My career as a university mathematics professor goes back 30 years, and it feels like I have spent most of that time grading. My views and practices about grading have evolved over the years, and have run the gamut from ultra-traditional points-and-percentages methods to alternatives like standards-based grading and ungrading. I have given a lot of thought to how and why we grade students’ work at the college level. I even co-wrote a book called Grading For Growth on this subject with my colleague David Clark, and we publish a weekly Substack newsletter about college grading with that same title.
We higher education folk don’t often discuss how or why we grade student work, or talk with our K-12 colleagues about pedagogical issues at all—and teaching and professional practices in higher education are the worse for it. With that in mind, in this article I hope to start a conversation with you about grading by highlighting three overall principles that guide me—an instructor who thinks a lot about grading reform—as I grade student work.
“Grading” for me means more than just marking mistakes and putting a number or letter on an assignment. This is because, for the last ten years, I have used specifications grading in all my classes.
In specifications grading, almost none of the assignments has a point value, and there is no partial credit. Instead, we have quality standards—“specifications”—set up for each assignment that describe what “acceptable quality” work looks like. Student work is evaluated on the basis of whether it meets those standards. If it does, then it joins a list of assignments the student has completed successfully. If it does not, the student can revise and resubmit it. The student’s course grade is based on how many assignments they complete successfully, not on points or statistics.
For example, assignments in my Discrete Structures class include quizzes that cover 14 different basic skills, application-focused homework assignments, and mathematical proofs. A student must demonstrate mastery of at least 10 basic skills, complete at least four homework assignments, and write at least three proofs to earn a B in the class. For an A, those numbers are 13, 6, and 6, respectively. If you’d like to learn more, here is the syllabus for this class, and here are the specifications.
Therefore, “grading” for me is essentially the same thing as “giving feedback.” While I do put marks on student work (either “Success” or “Retry”), the main work I do when grading is pointing out what went well and what needs improvement, so students can do a second (or third or…) draft that is closer to meeting the specifications. So the three principles below that guide my grading are really just principles for how to give useful feedback to students—or anybody else.
When a student turns in work that has significant issues—serious computational mistakes, logical errors, misunderstood concepts, verbal expression that’s unclear, and so on—it’s my responsibility to point these out so the student is aware of them. I need to be kind when doing so, but also to be clear and avoid sugar-coating things. In fact, when giving or receiving feedback myself, I think the kindest thing the person giving the feedback can do is simply be clear and direct.
But there’s a flip side to this principle: It’s not enough just to be truthful about some things. You have to tell the whole truth, and in grading this means pointing out not only what went wrong but also what went right. This means that the good qualities of student work (including obvious effort) need to be pointed out with just as much clarity as the mistakes. When the feedback students receive consists of nothing but mistakes being pointed out, they quickly come to dread receiving it—and eventually may stop reading it entirely.
And I don’t blame them. Any time I’ve ever gotten feedback—as a bassist, or in my promotion and tenure portfolio, or on a piece of writing, and so on—if the feedback is a relentless drumbeat of mistakes, it’s discouraging. While I appreciate being alerted to what I need to fix, I will be more motivated to act on those reports if they are leavened with a few notes about what’s good.
This doesn’t mean you need to praise students for everything they do right. Just a few remarks about anything noteworthy to let the student know their work was not a failure will do. For example: “Thanks for your work on this—it’s clear you put a lot of time and thought into it.” Or, “While there are some issues with your solution as shown in my other comments, you’ve got the right idea and should be able to easily fix things if you use the feedback I’ve given.”
Giving feedback is easy if you don’t care whether it’s helpful or not. My own grading, earlier in my career, embodied this: It consisted of large X’s angrily drawn through incorrect work, exasperated margin comments ending in multiple exclamation points, and incomprehensible abbreviations like “?????” At one point, I had a policy that if a mistake was really bad, I would switch to using a red Sharpie marker to indicate it. I was certainly giving feedback, but it would be a big stretch to call it ”helpful.”
