If there is one thing that I don’t enjoy about working at a university, it is grading. There are two aspects of grading that I don’t enjoy. One is simply the pure “manual” labor (I guess it isn’t quite manual – but it sure feels like it) that goes into reading the exam papers and trying to decipher what is written and trying to match the appropriate number of points to the partially correct answers in a consistent manner. Some of my colleagues do this while listening to military marches by the Johann Strausses, for instance, for better endurance results. But this is the less interesting aspect. The second is the more general job of assigning grades to people. I would much prefer to just teach them some interesting stuff without having to test them, but I understand that, even if I don’t like it, they would learn less of what I try to teach them if I didn’t test and grade them. Also, as examiners, it is part of our job to provide valuable information for the potential employers of our students (the signaling value of receiving an education). And testing is interesting as it is a bit of a game between me, who chooses what to test, and the students, who choose how much and what (if any) to study for the exam.

There are many interesting game-theoretic aspects of testing students. For instance, for me as an examiner, should or should I not use old exam questions? Ideally, I convince the students that they will certainly get new ones, and then actually use some old ones. And, as I typically cannot test everything I have done in a course, which topics should I test? Game theory would probably tell me that I should randomize (in both of these problems), which is in fact what I do, to some extent. The students, on the other hand, have the problem of how much and what to study. Do they study all the material or should they gamble on me not testing some of the topics and only study a subset of the material? How deeply do they need to understand stuff? Is it enough if they can repeat all definitions without fully understanding them or should they at least learn some of the recipes to solve certain problems or do they even need to really understand what has been taught? I certainly would like them to study so that they understand it all deeply, but I am not sure I always succeed. Well, I am, in fact, sure that I don’t always succeed. Well well, I don’t want to say it, but I probably actually never succeed.

But let me talk about another problem that I have, the problem of how hard the exam should be. I have two goals when I am teaching: One, I want the students to learn and comprehend interesting and useful new things; two, I would ideally like them to have good grades. [We don’t use a fixed grade distribution.] And what I noticed is this: the easier I make the exam the more the grade distribution doesn’t change. Ok, this is both grammatically and empirically not completely correct. When I make the exam easier, grades do go up a bit (they are on average better) with two caveats. One, this is more true for an exam that I just made easier relative to previous ones, but then grades go down a bit in the next exam with the same degree of difficulty. Second, this effect is less pronounced than I would have hoped. In fact, I have the feeling that there is no (low) degree of difficulty that I could choose that would induce all students to pass the course.

And why is this? Well, this is so because students choose their level of study effort strategically. I believe this to be true even for some of my students who are skeptical about what I teach them about people responding to incentives. If students expect the exam to be easy, they don’t study very hard. If they expect the exam to be hard, they also study hard, or at least harder. And this effect makes it hard for me to consistently create exams that induce students to get good grades. I guess, I should probably learn from this and care less about the grades and more about what the students learn. So, the next exams will be harder! I hope my students are reading this.