Doing the Math of Student Grading

One of the questions that has bugged me over the years is why teachers continue to use the mean average when it's obvious that it can give misleading information about the measure of central tendency with regard to student grades.

I had an entire year of statistics as an undergrad sociology major, so I was aware enough, as a teacher, to disregard extreme scores in my grade calculations. (In those days, I hid this from my peers and principal, and to myself and my confidants called it "The Fudge Factor.")

Most of my fellow faculty members uncritically used the mean average, some rounding up, and some being sticklers for decimal point accuracy (thereby alienating students).

Yesterday it occurred to me, after reading a blog post on salary averages, of all things, that there is a pretty good reason that teachers do not (and apparently never did) use the median average to arrive at a grade even though that is the way to achieve statistical integrity when seeking an accurate measure of central tendency in a student's collection of scores.

The author of the salary average post said that prior to the advent of the computer, medians were more difficult to ascertain. I immediately identified with that statement! After I learned to apply the median to individual student's scores (Spring, 2000, at an Albuquerque, NM ASCD Institute with Ken O'Connor), I found it very cumbersome to calculate those medians! Where it wasn't obvious by looking at my grade book, I wrote out the numbers by hand.

Mean averages can easily be calculated with mechanical adding machines or electronic calculators by adding the scores, regardless of order, and dividing the sum by the number of the scores. Medians would require the teacher, in pre-computer days, to physically lay out the scores from high to low and count from each end toward the middle. No wonder it never became common practice. (According to my wife, had I kept my classroom stats on Excel, I could have rank ordered the scores for each student and spotted the median instantly! But I didn't know Excel.)

Over time, as grades became of vast witch's brew of too many scores with dubious relative value, the distinction between the basic aspects of the mean and median was either lost or never conceived of, and a pervasive and dangerous grading practice -- reliance on the mean average -- was born. But ignorance, and possibly laziness, may now be laid to rest. With computers and grading programs like MarkBook, we can calculate medians with the push of a key, so there's no excuse not to ditch the bad math and hit the trail to more valid grade calculation.

A side benefit of getting on the median track is that the battle against the illegitimate "zero" grade eases up because occasional zeros, for students that turn in work on a regular basis, become a non-issue, but an issue we must pursue nonetheless.