There are two broad philosophies of grade levels. By grade level I mean things like B
in a letter-grade system or 7
on a ten-point system or 81%
in a percentage system or the like.
One philosophy says that a given grade level indicates a given competency level. If everyone learns the same amount, everyone gets the same grade. Grades like these are sometimes called criterion-referenced, though that term also sometimes suggests course or binary grading. In this post I’ll call them PvE grades
, in reference to computer games where each player plays against the game itself and ideally every player wins eventually.
Another philosophy says that a given grade level indicates a given ranking within the student body. Whether everyone does well or everyone does poorly, whoever does the best gets the highest grade and whoever does the worst gets the lowest. Grades like these are formally called norm-referenced, though that term also sometimes suggests a particular distribution of student performance. In this post I’ll call them PvP grades
, in reference to computer games where each player plays against other players and for every winner there must be a loser.
PvP grades lead to a variety of undesirable student behaviors; for example
break the curveand pollute grades overall.
I’m told that PvP grades were once very common, but they have dropped in popularity to the point where I know of only a very few courses that still use PvP grading.
PvE grades don’t have the same impact on student learning, but they still have problems; for example
The vast majority of college courses I am aware of use a PvE grading system.
I am aware of two hybrids in common use today. The curve up but not down
system used on many college exams computes both PvP and PvE grades and uses the maximum of the two. The national exams and class ranking
system used for many professional degrees like law and medicine, computes PvE grades, dropping students below a threshold, and reports PvP grades for those who remain.
It occurred to me recently that another hybrid is possible, which I outline in the next section
Many colleges release freely, or release under Freedom of Information Act requests, the number of students in each course offering that were given each grade. For example, Fall we find the following publicly available grade distributions (among many others):
| Course | A+ | A | A− | B+ | B | B− | C+ | C | C− | D+ | D | D− | F |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CS 410 | 162 | 13 | 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| CS 421 | 25 | 66 | 20 | 21 | 18 | 13 | 10 | 12 | 11 | 9 | 4 | 8 | 6 |
Suppose a student took both courses and earned an A‒ in both. I’m not overly familiar with either course, but I believe they both use PvE grading, so I would roughly expect an A− to mean some version of learned almost every course topic well
. In PvP grading, how would they have done in these classes? Because we have grade buckets, not raw scores, we can’t make a perfect ranking, but we can say this:
If we did this with a student’s entire transcript, we’d get an estimate11 Averaging intervals has some nuance, being an instance of nonparametric statistics that is difficult to get fully correct, but averaging the high and lost extremes separately gives a crude approximation. of their class rank for each course, and could combine those to get an estimate of their overall PvP grade. This can be done with data that is available today, without requiring any change in behavior by individual faculty.
I have mixed feelings about whether I wish for such a system to become widespread. Would it cause students to adopt the negative behaviors associated with PvP grading? Would it cause students to request that grade inflation reverse so that we don’t have cases like CS 410 above where the top 89% of students all get the same grade? I don’t know.
I also don’t know if this is already done. I’m not aware of it at an institutional scale, but I have spoken with people who hire many of our graduates who say that they ignore the GPA and look on applicants’ transcripts to see which courses they took with which instructors and how they did in each of those courses. If I was a hiring manager using the PvP summary of a transcript of PvE grades to rank applicants, I might describe that approach using similar words.
Beyond just PvP ranking, this approach could also give a rough sense of student decision-making. Detecting student agency is not always straightforward, but we could rank how easy the courses a student took were (in the grading sense if not necessarily the work sense of easy
). I could imagine a situation where I’d want to hire risk-averse students who took the same route through school or risk-taking students who took many courses with a high potential to harm their GPA. Of course, the meanings might change if PvP interpretations of transcripts became common, but until/unless that happens it might be an interesting measure for some decision-making.