Comments on Grading

One of the most unpleasant aspects of education, both for the student and teacher, is the assignment of grades. It would be nice if we didn't have to worry about this facet and could concentrate solely on teaching and learning. However, grades are necessary for a number of reasons. They provide a measure both to the student and to other interested parties of how much was learned, and they are a powerful motivator for many students.

It is a fact that grades open and close many doorways in life, but this is no different from the myriad of other ways we are constantly being evaluated. We all have strengths and weaknesses, and a weakness in one area does not signify failure in life. Rather it is an indication that perhaps another pathway is more appropriate.

Every semester I listen to a few people tell me that a grade of less than an A or a B will keep them out of medical school or graduate school or will cause them to lose their visa and will dash a life-long dream. These are heart-wrenching tales, and I genuinely feel empathy for the people involved, but not enough so as to compromise the integrity of the grading process. In many cases, I suspect the import of one grade in one course is being overblown, but I'm sure there are instances in which a person's future has been radically changed by a grade I gave.

Given that grading is necessary and desirable, how best is it done? We want to devise a system that is objective and fair, and that gives students some control by allowing them to work harder for better grades, but one that basically reflects their mastery of the material. At the same time, it has to allow some discretion for extenuating circumstances, and it has to allow implementation without inordinate effort.

The system that has evolved over many years is one of testing by examination. I realize that some people are good at taking tests while others exhibit test anxiety and don't perform up to their abilities. But the same would be true of most any form of evaluation. Many tasks in life are done under pressure, and so examinations are one indication of how one is likely to perform under pressure in the real world.

A portion of the grade is determined by the teaching assistant and is based on performance in discussion, homework, and lab. Although the TAs have been given general guidelines on how to construct this component of the grade, it is inevitable that different TAs will grade differently. These differences are taken into account at the end of the semester, so that you are not penalized if your TA is a hard grader and that you don't unfairly benefit by having a TA who grades generously. Each TAs grade is adjusted so that it has the same average and distribution as the exam scores of the students in his or her sections. Thus if your TA happens to have mostly high performing students, the lab/discussion grades in your section will be higher than other sections with mostly average students, although the differences are rarely more than two or three points out of 100. This is done so as not to penalize students in sections with a high percentage of superior students as would be the case if all the TA scores were adjusted to the same average. Similarly the grades are spread out (standard deviation) in a manner similar to the spread of exam grades so as not to penalize the strongest students and to ensure that the lab and discussion grades have the promised weight in the overall course grade.  If all students were given essentially the same grade in lab and discussion, whether it be the average or a perfect score, the effect would be to discount the lab and discussion in the final grading.

I know of one physics professor who made a practice of specifying an uncertainty in the grades he assigned. Rather than giving a grade of 85 he might give 85 + 5. In physics labs, we emphasize that all measurements have uncertainties, and then we assign grades, which are a measure of your knowledge, as if they were absolute. The assumption is that with enough exams for each student, uncertainties will average nearly to zero.

Students often come to my office especially after the first or second exam to say they are very concerned about their performance in the course and want to know what they can do to get a better grade. I appreciate it when students come to see me because I want to understand your situation and any difficulties you are having, but these discussions are often frustrating because there's not much advice I can offer beyond what I have already said. It's not as if there is some magic prescription for learning the material that I have kept secret from you. There is no substitute for hard work and practice. One bit of advice I often give is to take the practice exams under stimulated exam conditions, closed-book, but with a sheet of notes and a rigid time limit, and then to grade one's self and review those topics that were missed.

Students sometimes ask if there is work they can do for extra credit. Although I applaud your willingness to do extra work, the course is hard enough without my inventing additional things for you to do. The best extra work you can do is to solve more problems, and the extra credit is in the form of a better performance on the exams. It wouldn't be fair to the other students to grade you by a different standard, to change the rules in the middle of the game, or to give you opportunities to enhance your grade that are not generally available to everyone. You might try making up additional practice exams for yourself using problems from the text and working them in the allotted time using only the allowed aids.

There's always a debate over whether grading should be done on an absolute scale or on a curve. The proponents of the absolute scale argue that the performance of one's classmates should not effect the grade that a particular student gets. The proponents of grading on a curve argue that the most meaningful way to assess students is by comparison with their peers. Both methods have drawbacks. It is difficult to devise an absolute scale unless some kind of standard exam is given. It is surprisingly hard for an instructor to judge the difficulty of an exam before it has been given. Even these standard exams are in effect grading you in comparison with students at other universities. On the other hand, the last thing we want to do is to engender such a strong sense of competitiveness among students that you actually hope that your classmates will do poorly so that your grade will rise. On the contrary, we are trying to encourage you to work cooperatively in labs and on homework.

