Maybe-Mathematical Musings

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May 22, 2023

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Evaluating Students is Important, Too

There’s a classic dry academic joke that I retell frequently. My entire salary is just to pay me to grade; I do the rest of my job for free.

And this is first an apology for not writing much lately; we just got through finals, and that involves a lot of grading. So I’ve been a little occupied actually earning my paycheck. But it’s also a response to this excellent post by Adam Mastroianni of Columbia Business School on his substack Experimental History. I liked the post, and it reflects a lot of things I think about in my teaching. But I have a couple of big disagreements—in part, I suspect, because we’re teaching in pretty different contexts—and I wanted to write up a quick discussion1 of where I think we differ, and why I think giving grades is important and valuable.

Let’s start with Adam’s framing:

My teaching job, it turns out, is actually two jobs.

One job is instruction. Students and I enter the same room at scheduled times, I perform a series of actions, they perform a series of responses, and then the students leave the room more educated than they were before. This job rules. I like it when my students go “ohh!” and “I never thought about it that way” and “I get it now!” I like when they email me, years later, to tell me how they used something they learned in class. This all makes sense. In fact, I thought this would be my only job.

But I realize now that I have a second job, which is evaluation, or gatekeeping, or, most specifically, point-guarding. I’m supposed to award “points” based on what students do in my class. Students try to acquire as many points as they can, and I try to stop them from obtaining points too easily….

This part of my job makes no sense. For one thing, point-guarding makes students miserable…. For another thing, point-guarding makes me miserable…. Worst of all, the things that make me a better instructor often make me a worse evaluator, and vice versa….

He then discusses three specific reasons one might want to give and/or guard points, and largely dismisses them.

Do we need grades to give students feedback?

Adam says no, and I agree completely. Grades are often the vehicle we use to give feedback, largely because we have to give grades anyway. But you can give feedback without attaching a grade to it. I have taken many dance and music lessons, and they never had grades attached; I still promise you I got, and incorporated, a ton of feedback from these lessons, because that’s why I was there.

Conversely, while every grade comes with some feedback, just hearing “3/10” doesn’t actually tell our students anything useful that can help them improve. The need to give grades often channels our feedback into not terribly useful forms.

Do we need grades to motivate students?

Adam rejects this idea, because most people are naturally curious and if they’re not motivated to learn in our courses, the takeaway should be that our courses suck. But I think he’s a bit too quick to dismiss the importance of motivation.

First of all, people do like getting points. This is what drives the success of apps like Duolingo: people start using Duolingo because they want to learn Spanish, but they keep doing it in part to keep their streak alive and keep earning the fundamentally meaningless Duolingo XP. People find it surprisingly motivating to get a gold star and a verbal pat on the back, and “10/10” is one way of doing that.2

But I think I have a more substantive difference from Adam, which is shaped by the specific courses I mostly teach: introductory “gateway” math courses like calculus and linear algebra. I think these subjects are fascinating! (That’s why I became a professional mathematician, after all: I like math!) And in upper-division courses, “isn’t this cool” is actually pretty adequate to keep students engaged. (Most of my grad school classes had essentially no grading, and that was fine.) So it resonates when Adam says:

[I]f people need some extrinsic motivation to engage in my class, one of two things might be happening. Maybe they’re just not interested in what I have to offer. That’s fine! They should take a different class.

But most of my students aren’t taking calculus because they think it’s cool. They’re taking calculus because they need to know calculus to do other things they want to do. Their motivation is already extrinsic! And that creates a big problem of akrasia, because in the long term they want to have learned calculus, but in the short term they don’t “want” to sit down and do a bunch of exercises.3 And if you’re not doing exercises, you’re not learning math.4 A little bit of week-to-week prodding is valuable.

Moreover, I teach a lot of freshmen. They generally haven’t figured out how to manage themselves in college yet, and having some gentle guide rails (and metaphorical gold stars!) is really helpful.

Do we need grades to separate good students from bad students?

Adam just says he’s not interested in doing this: “What am I going to do, send the good students to heaven and send the bad students to hell?” And emotionally, I sympathize a lot. All my students are my students, I want the best for all of them, and I have no desire to draw judgments on their characters, or worth as people, or anything like that. Hell, I don’t want to evaluate them at all! Grading sucks!

But this is where I come back to the joke I started with, a bit more seriously. I don’t like grading, but it is a large part of what I’m getting paid for. Adam denies this:

Ranking my students doesn’t help me teach them, so I have no interest in doing it. But I understand why other people want me to do it.

In fact, they’re counting on it. Businesses need to decide who to hire, graduate schools need to decide who to admit, and scholarships need to decide who to fund, so they’d all appreciate it if I identified the best students for them. I can’t help but notice, however, that none of those organizations pay me. They pay headhunters, hiring managers, and program officers, after all, so it’s a little weird for me to do these people’s work for them. It’s especially egregious for these businesses and schools to force students to pay huge sums to get themselves evaluated by me, a guy who just wants to teach them psychology but ends up playing point guard instead.

But this is an aggressively shallow reading of the economics of academia. Sure, the businesses who are doing the hiring don’t pay me. But George Washington University does pay me, and they can afford to do that in large part because my students pay them.5 And my students pay for the degree because it gives them a credential they can bring to businesses and get hired.

