Well, it’s Final Exam week for me, so tests have naturally been on my mind. In teaching undergrads, (especially pre-med students), I’ve gotten many anxious questions about exam grading and how the exams might be curved. While I have no control about how grades are curved or scaled for my students, I’ve been thinking about the many different ways to accomplish this task, both traditional, and some more off-the-wall ideas that I’ve had.
First, the traditional ones:
What You See is What You Get
The scale is set ahead of time, and the percentage of the points that you get is your score, plain and simple, no haggling. While this seems to leave no wiggle room for the grader, the grader will no doubt consciously unconsciously scale the grades as he goes along, particularly if there’s partial credit to be awarded (and there almost always is). In addition, the grader may find himself choosing the letter grade that the solution deserves, and then adjusting the points to fit that grade.
Normalizing to Unity
Take the highest score, and add the necessary points to get it to 100%. Then add the same number of points to everyone else’s score. Really, to make it a true normalization process, you should divide all scores by the highest score to get the new percentage, but adding points is more beneficial to the students, and is what is usually done. The good thing about this is it has some ring of fairness to it — students can’t complain about unfairness, because at least one student got an A.
However, this approach can lead to civil unrest in the case of a “curve-breaker,” a student who scores significantly higher than the rest of the class, thus reducing the benefit of the curve. There are ways around this: either curve the outlier’s score above 100, or, if that offends you, just give that student less of a curve than anyone else. If they complain about getting “only” 100%, then tough noogies.
Normalizing the Average
Instead of rescaling the top score, rescale the average score to whatever you’ve decided the average grade to be, usually a B or a C. This can again be accomplished by either addition or multiplication, and faces the same potential problem of putting students above 100%. Also, what if the students score better than expected? Are you really going to scale them down to a C?
The Good ‘Ol Bell Curve
Find the average, find the standard deviation. Everybody within one sigma is a C. Two sigma is a B or a D, beyond that is an A or an F, where appropriate. I don’t know if this is really done much, and I always thought it was unfair, but I was in a class where the Central Limit Theorem really applied. However, in a huge state school like mine, scores might actually approach a normal distribution in the large lecture classes.
But do we really want to give 68% of our students a grade of C? I don’t think C means average to most people anymore, so if you were to use this one, you probably would want to make the average correspond to a different grade.
And now, for some more creative ideas….