How should the shape of your grade distribution change the way you teach?


I’ve received a number of comments about one of the recommended reads from last Friday. It was about the New York Times op-ed piece, about why people shouldn’t grade on a curve. And then, I asked, who does that anymore? The answer is: a lot of people. In addition to the comments on the post, I’ve gotten some emails and chatted with a few people (here while I’m at the International Congress of Entomology in Orlando, Florida).

One friend is in a department in which all faculty are rigorously required to conform their grades to a particular distribution, and they can’t submit their grades unless they follow this practice.

There was a second piece that reminded me of a topic that I’ve had in the queue of post topics for a few years. The link about how people often think they have bimodal grade distributions but they don’t actually have bimodal distributions. Quite a while ago — far enough that I can no longer recall or search it up — Jeremy Fox (of Dynamic Ecology) was thinking about if or how we should alter how we teach based on the structure of our usual grade distributions in a particular class.

I suspect many people think a central challenge in teaching is how to balance meeting the needs of high-performing students relative to the needs of the students who are challenging to just pass a class. Do you “teach high” and leave behind the struggling students, or “teach low” and fail to challenge the high-performing students?

In the last several years, I’ve come to decide that some of the teach-high-or-teach-low issues are predicated on a false premise. Students are in my class to learn a set of things that they don’t already know. This is both true for the struggling and high-performing students. The high-performing students can figure out out to get a high grade without much support from the course, because (for a bunch of complex reasons, independent of how smart they are, though I choose to defer to educational theorists about all that) they can figure out the things you need to get a high grade more readily. The struggling students, on the other hand, don’t have the academic savvy to garner high grades.

I want everybody in the class to learn the stuff that I want to teach. Oftentimes, the high performing students don’t necessarily learn the stuff, but instead, learn to jump through the hoops to earn the grades they want. So teaching high-performing students is not that easy, necessarily, because if they can take tests very well, then they can only just do what it takes to get their A and never really learn what you’re teaching. On the other hand, struggling students who haven’t figured out to do what it takes to get that A could be struggling mightily to learn the material, and may have actually learned more than the high-performing students, but the tests just don’t show it, because they’re not expressing what they’ve learned on the tests.

We learn by struggling. Like building muscle tissue from weightlifting, if you don’t struggle, can you grow? In my experience, it’s more difficult to get high-performing students to struggle on the material that you want them to struggle with. I don’t want to give high-performing students more “difficult” stuff to struggle with than other students, because I want everybody in class to struggle conceptual with the material that I am trying to teach. I don’t think that’s done by making it harder, but by ensuring the use of critical thought and analytical reasoning, even in topics that are not considered difficult to learn. I want to make sure that my high-performing students actually struggle. If As come easy to students, then that means I need to find a way to create a way for them to struggle without just giving them more stuff. I want them to find struggle in the things that we are covering so that they actually learn it, and not just be capable of getting an A. You want to create a way in which everybody finds a need to stretch their brains.

Let’s say there are two sections of an introductory course. In Class One, based on past performance, you’ll expect a bunch of students to get As, and the remainder to get Cs. In Class Two, based on past performance, you’ll expect the majority to get Bs, but with a range including As and Cs, and a tail to the left. In other words, in one class you have a clear bimodal distribution, in the other, a clear normal distribution.

In the bimodal class, in the K-12 model for sure, you’re expected to differentiate instruction, to provide support to each group of students in a different way. In a unimodal class, you don’t have two discrete groups in your class with differences in academic performance. At the university level, do you teach these two different sections differently?

That’s a sticky question for me. I don’t know how I’d deal with this hypothetical situation. What do you think?

4 thoughts on “How should the shape of your grade distribution change the way you teach?

  1. I’ve read this twice to try to understand the underlying issues, but I still can’t find a single strand of, well, anything to work with. What a mess! I always sympathized with teachers for this very problem. They are graded based on the grades of their students. I even had one professor (on their last semester at the institution) admit to us that they had been reprimanded because all of their students had gotten A’s and B’s in the previous semester. It was ‘expected’ that some would fail. The administration had a bell curve formula that they used… if you didn’t ‘fall’ into that range, then you were doing something ‘wrong’ (the implication meaning that you taught to the test, or allowed cheating, etc…).

