A New Approach to Grade Inflation

Using two formulas may result in a better picture of what's really happening in the classroom, writes Abbott Katz.

July 1, 2008

You can count the number of grading options in the Stanford University Law School’s new scheme on the fingers of one hand and still leave your thumb free to beat a tattoo on your Blackberry. Just count ‘em: honors, pass, restricted credit, and no credit. No pluses or minuses. No grade point averages. That decidedly minimalist scale of intervals was compiled the better to divert students from GPA angst and an associated concern with grading equity, and to direct them instead to the business of hand - the learning of law. How the new system plays out remains to be seen, of course; whether a “gentleman’s pass”, for example, will become the default grade is but one of an assortment of questions that could be asked of the idea.

It may not be too much of a reach to surmise that the Stanford initiative accords with a wider, centrifugal pull away from quantifiable precision in student assessment, corroborated by the anti-SAT vanguard; and what makes the Palo Alto case all the more instructive is its juxtaposition to the very different fate suffered last year by the Achievement Index (AI), an ornate alternative to the standard GPA fashioned by statistician Valen Johnson that was proposed, and beaten back, by the University of North Carolina at Chapel Hill (as well as a variant at Duke University in 1999). Attempting to factor class-specific talent levels into its equation, in part by decreeing that "...the impact of grades in a class depends on the academic achievement that the students in the class have demonstrated in their other classes," the AI proceeded to spur a raft of apprehensions, including unease over the global curve it would have instituted and a (not entirely unjustified) sense that its formulaic obtuseness would cow the students who would be subject to it.

While of course a discomfort with complexity could be written off as a philistine cavil, the AI doubters nevertheless had a point. Students live with the GPA, know how it’s figured and what it does; and an insurgent bid to retool that life-impacting metric into something multivariate and opaque might indeed be seen as a little scary.

On the other hand, in a perfect world one could stand the Stanford position on its head, allowing that a proper and just assessment of performance should exact ever greater precision in measurement, thus awarding students exactly what they deserve; and in fact some industries don’t shrink from that desideratum. Imagine Major League Baseball suddenly deciding to round off batting averages to only two decimal points, thereby enabling .351 and .354 hitters to share a batting championship, for example. That sounds silly, but the coarse-grained Stanford “Pass” presents itself as a rather large case of institutional rounding off.

Of course that analogy isn’t completely fair, because apart from the occasional official scorer’s clarification, a baseball “hit” is a rather unambiguous thing - even as university grading practices vary hugely and distressingly. Thus the Stanford case really pairs two different but concomitant concerns - the call for a proper exactitude in assessment, and the now-perennial stammering over grade inflation. And in light of those problems, I hereby offer what I’ll dare to characterize as a simple, lucid, and anti-inflationary take on student evaluation, one that might serve to level a playing field trod by graders both draconian and hyper-indulgent. Allow me to explain.

The measure I propose, called the Composite Index (CI), begins with standard alpha grades and submits them to two simple formulas, the results of which are then averaged. The first formula comprises a very basic calculation, the Relative Grade, computed for each student in a class:

Student’s grade/Class aggregate GPA (less that student’s grade)

That is, each student’s grade is stood atop the baseline of the class average. Thus an A (4.00) grade in a class sporting a collective 3.20 yields a 1.25.

The second, partnering formula, the Relative Rank, ranks and then divides each student’s grade by the class’ midpoint rank, assigning students a top-down slotting (i.e., higher achievers receive higher rank numbers). For example - if one student in a class of 20 earns an A, he/she receives a 20. Divide that by the class’ ranking midpoint - 10.5 - and you get a 1.90. If three students share that A, each receives a 19 -- the average of student positions 18 through 20 they occupy in the class grade hierarchy, and earn a Relative Rank of 1.81, a slightly diluted score. The next student down - say, one holding an A- -- would inhabit rank 17. If six students check in with an A-, they each earn a 14.5, reflecting their averaged occupancy of class positions 12 through 17 and returning a Relative Rank of 14.5/10.5 -- 1.38.

We then simply average the Relative Rank with that of the Relative Grade, yielding the student’s CI for that class. Wind up the process with the usual (credits*CI)=quality point equation, divide by all credits as per the current system, and the student’s overall CI is duly computed.

