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….
Take the Square Root
Take the score as a percentage, then take the square root. This will shift everyone up, but some more than others. Students near the extremes of 0 and 1 get the least benefit, and students at .5 get the greatest benefit. However, if you write the test such that everyone gets above 50%, then you are squishing the scores together closer to the top. I’m not sure what tangible benefit this would have, other than helping out the poorer students.
Weight Your Own Grade
Let the students put a star next to the question that they are most confident about, and count that question double, renormalizing appropriately. In most things, it’s good to get the right answer, but it’s worth a lot more to get the right answer and know for certain that it is right. Otherwise, you’re just guessing and asking someone else to check your work, which is significantly less valuable.
This scheme rewards the best students, the ones who arrive at the correct answer confidently. You can also make the weighting optional, so that less confident students don’t have to star any of the questions.
There are other possible variations of this: you can have the students rank their confidence in all the questions on a scale and weight appropriately, you can allow them to star more than one, etc.
Partial-Credit Multiple Choice
Many multiple choice tests have some wrong answers that are plausible (off by a small factor, for example), and others that show that the student has no understanding of what he or she is doing (saying that the Mississippi River is 2 inches long). It should be fairly simple to devise a method for giving partial credit for reasonable but wrong answers, and it might make multiple choice exams more viable in higher levels of education.
“No One’s Perfect”
Normalize to 99%, even if someone would otherwise have a perfect score. I actually had a professor in undergrad who did this, shrugged and said “Hey, no one’s perfect.”
Oral Exam to Earn Back Your Points
The same professor also had an oral part to our exams, where we had to come into his office, having studied the problems that we got wrong on the exam, and he would ask a question about one of them. We had to answer on the chalkboard, and he would give back points as appropriate.
The 0% Gamble
A multiple-choice final, graded normally. But if you get EVERY question WRONG, you get an A for the entire semester. How many students would take this gambit? Would it really be as difficult as it sounds? The world may never know…
Give everyone a B+. See if anyone notices or complains. Try the same thing with an A+. Compare notes.
The Stair Method
Take the box of papers to the top of a stairwell, and toss them in the air. The papers that land at the top are A’s, the papers at the bottom are F’s, and scale the ones in between appropriately.
Good luck to everyone on exams! And to my fellow TA’s, have fun grading. If you have any other good (or interesting) ideas about how to grade tests, leave them in the comments.
Another opinion on curving grades here.