It occurred to me somewhat after I had announced the topic of Thursday's Brown Bag to be the chasm between what we want to accomplish with our tests and what we actually accomplish that I was taking a high risk of a reaction of "What chasm?" Not so, though, at least among those that turned up talk about it. In fact, Bill Birnbaum articulated the philosophical gap far better than I: the joy of teaching is its reciprocity. It is exciting to be able to inspire a curiosity, and then help satisfy that curiosity, and a good test should be part of that process. The ever-present danger, on the other hand, is that a test will be something akin to quality control of light bulbs on a conveyor belt. It's a danger that shoots up in direct proportion to the length of the class list.
So what is there to do? One of the most radical tacks was taken by Judith Arms last quarter. When her class of 140 calculus students came to grief over a midterm she decided to permit them a make-up, but only on condition that they earn it by working out a carefully selected set of problems and bringing them in to discuss with her. Thirty-five students took this option. Judith spoke with pleasure of the resulting mathematical conversations, and with pride of the progress a number of the students made in mathematical focus and autonomy, and with distress of the enormous number of hours the whole scheme cost her. Will she do it again? Well...
Monty McGovern came up with more moderate--and hence more sustainable --version. He refrains from handing out a solution sheet, and lets students bring in a correctly worked out copy of their test, to be presented in person and discussed with him for SOME replacement credit.
These tactics and others like them address one of the issues nicely--a student invited to present a corrected solution in person is not a dead light bulb. Another side of the situation is the fact that tests must also necessarily function as one of our ways of determining how much of what we have been attempting to teach our students has in fact become part of their usable knowledge. This is a particularly sticky issue when it comes to testing the student's capacity to solve interesting problems, because whatever the level of the course if a problem is truly interesting and has some depth, then it is unreasonable to expect most students to grapple with it successfully in a highly limited chunk of time. And on the other hand, if we restrict our tests to the boring and the shallow, what kind of a message are we giving about what we value in the course? I have enjoyed two twists on that one in my 170 course. One is the (not uncommon) tactic of giving out a set of pretty challenging problems a week before the final, and telling the class that every single peoblem on the final will be one of the ones from the set, with only very minor changes in numbers so that pure memorization will be of no benefit. The other is a midterm which the students take twice in the space of one (90 minute) class. The first time they take it individually, the next in a group they have been working in since the beginning of the course. Their grade is the sum of the two grades. In a course that emphasizes group work it has a rather nice impact.
Discussion of the mechanics of this led naturally to another bunch of interesting topics: what is the impact of allowing students to bring notes? books? calculators? pets? (well, no, not that one.) A variant that was new to me was the giving out of a crib sheet designed by the class and produced by the instructor. Interesting possibilities there.
It was a good conversation. I wouldn't say we had done much to diminish the depth of the chasm, but at least we looked at a few threads stretching from one side to the other.