By this point in the semester, I have given two exams in my Calculus class and one in my Real Analysis class. Grading is always a pain, but I have struggled much more recently with what to say as I hand out the exams. Giving statistics on the exam might be helpful for students so they can see how they stand with respect to the rest of the class. But is that really important? Isn’t it more important that the student only know how they did, and perhaps how they can improve? I really don’t know the answer to this question. I used to never give statistics on the exam. If my students asked, I would say that averages and medians were not a great way to summarize their performance, and that they should really only worry about their own performance. But I have recently caved, mostly because I realized I was one of the few people who did not give any stats on the overall class performance, and the students were sort of expecting it. After a couple of awkward incidents this semester, I’m considering going back to my “no stats” policy.
The first thing to think about is why would you want to know how everyone else did? Especially if the professor doesn’t curve, and so the performance of others will not affect your own individual performance. So what does it matter if you were the only A, or one of the many A’s? But of course, it matters. Everyone wants to feel like they’re doing better than average, so they want to know the average. The paradox here is that there have to be people below the average! I remember telling my Calculus students, on their first exam, that the median was an 89. I was congratulating them, because as a class they performed well. But as soon as I explained (to the few who didn’t know) that the median was the cut-off between the top 50% and the bottom 50%, a lot of them looked very concerned. They realized that 50% of them had gotten an 89 or less. So somehow, this makes the people who didn’t get an A feel worse, and at the same time it makes the people who did feel less special. So my attempt to congratulate and praise kind of backfired.
And then we have the problem of what that praise does to the students’ performance later. For example, the average and median on the second exam were a lot worse. And I know in part it was because the material got harder (the material always gets harder), but I wonder if maybe they got a bit complacent and overconfident, and decided to blow off this exam. Of course, I have no way to prove this, and because I had done it for the first exam, I gave them the stats for the second. One student asked for more information, like what was the spread of the grades. This is a good statistical question, but I don’t like to give the highest and lowest scores, since then I make the student with the lowest score feel really bad. I gave the highest score, because I decided no one would mind, and then the student with the highest score came up to me and said that that made them a little uncomfortable. I didn’t say any names or indicate that they had been the student with the highest score, but then I realized that their friends could probably figure it out, and I guess that’s something that people are not always comfortable with sharing.
This reminds me a bit of my Real Analysis exam, where the median was an A-. I wanted to share that with the class because the exam wasn’t easy, Real Analysis is not easy, and I wanted to congratulate them on their accomplishment. But again, my mistake was in forgetting that there were still people who had not done very well, and thus I was essentially making them feel very bad about themselves. I am also not sure if this improved morale in the class, since an A in Analysis, which would normally be exciting, now didn’t seem like such a hard thing to attain and thus was made less special.
Of course, it could be much worse. When I was in college, my Linear Algebra prof liked to hand out exams in descending order. So if your name was called first, you knew you had the best grade in the class. As names were called, you got increasingly worried. Whoever was called last had to do the long walk of shame to the front of the class to pick up their exam, which we all knew was the worst. I was called first only once, and I was very pleased with myself, so I guess the method did improve my self-esteem. I’m not sure this method helped anyone in the bottom half, though. In any case, I believe that this would be illegal due to FERPA rules, so it’s not even something to consider.
All of this is a long way to say that I’m considering not giving any statistical feedback on the exam. Maybe just focus on common mistakes and things to work on for the final exam, and perhaps I could take a bit more time on each exam and write personalized feedback on the exam instead. I do tell everyone who got less than a 70 to come talk to me during office hours, so that’s another place to give feedback and comments or suggestions on a student’s individual performance. It is tempting to praise a class that did well, but it’s possible that I’m doing that more to stroke my own ego (look how great a teacher I am!) than to improve their morale. Each one of them knows how they’re doing, and I think now that that should be enough.
How about you, dear readers? How much feedback do you give to the class as a whole on their performance in an exam? Have you had uncomfortable situations stemming from this? Do you have suggestions for how to praise the students without making others feel bad? Please share your thoughts in the comments section below.
I’m running into that same issue. I have been kind of lazy about calculating statistics on the exam (the website we use for grades doesn’t do it automatically, so you have to export it to excel or something, which is one step too much for me). When students have asked about the average grade, I have given them a very vague “I didn’t compute a lot of statistics on the exam because I don’t think they’re very helpful. The mean was around a [round number].” They have basically been satisfied with that, or at least haven’t pushed too hard. I try to be careful when handing out exams not to let students see other students’ grades. I find it kind of appalling that someone would hand them out in an order that would let people know who had the best and worst grades. Yikes!
Then it seems clear: “Class, I’m very disappointed that after all the hard work we’ve done together, 50% of you got exam scores in the lower half of the class.”
I think the demands of the job to be done are tricky enough already without including the idea that you not make people feel bad.
More constructively, I think you’re giving up a trick if people are in general doing better on earlier tests than later. If the first test is hard, some people will be spurred to work harder, and (it is always argued to me) some will become despondent and give up prematurely. If the first test is easy, some will slack off, but I don’t think hardly any will say “This isn’t so bad, maybe I should make a real effort at this class after all!” who weren’t already doing so.
