Anyway, at the end of the term, I had done pretty well but suspected I was borderline A/B. I visited the professor’s office and saw “grading on a curve” being done in real time. The TAs had generated a frequency histogram for the entire class and had printed it on one long computer printout, many feet long. The professor was on a ladder attaching it to the top of a wall so the entire chart could be seen. Climbing down, he stepped back, had some conversations with some of the TAs and directed one of them (on the ladder) to draw dividing lines at four specific places. The five groups separated by the lines became A, B, C, D and F. He was kind enough to explain his rationale to me – he knew that grading was imperfect and the means he used to evaluate student performance (tests and quizzes) was at least partially subjective. He wanted to avoid having students miss a grade cutoff by a small number of points so he looked for large gaps on the frequency histogram. He used these gaps as cutoffs and had found them to be beneficial when students came to inquire about how their grade had been determined.

I hadn’t decided to become a teacher yet – that would come a couple of years later – but this highly illustrative example never escaped me as I, in turn, came to grips with my own grading dilemmas. Histograms of small group performance didn’t always generate the desired natural breaks for A/B, B/C, etc. but it did the trick much of the time.

f(x) = x + (100-MAX)

No body scores over a hundred, it’s easy to explain and calculate, and really is there to correct for my making bad questions that the top students cannot answer. Usually this comes out to +2 points or so per exam, but I’ve had it as high as 15 points.

f(x) = target mean + target sd / raw sd (x – raw mean)