The solution that we have devised is a hybrid scheme in which we try to preserve the best of both systems. Students are ranked by grade from high to low, and grade boundaries are drawn. Initially these boundaries are somewhat arbitrary. Historically about half the students in general physics courses get A's and B's, and I use this as a guideline to prevent grade inflation. As time goes on, I might develop a sense that the class as a whole is doing well, in which case larger percentages of high grades are given, or that the class is doing poorly, in which case the opposite is done. One of the things that would convince me to raise the grades is the impression that there is a strong communal sense of learning and cooperation. And so contrary to what you might think, being helpful to your classmates is at least as likely to raise your grade as it is to lower it. This is in addition to the fact that there is no better way to learn something than to explain it to someone else. Trust me; I've been teaching for a lot of years, and I learn something new in just about every lecture I give. Furthermore, in a very large class, the help you give a few people is likely to benefit your grade far more by helping you understand the material than any slight detriment from raising the grades of your classmates.

One consequence of this grading scheme is that the letter grades for individual exams are not a guarantee of the grade you will get in the course. It merely reflects the grade you would be assigned if the course were based solely on those particular exams. I continually caution students not to take letter grades on individual exams too literally. There are many other reasons that letter grades move around a bit, including students who drop the course and special circumstances such as illness, family emergencies and the like.

Even without readjustments in grade boundaries, drops, and special circumstances, course grades may change in ways that surprise you. For example, it is possible for a student who gets an AB on every exam to end up with an A in the course. To see how this might happen, consider just two exams. Imagine that all the students who got an A on exam #1 got a C on exam #2, and all the students who got an A on exam #2 got a C on exam #1. Thus even though you didn't get an A on either exam, you end up with a higher average than any of those students. (This is known as Simpson's paradox.) Unfortunately, the opposite can also happen. If you consistently make low C's on all the exams, it's likely you will get a D in the course because many of the students who had D's and F's on individual exams will pull their grades up on subsequent exams. Thus a consistently good performance is rewarded, and a consistently mediocre performance is penalized.

This is a partial answer to the frequent question of whether we take into account a situation in which a good student has just one poor exam grade. Such cases are automatically accounted for by the grading method, but it is also one of the factors we consider when someone is near a grade boundary. Since the exam scores are added together to get a final grade, those exams with higher scores contribute more toward a student's grade than exams with low scores, both for the class as a whole, and for individual students. We also notice situations in which there is a strong improvement over the semester, and this is another factor considered for students close to a grade boundary. We look especially carefully at the final exam of students who did poorly early in the semester to see whether that material was eventually learned. Note that the final exam counts more toward the course grade than the early exams do, and it retests material that was previously tested. This is done to reward automatically the student whose performance improves throughout the semester and who eventually learns material that was not learned early in the semester. A certain number of students are always very surprised at the grade they get in the course. As you might guess, I mostly hear from those whose grades are lower than they expected. I don't recall ever getting a complaint from a student whose grade was higher than expected, although there must be at least as many of them.

I know that some instructors will drop the lowest exam grade from the average for each student. On the surface, this seems reasonable since it is akin to forgiving one mistake. However, I have never done that and don't intend to because it strikes me as rather unscientific. It amounts to discarding data, which is bad practice in the laboratory, and I think the same is true in grading, which is basically a sociological experiment. Also, it has the effect of penalizing those students who are consistent and make similar grades on each exam. In any event, it would only very rarely change anyone's letter grade, and since I give approximately the same proportion of each letter grade, it would lower as many grades as it would raise.

One feature of letter grades is that students with rather different performance in the course can end up with the same letter grade. Someone has to have the highest C, and someone else the lowest C, and there can be quite a difference between them. I'm always especially concerned about those students near the top of each grade range, and we give extra consideration to them to see if there is any way we can justify giving them additional points. If we did that, the problem would just move down to the next student who is now at the top of the grade range. I usually try to draw the boundary between letter grades where there is a significant gap in numerical scores, but this isn't always possible. If you find that you have missed getting a higher grade by only a few points, you have my sympathy, but over your academic career, you will probably just as often miss getting the next lower grade by only a few points. In fact, you probably benefit more often, because most instructors don't look at those at the bottom of grade ranges with the thought of deducting a few points. Thus, over your academic career, these inequities should at least average out. In any case, when I write letters of recommendation, I always state how you ranked in the class as a percentage, and not just your letter grade, which is less meaningful.

Although I may assign D's and F's to many students on a given exam, it is a rare semester in which more than about 5% of the class ends up with a D or F for the final course grade. I do this as a wake-up call to the students who are having the most trouble with the material. In particular, I would not normally give an F to a student who took all the exams, handed in all the homework, did all the labs, and attended discussion and lecture regularly. A grade of F is normally reserved for those students who just gave up somewhere along the way, in which case I tend not to be very generous.

This leads me to the last point. After grades are turned in, there are always a few students who come to my office with very long faces, disappointed and perhaps puzzled by the grades they received. I often hear the saddest tales at this time. What you must understand is that once grades are turned in, they are out of my hands. This is to prevent hoards of people from pleading for higher grades and to preserve the integrity and fairness of the grading process. There is a mechanism for changing grades, but the form requires the signature of the Department Chair and the Dean. I have to give a reason for changing a grade. The only reason the Chair and the Dean will accept is "clerical error." Certainly if there was a clerical error, you should bring it to my attention and I will fix it, but please don't ask me to claim there was such an error when there wasn't.

I hope this little essay gives you a better idea of why and how grades are assigned. I wish you well in life, and I hope that what you learned in this course will repay you handsomely in the years to come. 

 J. C. Sprott