Remarks on student talks in undergraduate classes

by Bill Casselman (written originally in 1998)

In the past few years, I have arranged undergraduate talks in several courses, most recently in the Spring of 1997, in Mathematics 309 (topics in geometry). There are a number of points about this idea that I think should be recorded for the future. Several of these points arose from an informal discussion with one of my classes, so for those students of mine down the line who are reading this: much of what is on this page is free advice (worth every penny you are paying for it!) offered down to posterity by your peers. But as will be clear, some of this advice is also for colleagues of mine who would like to try this idea out.

• Student approval of the basic idea was, as far as I could tell, unanimous---among those who spoke and also among those who listened. It seems to be a sure winner all around in those courses for which it is feasible.

• In every case I had the students' talks given at the end of the term. In an informal discussion, many students commented that it would be better to announce the option clearly at the beginning of the term, and arrange to have them given all along during the term.

• In large classes it is perhaps not possible to have every student give a talk. In Mathematics 309 (a section of about twenty students) it was offered as an alternative to a written term project. Both written and oral presentations were graded on the basis of clarity, correctness, and difficulty, but in addition the talks were expected to be interesting and well timed.

• The biggest single problem with talks was timing. It is very difficult for an inexperienced person to judge how long an exposition will take. When asked what to do about this problem, responses from the listeners tended to be extremely harsh (summary execution, limb mutilation, expulsion, etc). Towards the end of the talks this term I worked out a system of signaling to let speakers know how much time remained. But if the speaker doesn't look at the instructor? An alarm clock? At any rate, in the future I shall discuss the problem ahead of time with the class so one policy is agreed upon by everybody.

• For the instructor, the most important point is not to dominate the audience. Rude behaviour on the instructor's part will lead to the class uniting against him! Of course, uniting the students in a class is perhaps always a good thing, but perhaps also there are better things to rally them around.

• The talks that turned out best this term were those where overhead slides were used. The real point here is not that slides are intrinsically superior to black board presentations, but that preparing slides forced a speaker to think about time and quantity of content more carefuly. In either case, one minor problem was that students had a slight tendency to talk too much and write too little.

• Students also tended to try to cram too much material into one lecture, and to speed up speaking as the talk proceeded. Like almost all the other faults pointed out here, this problem is by no means restricted to students.

• In one case, two students shared one period of fifty minutes. That is to say, each gave his own individual presentation in that period. Bad idea. Students again almost unanimously agreed that each speaker should have a full period to speak in, and that the last ten minutes should be allotted for questions.

• Students suggested that each talk be evaluated by the audience. They did not agree on whether or not these evaluations should count in the assigned grade. My own opinion is not, but that it would be extremely useful to have talks rated by the student audience in numerical terms (1-5, say) in the different categories.

• One common error in these presentations was that speakers frequently launched into derivations without saying where there they were going. There is lots of advice freely given on the general organization of talks: my own ideal is (1) What is the problem? (2) History of the problem. (3) How this talk is going to solve it. In other words, everybody likes a puzzle. On the other hand, in the first volume of their series on analysis and mathematical physics, Reed and Simon quote the preacher's advice: "First you tell'em what you're gonna tell'em, then you tell'em, then you tell'em what you told'em."

• From an instructor's point of view, student class presentations are nearly ideal. (1) Fewer hours to prepare for! (But in practice giving advice ahead of time made up for this saving.) (2) The students will realize what the instructor himself faces. Sometimes you can see the change in a lecturer's face when this moment of realization comes to him---when he suddenly sees that he really is for the moment an instructor. Poor b----r. (3) The instructor will realize what the students face. Ho ho! (4) Related: students become more perceptive and more active listeners if it is in their mind that sooner or later they might have to model themselves on an instructor's style---or not, as the case may be.