Academic Assessment, Tripos-Style
It’s still the exam period, but I’m going to break the cardinal rule of exam etiquette and talk about exams. Those who might feel queasy are too busy with revision to be reading this, anyway.
Part III of the Cambridge Mathematics Tripos
The Cambridge mathematics departments’ Part III is a truly unique one-year course. For the majority of students, a `distinction’ on Part III exams is a prerequisite for a PhD offer from the mathematics departments. From the departments’ perspective, the course is a chance to `test drive’ 200 students from around the world and select PhD students among them.
There is no official assessment until the end of the year. Over the preceeding two and a half terms, one is free to choose lectures to attend. The Michaelmas (fall) and Lent (winter) terms are eight weeks long, with typical 3-unit courses having 24 lectures. That works out to 3 lectures per week: either Monday/Wednesday/Friday or Tuesday/Thursday/Saturday (that’s right, Saturday). Supplementing these lectures are four revision classes where a graduate student goes over solutions to (optional) example sheets. The Easter (spring) term also offers 3-week, 16-lecture courses for 2-units each. Between these terms are six-week breaks during which students are expected to revise their notes and catch up on example sheets.
Students are expected to present between 17-19 units for examination. They needn’t select which courses they will examine until May, though they usually have a good idea by the end of the Lent term in March. In place of a 3-unit exam, students have the option to write an essay (essentially a literature review) on a research topic suggested by an adviser. These essays are not meant to be original research and are around 20 – 30 pages.
Now on to the exams. Compared to the fantastic amount of freedom during the academic year, the exam period can be sobering. Each exams is 2-3 hours long and are a rather big deal. Students are ranked according to their exams and PhD positions are offered largely based on exam performance. To top it all off, Part III is where 200 talented mathematics students come together to the self-described “hardest/oldest/most famous” mathematics course in the world. The exams then rank these students against one another, so one can imagine that the stakes are high; even when the stakes might just be bragging rights.
(A side note: the tripos calendar is also a bit unique since exam results are announced well after most other PhD programmes require a commitment from applicants. Thus many students enter the exam periods with PhD places elsewhere. This seems to be the case with most American students, for example.)
Having a one-year course is a fantastic opportunity for the mathematics departments to pick students that they have gotten to know a bit. In this way it is free from the bias of `big name’ recommendations and disparities between different undergraduate programs. There are at least a few Part III students whom I am sure would have had their choice of top US physics graduate programmes if they had recommendations from professors within the North American research community or if they had completed their undergraduate degrees in the states. Instead, these students didn’t get any offers from across the pond — though rest assured they’re poised to have very successful research careers in the UK.
This effect is mitigated in Part III since the mathematics departments can admit a large number of applicants with a wide range of backgrounds. They can then assess each applicant on an `equal playing field’ with respect to others. The chance to write an essay with a potential supervisor is, for example, a small way to test-drive the advisor-advisee relationship with a member of the faculty. As discussed below, however, perhaps the tripos does not fully take advantage of the opportunities to assess students with respect to research potential.
Another important positive that should be emphasized because Part III is not a research course: the teaching is generally well-coordinated and well-organised, with a good selection of courses across pure and applied mathematics. Ultimately, however, the greatest benefit and resource that Part III offers is the chance to interact with the other students. However, my primary focus here is academic assessment, so I’ll discuss my broader thoughts of Part III another time.
It is with no disrespect to Part III that I speculate that there are a few aspects of student assessment that could use some work. For example, even though students are here for one year, they are ultimately judged based on a set of `standardized’ exams. Are sit-down written examinations really the best way to test one’s research potential? Such exams reward/penalize students based on test-taking ability/familiarity, not to mention students who get sick or are prone to exam-jitters.
It’s hard to give a 3-hour examination that tests ingenuity and creativity while avoiding becoming a speed and memorization test. When it boils down to it, what’s really being assessed is how hard someone is willing to work for the privilege to be a Cambridge PhD student. Of course, there’s nothing wrong with this — hard work is the foundation of every PhD, but if that’s all one were measuring, one might as well have asked students to spend the year training for a marathon. It’s not easy to objectively and fairly test what makes a good PhD student: curiosity, enthusiasm, orthogonal thinking, collaborative ability, sheer luck. But if an exam boils down to memorizing a list of equations and regurgitating some calculations, then it’s more likely a clever student might be overshadowed by a student with a photographic memory.
