The trouble with candidacy exams

Last fall, the departmental graduate committee…

The [graduate affairs committee]’s job is to promote advanced mathematical formation by supporting both faculty and students. Our proposals are intended to provide structure and guidance with minimal bureaucracy.

… came up with two proposals. The first one has already been approved, over my objections. The second one has been tabled for now but will likely be brought up again. This post is about the first one; I’m saving the second one for a follow-up post a little bit later.

The first proposal concerns candidacy exams, or comprehensive exams as the Faculty of Graduate Studies calls them.

 

A comprehensive examination is held after completion of all required coursework. It is intended to test the student’s grasp of the chosen field of study as a whole, and the student’s ability to communicate his or her understanding of it in English or in French. The student’s committee will set and judge this examination in a manner compatible with the policy of the graduate program concerned. The comprehensive examination is separate and distinct from the evaluation of the thesis proposal.

This is distinct from the qualifying exam, the written exam on graduate-level algebra and undergraduate-level calculus held twice a year. The latter is a part of Mathematics Department degree requirements but is not mandated by the FoGS.

The proposal defines the format of the exam: a written report (15 pages) on an advanced topic in the student’s research area and an oral exam before at least three members of the student’s supervisory committee, consisting of a short presentation based on the report and a question period. The particularly contentious part – to which many faculty members were opposed – is that the exam is to be chaired by a fourth faculty member who is not on the student’s thesis committee.

The rationale for this wasn’t clear (“intangibles” was the word repeatedly used at the faculty meeting). It will make the exam a little bit more formal, we’re told. Yes, I suppose it will, but what’s the point? Many top graduate schools, including the University of Toronto where I was a graduate student, either do not mandate this type of exam at all or waive it if the thesis supervisor deems it unnecessary. That hasn’t yet hurt their reputation a slightest bit.

The other part of the rationale – and this is where I really have a problem – was “promoting collegiality in the department.” As the main research groups in the department get bigger, they tend to become more insular [who could have guessed?]. The practice of having people chair qualifying exams in other areas will encourage interaction between groups. Or so does the graduate committee think.

The reality is that large groups become insular because they have enough going on within the group to keep everyone busy. In response, small groups become insular too, because of the obvious dangers of dealing with politically well-placed groups several times our size whose interests are orthogonal to ours. It’s a fact of life. You can’t change it by forcing people to sit in on lectures that they’re not interested in. And it’s completely inappropriate to use the candidacy exam as an opportunity to mend the otherwise damaged relations between faculty. Because, look, it should be about the student, not about us.

It’s not clear whether the chair’s role is only to ensure that the correct procedure is followed (as with the final thesis exams) or whether she is to judge the merit of the case. Nor is it clear how the chair will be chosen. I’m guessing that the large groups will simply propose a fourth member of the group to chair the exam. The really small groups, on the other hand, already have trouble putting together the 3-person thesis committee.

But what if the graduate committee insists that the chair really should work in a different area? Is it not possible for someone to become interested in a new topic after attending a lecture on it?

Not in my experience. Not to the extent that we would invest any significant effort in learning a completely new area just because we’ve attended a nice seminar. There would have to be more to it.

What does happen is that after hearing a lecture on an area unfamiliar to us, we might know a little bit more about it, understand a little bit better what drives the people in that area, have a somewhat higher opinion of it. That, however, requires an experienced and skilled expositor, and the talk in question has to be a high-level expository talk aimed at a general audience.

Now, first of all, I don’t think that we have any right to expect that sort of expository skills of second-year graduate students. Sure, there are people who have a natural gift for exposition and are good at it right from the start. Others become better at it gradually, after a lot of work and many years of practice. Some of us never get to the level of being able to inspire audiences in that way. Whatever the case may be, a candidacy exam is not the place to expect, or test for, such skills.

And that’s where we get to the point. The purpose of the candidacy exam is to ascertain that the student has enough specialized knowledge and a well-enough developed plan to embark on a thesis project. This calls for a specialized presentation addressed to an expert audience. In 25-30 minutes, the student has to outline an advanced problem and make the case – to experts qualified to judge it – that he will be able to make progress. This is quite different from high-level exposition. The student’s presentation should not be addressed to a non-expert and should be expected to be inaccessible to him. The non-expert just doesn’t have any business being there.

Coming up – more about the proposed cap on the number of credits for reading courses.

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