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
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
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
(2) The students will realize what the instructor himself
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.
(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.