When we grade our students each semester, inevitably there will be students who fall a very miniscule percentage point below some grade cutoff. For example, I award an A to students scoring a 94% or better, an A- to students scoring from 90% up to and not including 94% and so on. There is always a student who scores something like 93.92% and it would not be uncommon for the student to think they should get an A. But I don’t round up, and since I teach rather large classes I assign grades anonymously – in the sense that I simply do the calculations and submit the grades based only on those calculations.
Two reactions I suspect are typical in these situations. First, some students may sit there kicking themselves by saying something like, “if I just got one more problem right, of if I just spent an extra 15 minutes on that paper then I would have achieved an A.” Of course, this is self-torture, since no one question is responsible for causing you to fall just short, just as it is very likely that you overachieved a little bit to get yourself to the situation where you were even as close as you are. Yet I’ve never heard a student say, “good thing I got lucky on that question I guessed on because that got me to within breathing distance of the better grade.” A second approach would be for students to think I should round up their grade since it was so close and that grading is not a precise science. But this is a somewhat stranger position to take. A 94% for a cutoff of an A is really an arbitrary number – would the student with the 93.92% score be kicking themselves if the cutoff happened to be a 96% Or to put it another way, no matter where I put the grade cutoffs someone would always be very close to making it. So does being close to any arbitrary cutoff entitle someone to get put into the higher grade category? Would all students within 0.1% of the cutoff be entitled? Then if all 93.9% students actually get an A, then now what do we argue about the 93.8% students, after all, they are all 0.1% points below the new A grade? On what grounds do we then decide to say yes or no.
Sports fans should be familiar with these sorts of justifications. Think about how a baseball manager is excoriated for a particular decision made in the 9th inning or how a football player is chastisting himself for some particularly poor play late in a game?
But I really had the intention of discussing two other topics here. One related to grades, and one related to economics. We’ll hold off on the economics until Monday. When it comes to grades, every single case of there being a student just 0.01 points from the next grade cutoff there is also a student who finds himself on the positive side of such cutoffs and who benefited by being only 0.01 points just above. I’ve never in my academic career heard anything from a student who found themselves in these positions. For example, “Professor Wintercow, I was just above that cutoff, surely you shouldn’t feel obligated to give me that A, after all, we worked over an entire semester and I was only 0.01 points above it, so you should consider giving me the A-!” Or to put it in somewhat blunter terms, let’s think about the four terms that I have taught Intro Econ here at the U of R. Over 4 terms I have averaged about 280 students per class, and each class has had about 3 exams (among many other assignments) with each exam having on average 10 essay questions for students to complete. This means I have collected and evaluated something north of 33,000 questions in my Intro class since 2008. Do you know how many times I have had a student come to me or a Teaching Assistant asking us to reconsider a grading decision that appeared to be “too generous?” Do you know how many students have come to me telling us that we made a mistake in their favor, either in the evaluation of the question or the adding up of points on the exam?
Do you know?
It’s not 1,000 or 500 or 100 or 50 … or even 10 … or 5 … or even 1 … how about zero? Now I totally understand that it is not in anyone’s individual interest (or is it?) to be honest with me when things work out in their favor, but zero out of 33,000? Maybe I am a megalomaniac, but I am not so much of one to expect that in 33,000 questions I never ever once made a mistake in a student’s favor? It’s not like we as professors and teaching assistants go into exams with the intention of marking students down and taking points off, indeed the incentives facing us suggest we ought to do the opposite. There are of course many lessons implicit in this post – including the suspected motivations of us as graders and instructors, including the importance of the Rule of Law, including a fun application of probability and finally a launching off point for some more important economic analogies. We’ll cover one of them in the first real post after the New Year’s holiday.