The Exam, the Rocket and the Grateful Dead

After a couple of posts whacking teachers’ involvement in VCE exams, it seems only fair to tell a story about a university exam debacle.

Once upon a time, about eighty years ago, I was a PhD student at a pretty good American university. Let’s call it Stanford. As part of the scholarship, PhD students were required to assist with the undergraduate teaching, which was a plus. The teaching was not onerous or overly time consuming and, unsurprisingly, the Stanford undergraduates were excellent students. Even the humanities students, reluctantly completing their “math requirement” and typically weak in maths, were smart and had a good work ethic.

The first year mathematics was taught in bulk at both the slower, “humanities” level and at the faster, “science” level. This faster level, for a couple hundred students, was a solid first year calculus course, taught from one of the very good monster texts: Edwards and Penney, when I was there. There were five lectures a week, three from the main lecturer with the students altogether, and two sessions with the undergrads split off into smaller groups led by us PhD students. These smaller groups were not that small – 30 to 40 in a class – and the sessions were still very lecturey: new material had to be covered, albeit not as densely as in the main lectures. There was decent space for back and forth and, once one was experienced enough to not be scared to death, the sessions were a lot of fun.

The lecturers in these subjects tended to be the younger academics, post-docs and the like, rather than the tenured or tenure-track staff. So, they were not the Stanford elite, but they were there for a reason and tended to be very smart guys. They also tended to be good guys; they were younger, not sure of their future and had natural empathy with we very unsure PhD students. One term, however, there was an exception.

I have no idea where “Bill” came from but he was a complete screw-up. Bill was a Grateful Dead fan, which was no big deal. Bill also appeared to be tripping a lot of the time, and even that wasn’t that big a deal. This was California after all.¹ And it was not like we were prudes or untarnished innocents. It was broadly, sensibly accepted that what mattered was doing your job properly. Bill didn’t.

Bill seldom finished the lecture content. According to the undergrads, he chatted away in the lectures about this and that. Which can be a good thing: lectures are theatre and engaging with students, backing and forthing, is a way to make the lectures fun and to make the subject alive and meaningful, particularly if such exchanges are conducted with purpose and thoughtful control. But, notwithstanding the value of ad libbing, there is still a script and the lecturer has to pay attention to it. If your lecture finishes with a critical example half-done or not begun at all then you’ve screwed up. Which Bill did, repeatedly. But not to worry: the PhD students could make up for the missing content in their sessions, which, every week, Bill demanded we do.

Of course this was exhausting and infuriating. We had our own material to cover, as well as trying to inject a proper tutorish element to the sessions, allowing extended discussions on points of concern. Bill was also nasty about it. If we objected that we had no time to cover the extra material, if we suggested to cut short aspects of the material or to have him make up the time, he would boom as Lord Lecturer that we had to do what he said.

Bill was a screw-up and an asshole and the undergrads also knew it. They were remarkably understanding, and we all suffered through it together. But then, at the end of term, the final exam had to be written, with zero interest or energy with which to write it. It went as well as might be expected.

Exams for these subjects were always written pretty quickly and efficiently, with everyone bringing questions or ideas for questions and then hammering it out together. There were drafts and proofreading, but not to the nth degree, and minor typos and errors were not uncommon. These were easily sorted out during the exam; lecturers proctored the exams themselves, so if and when a student raised a valid issue it was announced to the entire theatre and the correction written on the blackboard at the front. The system typically worked well, without driving anyone nuts. Not with Bill.

The exam meeting began with Bill suggesting something for the Lagrange multipliers topic, a story question on buying tickets for a Grateful Dead concert. It was appalling. There’s nothing intrinsically wrong, of course, with such a story framing and maybe buried inside Bill’s story there was a decent mathematical question, but none of us could see it. The thing was so self indulgent and clumsy and over-cute and over-egged, we PhD students quickly and unanimously vetoed it. Bill couldn’t overrule this unanimity but he was really pissed off. Bill’s contribution for the rest of the meeting consisted of sulking back in his chair and muttering “Yeah, whatever”.²

We PhD students did our best and cobbled together an exam, but our best was very bad. We were in no frame of mind to concentrate in the required manner, so the questions were thoughtless and pedestrian, and were quickly checked but no more. And someone came up with the rocket question. I remember it as a “rocket”, although the question was supposed to be pretty standard projectile motion. I don’t remember who came up with the question, quite possibly me, but I remember feeling there was something not right about it. But, like all of us, I was too tired and disillusioned to put my mind to it. Until the exam.

Bill was absent for the exam, of course, with three or four of us PhD students around to proctor. All went fine, for about fifteen minutes. Then a student came out, asking about the rocket question. The equation of motion for which, he noted, contained a +t² term. Which meant that the rocket was burrowing parabolically into the ground before emerging into the air.

Having drawn the short straw, Marty went to the front of the theatre to announce the screw-up to the students. Which was met with the predictable disbelief and laughter. I wrote the correction on the blackboard, to treat the rocket equation as a given. The bemused students got on with it, finding the time when the rocket sprang free from the Earth, and the exam went on fine. For about ten minutes.

Then another student came out, flagging another error. Not as bad as the miracle rocket, but an error is an error and Short Straw Marty went out again, to announce and to write up the new error. Then there was another error. And another.

I can’t remember how many errors there were by the end of the exam, maybe half a dozen or so. It was absurd and embarrassing, of course. Although, for all that, the exam functioned well enough for its purpose. With all the students in the one place, and with us proctors also being the graders, we could be human about the real-time exam adjustment and we could be human about the subsequent grading. A million miles from perfect but the damage control for a one-location exam for a few hundred is very different from that for a statewide exam for thousands.

That’s basically the end of the story. Some Stanford lecturers, who were aware of Bill’s screwing up, took us PhD students out for a sorry-and-thank-you beer. Bill did not reappear next term. And of course I learned my lesson and I’ve never again made an error in writing a mathematics exam.³

1. My first and very stressful PhD “Qual” exam was taken with the Stanford Marching Band blasting their excellent rendition of The Tubes’ excellent White Punks on Dope just outside the exam room. You got used to these things.

2. Soon after, a friend, also a Deadhead, noticed that Bill had whined about the veto of his question on a Grateful Dead newsgroup. All the replies were sympathetic, of course, incredulous that we would veto a question simply for being about the Dead. Which was nonsense. We vetoed the question purely and simply because it sucked. 

3. This is false, of course. But I really am paranoid about the signs of quadratic terms.