(To be fair, there are opportunities for students to practice research skills: the essay and the chance to give student talks on topics of interest.)
And the ugly…
Figure: It doesn’t get uglier than this. Mold growing on gelatinised coffee left in one of the student meeting rooms during the exam revision period.
And so what happens when the carrot of a PhD place is dangled in front of students at the beginning of their research career — all they have to do is ace a few exams? Well, it can get ugly. The weeks leading up to exams breeds manic studying and general jitters. In this environment, some students feel (perhaps unconsciously) that making the grade takes precedent over learning physics.
In one case, during a revision class, a fellow student asked about how one derives a particular quantity. The example class leader wrote down the relevant equation and began to explain where it came from, but the student quickly interruped with something along the lines of, “ah, ok — so we just have to memorize that.” (That’s not an explanation and memorizing an equation is not learning.) In another instance that had me groaning, a student was very confused by a lecturer’s calculation. After a few repeated questions, he gave up and asked, “well, this isn’t examinable, right?” (These courses aren’t that long — if a lecturer took time to teach something and you’re planning on a PhD in this field… maybe it’s worth knowing anyway.)
Certainly not all students go to this extreme, and some students are relatively unperturbed. And, to be fair, such an is understandable, perhaps even pragmatic. But I can’t shake the notion that this kind of `learning-for-exams-only’ is unbecoming of a young scientist. Do great physicists look back on their lives and think, “yeah — back in my first year of grad school, I only learned physics to do well on exams”?
Following the exam term, there’s (apparently) a week of Cambridge-style debauchery called May Week. Don’t be confused — May Week is in June, but post-exam students are so discombobulated that they don’t notice. Activities include black tie `May Balls‘ and garden parties. Afterwards, in lieu of a graduation, Part III results are read in the Senate House (photo from Wikipedia). This ceremony involves reading out everyone’s names and stating whether they achieved a distinction, merit, or pass. Unfortunately, I’ll be missing the ceremony this year to attend the Coseners Forum on Heavy Flavour Physics… in Oxfordshire. (My neighbor, Steffen, has remarked that this must be some sort of act of rebellion against Cambridge.)
Miscellaneous `Cultural’ Notes
As an international student, my natural instinct is to compare how Part III is similar to and different from what I am used to in the US. As always, things are neither necessarily`better’ nor `worse,’ just `different.’ Here I offer some rough notes:
- My undergrad institution (and at least a few others that I know of) had unproctored exams as part of the university honour code. This is in contrast to the presence of an “invigilator” at all Cambridge exams. I was feeling a bit cheeky during an exam where I sat in the front row and tried sticking my tongue out at the invigilator. He didn’t respond, not even a smile! I suspect that being an invigilator is excellent training for a career as part of the Queen’s guards.
- Also, in my last two years as an undergrad it was common to have `take home’ examinations. Such an exam might be assigned over the course of the week with the course texts as allowed reference material (no collaboration). These exams were necessarily more difficult, but allowed deeper research-type questions.
- Speaking of texts, they’re used differently in Cambridge. (And, as I understand, generally in the UK.) Instead of one or two course textbook that closely follow the material of the course, one is presented with a list of suggested references that `may’ be useful. The expectation is that the course lecture notes and example sheets will define the corpus of knowledge required for the examinations, with minimal (if any) required reading beyond what is explicitly given.
- Also something different in the US: example sheets (i.e. homework) are mandatory and graded. In Cambridge example sheets are a good idea, but not compulsory. (This is less true for Part I and II students who have tutorials in-college.)
- Unless they’re unsatisfactory, grades mean much less in the US. Some schools are known for `grade inflation’ while others are known for being rigid about maintaining a standard distribution of grades. At the end of the day, comparing the quantum mechanics grade of a student at university X to that of a student at university Y is like comparing two quantities in different units with no conversion between them. As a result, graduate school positions depend more on past research experience and letters of recommendation than direct examination.
- The US is much less structured in its course offerings. Students are generally expected to take a breadth of courses from multiple disciplines in addition to focusing on a major. Further, the order in which courses are taken is usually a recommendation rather than a requirement. In Cambridge, the cost of having the a `seamless’ prorgam is that there is less flexibility for students who would like to get ahead or explore other things. A first year student can sign up to take an advanced graduate course without too much fuss. This past year I got to know a Part II student who was sitting in on Part III courses for the second year in a row. But because he’s a Part II student, he’s not allowed to take Part III exams.
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