What exactly makes feedback “helpful”? Or, put differently, “helpful” for what purpose? Let’s look at an everyday experience to understand.
My 15-year-old son loves to cook. Sometimes he tries out new recipes for our family. I don’t always give him feedback on his cooking, but when he asks for it, I try to tell the whole truth as I described above. The purpose of this feedback is for him to become a better cook. What’s helpful for him, based on that purpose, is to make sure the feedback is:
Feedback, whenever we encounter it, is “helpful” to the extent that it is instructive. Grading, thought of this way, is a natural extension of our classroom teaching roles. So being clear, complete, and correct is an economical way of describing helpfulness; it describes both good feedback and good teaching in general. And not coincidentally, that trio of adjectives is how we typically describe good student work. In other words, helpful feedback is that which is being held to the same standard as the work we are giving feedback about.
But beware of being too helpful. Being a teacher involves having a natural inclination to help people. But sometimes what we intend as “help” ends up not helping. For example, if I tried to help my son learn to cook by making the meal for him, this is not really helpful. Likewise in grading, sometimes the most helpful feedback we can give is not a direct explanation followed by instructions on how to fix, but rather pointing out issues, providing questions for students to investigate, and letting them work the rest out for themselves.
This last point gets us to the third principle:
Everything significant you have learned is the result of sustained engagement with a feedback loop: You attempt a task with some idea of what a “successful” attempt looks like; you get feedback from a trusted source on that attempt (which typically, at least at first, does not meet that success standard); you then interpret the feedback and make a plan for adjustments; and then, critically, you make another attempt based on your plan. And the loop continues until you are successful.
Most things in life are engaging and fruitful to the extent that they get you involved with a feedback loop. Most of our favorite games or sports, for example, involve taking a turn, seeing what happens, and making a decision based on the results. This is why they are fun. Imagine the game of Wordle, except without the feedback loop, so you only get one turn to guess what the five-letter word is, and you either guess right or you don’t. Removing the feedback loop removes the enjoyment.
I want my classes to be learning experiences that are both significant and enjoyable for every student. So I need feedback loops at the center—this is why I switched to specifications grading, where reattempts without penalty is the norm.1 In my view, the goal of grading is to invite students to join me in participating in that loop.
While I need to be clear, correct, and complete, and tell the whole truth when I grade, I must make sure not to inadvertently shut students down by making snarky comments, insulting their intelligence, overloading them with feedback, and so on. I also have to make sure that my feedback prompts students to respond. For example, “You made an algebra mistake in line three” is just a statement of fact; “You made an algebra mistake in line three; what is the rule about exponents that applies here?” still states the fact but also invites students to continue their work by posing a question whose answer will guide them to the right processes.
Not everyone reading this article may be in a position to implement specifications grading or another approach where reattempts, and therefore feedback loops, are possible. If this is your situation, I encourage you to try reattempts on a small scale; for example, taking one quiz or homework assignment and allowing students to reattempt it once, with your feedback. You might be surprised at the impact that such a small change can have.
There is one overarching belief about grading that governs the three principles I’ve outlined here. That is: the purpose of grading is growth. We grade students’ work not to rank and sort them, or so others can do this (although unfortunately this is how many colleges and universities use grades). We grade because we care about student growth and want to enable and activate it. For me, as a college professor, I’m aware that for many of my students, the class I teach is one of the last interactions they will ever have with formal schooling. After college, learning is something they do for themselves, and the only meaningful goal I can have for my teaching is to give them the tools to learn and grow throughout their lives. If I follow these three principles, my grading can help students move in that direction one assignment at a time.
1. “Reattempts without penalty” does not mean “reattempts without limits.” In my Discrete Structures class, for example, students can revise any homework set they want—but only once. They can revise proofs up to three times a week. Putting reasonable limits on reattempts is essential to maintain a manageable workload!
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