consisted entirely of pen, paper, and the human voice. In my third year, a number of my first or second year friends were taking many of these same courses. Every lecture was now accompanied by a set of downloadable PowerPoint slides summarizing the main topics of the day's lecture. These were not math courses, however. The portable projectors did make an appearance every once in a while, but just like for overheads, they were only used to illustrate the concept of the day, and thus were only used for a small portion of the small number of classes they appeared in.
I was sceptical that the PowerPoint slides were of any significant value in any class. I was even more sceptical that they would ever be worth using at all in math class. I never experienced it personally, and being finally finished with school, I likely never will. I have, however, been to a fair number of math seminar talks that used PowerPoint (or some variant thereof). Not many of them have used the technology effectively. After one seminar talk at RMC, one of their math profs was talking about pressure they were getting to use slides in their lectures. Everyone who said anything thought it was a bad idea. I agreed. In fact, most mathers that I talk to feel more or less the same way.
I taught one course in the Winter term of 2007. There were a few instances where I could've used the projector to demonstrate how to use computer software to solve certain problems, but never once did I feel that using slides instead of the blackboard would've been preferable.
This past fall, I started teaching another course. The only thing I inherited from the previous instructor was the topic schedule for the year, which I've tried to stick to as closely as possible. At first, I was using the blackboard exclusively. But according to schedule, before the end of the first chapter, I was already at least a week behind. I knew that the professor who designed the course did all of his lectures using an overhead projector. I don't know exactly how he did this. I assume he had some overheads with stuff already printed on them, and then wrote more on them in class. I didn't consider this an option for me, since my handwriting isn't that great to begin with (occasionally, though, it has garnered compliments, which mystifies me). It would be worse with my arm positioned awkwardly over the projector, while simultaneously trying to maintain visibility to the students. Not only that, but my fine motor skills seem to disappear when faced~ with the not-so-relaxing task of speaking in front 100 or so people.
On the first day of class, I made an attempt to use presentation slides to cover some administrative details of the class, such as office hours, tutorials, test and assignment dates, etc. It didn't work. My computer didn't appear to recognize the projector. So later in the term, when it was becoming clear that using using blackboard was taking too long, I decided put some of the material on overheads, which were nothing but printed out slides. Using overheads made some things worse, and other things better. I still relied heavily on the blackboard, which meant a lot of running back and forth between the overhead projector and the blackboard (the front of the classroom is 6 blackboards wide). There was also no way to adjust the lights (that I could figure out) so that both the blackboard and the screen were clearly visible to the students. On the other hand, since I intended to post my overheads to the course website, they didn't need to write as much down and could focus on what I was saying rather than just trying to write it down. Not only that, but having most computations completed on the overheads meant that I wasn't going to make copy errors. Aside from one student's request to post the completed overheads on the course website before I finish making them, I didn't get any feedback from my students. So perhaps I hadn't made things better, but at least I hadn't made things appreciably worse.
Near the end of the term, the instructor for the class that took place right before mine in the same classroom showed me how to get my laptop to work with the projector. It turns out I had taken a more complicated route than I needed to (which is necessary if I want to use a tv as the display) I decided to make use of my newfound abilities and delivered the last two lectures of the term with slides.
When the winter term started, I tried using the blackboard, but by the third week (Jan 21), I got to a point where I needed to project something onto a screen by some means. I decided I would use slides, and not wanting to deal with the hassles of transitioning between blackboard and projector, I decided to carry out the whole lecture that way. From my perspective, things seemed to go more smoothly. From the students, I heard one positive comment and one negative comment which included another request that I post the completed slides before I've completed them.
One of the most obvious mistakes in using slides is that the presenter tends to plough through the material too quickly. I'm reluctant to say that math is hard to understand (though I'm sure many in my audience don't share that reluctance). But it's certainly hard to understand a slide containing math in the brief amount of time that a careless presenter leaves the slide up. Writing on the blackboard, on the other hand, forces the presenter to pace himself. Leaving the slides up longer would mean talking longer than I need to, or else standing there silently (and feeling awkward) trying to guess the point at which a sufficient number of students have comprehended what I'm going on about.
To guard against the tendency go too fast, I tried to structure the slides, as much as it was possible, to resemble how I would write the same material on the blackboard. For example, if there was a calculation with many steps, each step would get its own line, and the lines would be displayed one at a time (with spoken explanations of how I got from one line to the next, as each line was being displayed). There were times, however, where I was forced to split something up into two slides when it would have been better if all it could have been put on one. This, I think, gets at to one of the other primary disadvantages of using them in math. In almost all classrooms there are at least two blackboards (or whiteboards in some newer classrooms). One could see how the material on the blackboard I'm writing on would relate to blackboard I've just written on. Being able to display only one screen at a time is analogous to having only one blackboard to write on. Since they would be able to download the slides later, though, they could go back and see for themselves how the different slides relate to each other (whether or not they would is an entirely different story). I weighed these and other factors, and decided to stick with slides.
I continued to deliver my lectures using slides for about a month, until I got to a point where I couldn't come up with a sensible way to make slides for a certain topic. I decided, at least for the time being, that I would go back to the blackboard. When the day came (Feb. 27) to present that material, there were still some slides that I didn't get through in the last class, so obviously I presented those first. When I finished with the slides I announced that I would be going back to the blackboard. At this point there was much rejoicing. Well, it wasn't quite rejoicing. It was more like a handful some scattered murmurs, though with a definite tone of approval. This is a math class, though. Aside from cancelling a class altogether, how much rejoicing do you expect?