    I think what’s wrong in this and a lot of problems is that we continue to mistake statistics as truths. Means and averages are tools… I don’t think that we should get rid of Grades, but I think that we should remember that Grades are just a measurement, like a ruler, or a tape measure, or graduated cylinder… we are letting the wrong thing lead… and we are being bullied by those above into thinking that it is important, because they are threatening to fire people that don’t fall in line.

    I wish you well. I am working with similar issues, but just a different venue.

    Thanks for the post.

  2. I too recall that old conversation but can’t find it just now. As I recall (and I may not), it sprang from a discussion of “lecturing is unethical” rhetoric, specifically the argument that lectures put certain groups of students at disproportionately high risk of failing the class…

    A few thoughts:

    -I’m both surprised and horrified to hear of places that require grades to conform to a particular distribution shape!

    -I’ve never seen a bimodal distribution of marks in any class I’ve taught. I’m sure they must exist, but I suspect they’re pretty rare. I take it you’ve never encountered one? Your hypothetical might be, um, pretty hypothetical.

    -If I ever did encounter a bimodal mark distribution, my first instinct would be to see if there was some obvious difference between the students in the two modes, and then proceed accordingly. For instance, imagine a course which students can take if they have either one of two prereqs, and it turns out that one of the prereqs is now being taught differently and so no longer is adequate preparation for the course. So all the students with the now-inadequate prereq are doing poorly, while all the students with the still-adequate prereq are doing well. As another hypothetical example, if part of the class has a roughly normal distribution of marks from As to Cs, while the rest failed or got no mark because they gave up on the class and stopped showing up, I’d try to figure out why some students were giving up and do something about it.

    -It hasn’t been my own experience that students who get high marks are mostly just learning how to do well on exams rather than actually mastering the material. But your mileage may vary, I’m sure.

    -How to best teach a class in which there’s likely to be a wide range of student performance is indeed challenging. But I guess I see that as challenging independent of the shape of the distribution of marks. A normal-ish distribution with a high variance is about as challenging as a bimodal distribution, to my mind. Either way you have some appreciable fraction of students whom you can expect to really master the material, and an appreciable fraction whom you can expect to struggle badly. I agree with you that the way to deal with this is to ask questions that all students will have to think their way through. Some will inevitably think their way through better than others. But nobody’s going to get an A solely through being better at memorization or solely through being better at taking tests. And hopefully nobody’s going to be bored or feel held back. In theory, having them think through problems in small groups comprised of mixes of students (stronger and weaker ones) could help pull up both groups without holding anyone back. But in practice, the first time I tried it it didn’t really work (

    -At the university level, I don’t think you can do differentiation within a single course, though there are ways to do it across courses. For instance, think of intro science courses for majors vs. non-majors. Or think of how some places have lab courses with “honors” lab sections, for which only honors students (those with a sufficiently high GPA, or whatever criterion) can register.

  3. Hi, I have a problem and I’m not sure who to ask… this seemed like a suitable post to ask on.
    I’m… you’d probably call it a ‘junior’ in college, studying science, and I was just wondering: what’s an appropriate way to tell a professor before the end-of-year feedback that his teaching could use some work? I mean, I’m all for giving feedback to help teaching staff improve for next year, but I’m not that altruistic – I need him to be better now. We are talking a reading-off-the-Powerpoint-counts-as-teaching, no-office-hours-or-available-time, doesn’t-answer-questions-in-class, tells-you-what-he-thinks-you-don’t-know-rather-than-what-you-really-don’t-know professor teaching the hardest part of the course, and then setting assignments involving calculus that only the lone physicist in the class can actually handle. (The physicist isn’t me.)
    What can I do? This guy is teaching my major subject; I need to pass this course and the professor is not helping.

  4. I just added a blog post on “Precarious Physicist” about this:

    “Teaching A Class With A Bimodal Distribution — If You Have One!”

    The summary is:

    You may not have bimodal distribution at all, just statistical noise on a normal bell curve.

    If you do have a bimodal distribution, see if you can isolate factors giving rise to this, and try to address weaknesses of the underperforming students.

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