Doing the Math of Student Grading

One of the questions that has bothered 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.


6 thoughts on “Doing the Math of Student Grading

  1. Bummer—looks like MarkBook might not be available in the states.

    We’re on the hunt for an electronic gradebook program which plays nicely with a standards-based grading and reporting system.

  2. I have an email in to the management. The MarkBook program I used was produced by a Canadian company. I’m thinking they were bought out.

    I’ll let you know when and if I hear from them. Meanwhile, I’ll do a some more research into grading programs.

    Our head IT guy (we call it Information Services, or IS) is supposed to let me know if eSIS is capable of doing median averages for grades. That’s the student data management system we’re going to, but those decisions were made before I came aboard.

    BTW, Nice to see you here!

  3. For anyone interested in median grade calculation (all of you, I hope), MarkBook still does it. And for each student, you can compare the different methods of averaging with the click of a key. (Oops, your mean and median are waaaay apart? Better pay attention to that one!)

    I downloaded a trial version that works with WIN 98 SE through Vista, and stumbled through that crucial verification. The program is powerful, but you have to pay attention to get it right.

    The only significant thing that annoys me now is something that annoyed my in the years immediately preceding my retirement: there’s a Zero! key to zap the student who didn’t do the assignment. (It’s damned near impossible to get zero as an actual score!) I’d rather see an INC key that wouldn’t affect the calculation, but would show up on the report so the teacher could exercise some judgment.

  4. Surely, any package will calculate the median, though if you do more than just look at central tendency, there are better ways to deal with the effects of outliers, such as trimmed means. I have around 240 students in each class, though, so I have enough data that I always end up with normally distributed scores, and don’t have to worry about the effects of outliers.

  5. Thanks for the new info, rwp.

    I’d like to hear about “trimmed means” if you have time.

    Meanwhile, I’ll be looking out there for other software aimed at secondary schools that features a median average calculation.

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