So those businesses (and graduate schools and scholarships etc.) aren’t paying me directly, but they are responsible for me getting paid. Sure, I’m a guy who just wants to teach them math but ends up playing point guard instead; but that’s why I joke that my salary pays for the point guarding and I do the actual teaching for free.

Evaluation is important

Beyond the purse strings argument, sometimes we do need to evaluate people because we, as a society, need to know whom to trust. We don’t need to send some students to heaven and others to hell, but we do need to send some students to medical school and others to places where they won’t accidentally kill a bunch of people. And Adam fully concedes this at the end of his essay:

But look, we need some evaluation. People have different talents, and they should get opportunities that tap those talents, not just because it benefits them, but because it benefits everybody. If I’m drowning (God forbid), I want to be saved by a lifeguard who’s good at swimming. If I get hit by a bus (God forbid), I want to be operated on by someone who’s good at surgery. If I take a math class (God forbid), I want to learn from someone who’s good at math. For that world to exist, someone, at some point, has to evaluate people on their swimming, surgery, and math.

But he doesn’t want to do the evaluation. And he speculates about the benefits of completely separating teaching from evaluation.

To some extent this sounds appealing. First, because if I could keep my job except without the grading, that would be fantastic.6 Second, because having more uniformity in evaluation would be good: if my “A” isn’t the same as your “A” then this doesn’t do a good job of figuring out who knows math and who doesn’t. This is why a lot of departments do common final exams—and while those sound logistically annoying, I’m basically in favor of them, and that is a move in the direction Adam is suggesting.

And finally, Adam’s plan is appealing because writing good evaluations is itself a major skill, and a lot of professors write pretty shit evaluations. I did a short fellowship with the College Board this semester helping them evaluate the Calc AB AP test, and I was blown away by the quality of the questions and the meticulousness with which they were put together.7 They have a large team of skilled professionals who put in a ton of effort to write an exceptionally good test, which is exactly what Adam asks for, and that’s extremely valuable work.

But while the College Board test writers are great at their jobs, there’s also a reason they wanted to workshop the test with professors: we are, in actual fact, the experts in what skill at calculus looks like! If you want to know if people understand calculus, you need experts in calculus. If you want to know if people have learned psychology, you need experts in psychology. For better or for worse, we need to be in the loop somehow.

Evaluations that don’t suck

But another thing I agree with Adam on is that we need to take evaluation seriously, as its own task. Most professors don’t really think about this a lot, but honestly most professors don’t think about pedagogy all that deeply.

Education theorists talk about “formative” and “summative” assessments. Formative assessments are mostly about teaching you something. I assign weekly problem sets because I want students to do those problems—because if they don’t do the problems, they won’t learn much. It’s not really an attempt to evaluate them. (And to be fair, I don’t think Adam is complaining about formative assignments.)

Summative assessments are the ones where you’re trying to really evaluate your students. And there are a few problems with the way we do those right now, but one is that we haven’t really committed to what these evaluations are supposed to say. Are we judging students on work ethic? On punctuality? On generally being good people?

And honestly, a lot of the time the answer to those questions is just “yes”. But if evaluation sucks, then evaluating “is this student a good person, overall” sucks twice. I don’t want to send my students to heaven or to hell, or try to tell whether they’re “good people” or not. And even if it’s possible, I’m not equipped to do it well.

What I am equipped to do is evaluate whether they know calculus. And that’s my job, right? My students need calculus so they can go take other classes that assume they know calculus. And I need to tell them, and everyone else, whether they do in fact know enough calculus to succeed in their next class.

And once I really embraced this idea, evaluation became a lot simpler.8 It lets me be kinder about some things, and stricter about others, but fundamentally it means I’m evaluating something I’m equipped to evaluate: do my students know calculus?

And that’s what I care about after all, isn’t it?

What do you think? Is grading worth it? Is there a better way? You can tweet me @ProfJayDaigle, make a note on Substack, or leave a comment below.

  1. I also want to experiment with writing shorter posts to intersperse among the multi-thousand-word behemoths that take a month and a half to write. 

  2. You can give me a gold star and motivate me to keep writing by leaving a comment here, or on Twitter, or Substack, or by donating to my Ko-Fi

  3. And when I was taking piano lessons I never played enough scales. This is pretty much a human universal. Good practice is rarely fun. 

  4. I have a lot more to say about this, but if I tried to say it here then this post would become a multi-thousand-word behemoths that takes a month and a half to write. 

  5. Yes, universities have a lot of revenue sources other than student tuition. But most of those sources rely on them continuing to be prestigious universities whose students go on to get good jobs and have successful careers, so I don’t think that changes this argument substantially. 

  6. Actually, the grading isn’t the worst part. Answering emails about the grading is the worst part. One place I agree with Adam completely is that I don’t want to get detailed rundowns of my students’ personal issues, and I don’t want them to have to share them. 

  7. Disclosure: I did a short fellowship with the College Board this semester helping them evaluate the Calc AB AP test. Wait, I already said that. 

  8. I have a lot more to say about this, but if I tried to say it here then this post would become a multi-thousand-word behemoths that takes a month and a half to write.

    No, I didn’t duplicate a footnote by accident. 

Tags: teaching math testing grading mastery grading