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There’s Always Someone Just 0.01 from the Cutoff

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?

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.

1. The interesting exception to this phenomenon appears to be golf, where players routinely call penalties on themselves during a tournament. After being exalted for his honesty by the press, Bobby Jones famously quipped, “You might as well praise a man for not robbing a bank.” I believe the culture of golf is such that you would be shamed in front of your peers in the case where you were caught cheating in this manner, and thus the self-policing is somewhat out of fear (at least for some).

In other sports, feigning injury or exaggerating a foul are considered part of the game. In academics, my guess is that the win-at-all-costs mentality is presumed among peers. This makes grade-grubbing paramount for students on the margin as others are competing for the same scholarships, grad school spots, and teeming grade groupies who blindly throw their affection at the highest GPA (they have those, right?). Everyone else is doing it…

2. One of the “weeding courses” at my college was Chemistry 101-102, elementary chemistry. Over half of my entering class were “pre-meds,” one of the few hybrid majors at the college. The chemistry department had a total of four professors, two associate professors and four instructors, and the department maintained high enough standards to be regarded among the best two or three college chemistry departments in New England. Thus it became the mission of the chemistry department to weed out all the potential slackers before they would dare to take qualitative and quantitative analysis.

At the same time, my freshman class was filled with people who had been academic stars at their prior high schools. Grade inflation had not infected education yet, and very many of my classmates thought of themselves as medical school material, having done well in their Sputnik-era science classes.

So here’s how Chem 101-102 worked: labs counted for 25 percent of each semester’s grade, while quizzes counted for 20 percent and tests 55 percent. Lab grades had a degree of flexibility in them insofar as the documentation in your lab report counted for part credit, but the answer for the lab had to be correct according to slide-rule accuracy for one to get a grade higher than C.

On tests and quizzes, there was no part credit at all. The quizzes were usually three or ten questions, so it was possible to get a 90 on a quiz with one wrong. Tests, however were all three-question tests, so the grades attainable were 100, 67, 33 and zero. There was no part credit for your work: if the answer was not correct to slide rule accuracy (three digits, usially, depending on how many significant figures there were), one wrong meant a 67 on a whole test, with only four tests per semester. Fortunately for me, I had only two 67’s and two 100’s my first semester, and I wound up with a C+ for the semester. (The semester exam had ten questions on it.) I worked my backside off the second semester and got a B for the semester and a B- for the year, which put me toward the top of my fellow chem students.

Looking back, I wonder what I might have done for a living if I had gone to a different college where they did not have to weed out pre-meds. By the time I graduated, over half of my class had applied to law school, destined to sue the doctors who had beaten them in the battle to qualify for Q&Q and Organic.

When your students complain about the final calculation of their grades, maybe they should consider the concept of significant figures.

3. Are your test questions all five-item multiple choice? One of the things I learned in Psych 101 was that five-item multiple choice questions were the fairest as long as they were carefully crafted to eliminate ambiguity and to prompt recall of the information one should have learned in class or in reading and study.

1. What kind of test questions are the fairest?
A. Essay questions
B. Fill in the blanks
C. Matching
D. Five-item multiple choice
E. The questions on a typical Dr. Wintercow Econ 101-102 test — like, I mean, you know, those Pear Harbor surprise questions we had to answer on the last test.

2. What happens to students who complain about a freaking 0.01 percent on their final grade, for goodness’ sake.
A. Exile to a college with a colder climate than Rochester. Like the University of Winnepeg.
B. Waterboarding
C. Skateboarding
D. Being made to eat, page by page, The Road to Serfdom
E. All of the above

4. As a teacher do you get frustrated if someone complains about an addition error?

5. In 4 years at Rochester I found 3 addition errors ranging from 3 to 11 points (biologists have a tough time adding I guess), and I never felt that I was doing something I shouldnt have by making this known.

6. A number of instructors at two different universities that I attended graded purely on the basis of attendance and made that perfectly clear from the beginning. No misunderstandings with those fellows.

7. Is the student response not the basic human reaction to risk? (Would you rather get \$500 now, or flip a coin to win \$1000? versus Would you rather lose \$500 now or flip a coin to lose \$1000?)

The quote from Bobby Jones is interesting, though. It speaks to a high minded nature that is beyond homo economicus. As a sidelight in the Ian Fleming novel GoldfingerM James Bond knew he had his man early on when Goldfinger did not exactly cheat at golf but only jumped up and down over the ball (ahem).

In any case, it speaks to character.

I have a shaggy dog story that I will spare you, but after a direct challenge to the professor in which I chose to do more work than he asked for, I got the lowest B-minus in the class, rather than the highest C-plus… and three slackers ahead of me lucked out…