As envisioned here, the quintessentially average student scores a 1.00 in both formulas, culminating of course in a final, sleek, monadic, paradigmatic CI of exactly…1.00, registering a new and signal benchmark for comparative judgments. E-mail me and I’ll send you a spreadsheet demo you can play around with - you’ll see what I mean.

If this all sounds every bit as recondite as the Achievement Index, it isn’t. Consider these hypothetical examples:

Joe Rathskeller nails an A in that renowned, gut Hip-Hop Hermeneutics course, enrollment 20, collective GPA 3.50. Our Relative Grade formula for Joe yields

4.00/3.45 = 1.16

(Remember that Joe’s own A is excluded from the class GPA divisor; otherwise his 4.00 would be divided in part by itself, skewing the result fractionally. His A is compared to, and divided by, the average of the 19 other class grades).

Because 11 of our 20 imaginary students here have carded an A, their rank average figures to a 15 (reflecting occupancy of student rank positions 20 through 10). Divide that 15 by the class rank midpoint of 10.50, and Joe realizes a Relative Rank of 1.43. Then average 1.43 and 1.16, and Joe and his fellow A-holders emerge with a 1.29 - not bad, in light of the surfeit of As adulterating their scores.

Gina Geek, on the other hand, toughs out a B in that nasty String Theory and Its Discontents section, class GPA 2.60 (let’s again assume a count of 20 students). Her first formula yields:

3.00/2.56 = 1.17

For illustration’s sake, say a total of 7 students in Gina’s class bang out a B, topped by one intrepid, solitary A achiever. Because they hold down student rank positions 19 through 13, every B holder rank-averages 16.00. Again, by dividing that score by the class midpoint 10.50, Gina forges a Relative Rank of 1.52; and by averaging that with her 1.17, her CI actually tops Joe’s at 1.35 - her just due for having braved the more challenging, lower-graded course.

Student ID Alpha Grade Grade Points Relative Grade Relative Rank Composite Index
1 C 2.00 0.67 0.36 0.52
2 C+ 2.33 0.79 0.64 0.71
3 C+ 2.33 0.79 0.64 0.71
4 A- 3.67 1.30 1.45 1.38
5 B 3.00 1.04 1.09 1.06
6 A 4.00 1.44 1.73 1.58
7 C- 1.67 0.55 0.18 0.37
8 B- 2.67 0.91 0.91 0.91
9 A 4.00 1.44 1.73 1.58
10 B+ 3.33 1.17 1.27 1.22

But why, you may ask, does the CI bother to deploy two formulas? We use two because the one acts as a corrective upon the other ... and because the formulas pursue two redoubtable means of assessment. A class salutatorian is ranked number 2 irrespective of his/her grade disparity from the valedictorian. Second place, after all, is second place, and can be recorded as such; and that’s where the Relative Rank comes in. At the same time, the actual differentials in performance are germane as well - hence the Relative Grade. The two thus offer varying and pertinent vantages on student results.

But in addition, the proposal imparts a measure of smoothing restitution across the rough texture of university classes. Because the CI strikes a body blow against the easy A by relativizing grades to intra-class distributions, students would no longer be able seek refuge in the safe-haven sections of dubiously kind instructors. And by extension, never again would Gina’s index have to take a hit from her battery of fearsome classes - because under my plan, her Bs might map neatly atop Joe’s As - and that’s only fair.

And while lobbying universities to actually sign on to my plan might be pushing naiveté to the breaking point, student transcripts could at least be emended by posting CIs alongside a student’s traditional grades for comparison purposes. And finally, why couldn’t a student’s grading history be subject to a graphical rendering - say, by a two-line chart, in which one line plots all his/her traditional grades and the second tracks his/her CI equivalents in paired data points, this to be published on every student online transcript? After all, an A is a variably-valued thing in my plan, and a chart would incisively capture the variation. And I bet it would make scintillating reading for the folks in Institutional Research and Student Advising, too.

And the CI just might dissuade Joe Rathskeller from lunging for his next gut course. Right now he’s leaning heavily toward Lacan for Dummies.


Abbott Katz is registrar at MST College in London, but issued more than his share of grades in various teaching stints in the States.


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