Personally, I never ever give tests where the average is 89%, because I don’t want to quibble over 94% vs. 95%, nor tell people who got 70% that they’re hopelessly hosed and would theoretically need 115% on the final to get the grade they want. I much prefer the average to be ~60%. You can guess how well that goes over.
So far, I’ve had pretty good results with focusing my as-I’m-handing-back-the-test banter on content—”Everyone seems to be really solid on L’Hôpital’s rule”, “a lot of folks were tripped up in #7 by the absolute value”, that kind of thing. I also give them a paper handout that mentions the median and has the grade buckets (A: 29–38, etc.) along with lots more of the content stuff.
Of course, I’m sure that none of this keeps them from *thinking* about these kinds of points, but at least it seems to slow down the conversation about it, and that’s not nothing.
This is a great question! Effective feedback is very important. One effective strategy is to put the students in random groups and have them collaboratively rewrite the exam. Once they are done, I give them back an unmarked photocopy of their exam and have them find their own mistakes. Once the students are done, handing back their marked exam isn’t such a shock. Plus, this way most students will usually understand where the mistakes were made before having the opportunity to tune out or shut down once they know their grade. It is a bit time consuming, but most students do appreciate this reflective process.
Except for small upper division/grad classes I give them the five number summary with the understanding that, except for small adjustments to accommodate gaps in the spectrum, the top quartile represents an A, the second a B, the third a C, and the bottom should drop. That way they have the data necessary to make informed decisions, and I am relieved of any obligation to spare feelings, or to be overly invested if they don’t drop after they’ve been told. I often get asked if there is a curve, but I explain that the final letter grades are invariant under a monotonic transformation.
I don’t give stats at all. I might say something like, “I was really pleased with how you did as a class, though I know some of you won’t be happy with your individual score.” I might say something like, “A lot of you struggled with problem 4, which surprised me because we spent a long time on a similar example in class.” But no numbers.
In fact, this semester I tried something new: I don’t even put their score on the exam. They can look it up online (I put it in problem by problem). But I only put comments on the exam.
The grading process is a little tricker (I have to have the gradebook in front of me and enter scores as I grade). But in the past year, I read lots of education research that can be summarized thusly:
(*) If you give students just a score on an exam, they learn essentially nothing from having taken the exam, and they do not learn from their mistakes.
(*) If you give students just feedback, they actually learn a lot from their mistakes.
(*) Grades + feedback seems to be about the same as grades alone. That is, students focus on the numbers and ignore the words.
On the one hand, exams are assessments not learning opportunities. The point is that we can see what students have learned so far, what they can demonstrate on the exam. So maybe it’s OK that students don’t learn from them. On the other hand, why waste an opportunity? I appear to be physically incapable of *not* writing comments on exams, even final exams that won’t get handed back. If I’m going to write lots of comments, don’t I want the students to read them & learn from them?
I have done this with both homework and exams this semester. Students were a bit taken aback by it at first. But when I told them they could look up their scores online at any time, and the feedback would explain the number, and of course they could come ask me if they had questions… after the first round of handing stuff back, no one has mentioned it.
I don’t know if they are actually reading the feedback & learning from their mistakes… but I’m trusting the ed researchers on this one.
I can’t speak for how you wrote your exams, but typically exams are sort of “mini-comprehensives,” wherein a range of topics is covered and expected. The questions on most exams tend to be easily attributed to one chapter/section/concept or another.
It may be better to break down those statistics, because it proffers a more fine-grained feedback mechanism than aggregate score statistics. For example, students might have done fine on the questions involving trigonometric integrals, but stumbled on integration by parts. Or maybe they understood the concept of continuity, but not how it applies to differentiability.
Textbooks, syllabi, and lectures are organized categorically. This is how students envision the course, the topic, and the material. Breaking down the exam stats on a per-question or per-topic basis would probably be more enlightening, and it wouldn’t make any students feel bad, as it would be difficult to reconstruct the overall score stats, and most students will have decent scores on the other questions to feel good about.
It is the teacher’s job to provide feedback, as unpleasant to the student as that may be. Students need to know whether they are good at a skill relative to the group, or whether they need to change their study routines in order to become good relative to the group. Statistical information on exam performance is part of this feedback. If it is not presented publicly many students will not receive it, and some of the poorly-performing ones will delude themselves about their relative performance. I personally believe a student should choose classes and careers based on what they love, not on what they are proficient at, but that is for the student to decide, not the teacher. So while it is important that a teacher also emphasize the intrinsic values of learning, and the folly of students’ fixating on grades, the information about the median needs to be there.
Adrianna – thanks for the post. I had never considered not giving out median/mean information. You’ve given me something to think about.
If a student has done very badly on the exam, I send them an email the night before they get their exam back to give them a heads up. I really don’t want tears in the class! After imparting the mean/median information, I try to find something I can praise most everyone on. I always say, “If you did not do as well on the exam as you would have liked, please come see me about it after you’ve had a chance to look it over.” I then follow up with all the students who should definitely come see me. This has worked pretty well for me, since some students are devastated by a B and others are ecstatic. I don’t think the students at the bottom feel singled out, since the “cut-off” for getting help is not defined by a grade, but by what they want to achieve.