Complex Experiments with Grading Mathematics


While I’ve never managed to attempt an experimental grading system as the one I enjoyed in Real Analysis, I have tried a few more modest experiments. The one chance I’ve had to really go wild and do something I’d never seen before, sadly, failed, but let me resurrect it enough to leave someone else, I hope, better-informed.

The setting was a summer course, which the department routinely gave to graduate students as a way of keeping them in the luxurious lifestyle to which grad students become accustomed. For five weeks and a couple days I’d spend several hours explaining the elements of vector calculus to students who either didn’t get it the first time around or who wanted to not have to deal with it during the normal term. (It’s the expansion of calculus to deal with integrals and differentials along curves, and across surfaces, and through solid bodies, and remarkably is not as impossibly complicated as this sounds. It’s probably easier to learn, once you know normal calculus, than it is to learn calculus to start. It’s essential, among other things, for working out physics problems in space, since it gives you the mathematical background to handle things like electric fields or the flow of fluids.)

What I thought was: the goal of the class is to get students to be proficient in a variety of techniques — that they could recognize what they were supposed to do, set up a problem to use whatever technique was needed, and could carry out the technique successfully. So why not divide the course up into all the things that I thought were different techniques, and challenge students to demonstrate proficiency in each of them? With experience behind me I understand at least one major objection to this, but if the forthcoming objection were to be dealt with, I’d still have blown it in the implementation.

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