Reflections on a year of alternative grading
A 3x3x3 reflection on what I did this year, how it went, and where I'm going next
I taught 4 different classes this past academic year, ranging widely across our curriculum. I used a different variation of alternative grading in each. That included Calculus 2 (a service course often taken by first year engineering students in which I mostly use standards-based testing), Communicating in Mathematics (a bridge into advanced math in which I mix and match various grading approaches), Introduction to Mathematical Research (a brand new class for young math majors that I designed, largely using collaborative grading), and finally Real Analysis I (a senior-level course that our majors view as one of the most advanced courses they take, in which I use specifications and mastery exams to assess conceptual understanding).1
So, my year covered a lot of territory. Today, I’m going to try to synthesize a full year of teaching, and especially grading, by using one of Robert’s favorite approaches: A 3x3x3 reflection. I’ll take a look at three things from this past school year that surprised me, three things I learned, and three questions that I have as I look forward to next year.
Three things that surprised me
1. I’ve finally cut down my standards lists as far as they can go. We are always telling new alternative graders to keep it simple, and one of the most common ways that alternative graders fail to keep it simple is by having massive, unwieldy, unassessable lists of standards. Every time I teach a class using SBG, I look for chances to pare back my list of standards to something simpler, clearer, and more sharply focused on the core ideas in the course.
Pretty much every time I’ve planned a class using SBG in the last few years, I’ve sat back, looked at the standards list, and said: “Yep, that’s about as simple as it can get”. But by the end of the semester, I’m making notes about things to delete, standards to merge, and so on and so on.
This year, in multiple classes, something remarkable happened: I removed, merged, or simplified standards and then realized that I’d gone too far – I’d made them too simple! Here at the end of the semester, I’m taking notes on standards to add back in because I might have actually cut too much.
For me, this is truly a landmark.
So while my advice remains “keep it simple” (after all, it took me something like 12 years to get to this point!), I might have leaned into that a little too much this year. Next time, I’ll be adding a few standards back in, but only with thoughtful intent based on the things that I felt were missing from this year.
2. Students really liked “interleaved” deadlines. While deadlines aren’t exactly a grading topic, they’re certainly grading-adjacent. Setting reasonable but flexible deadlines helps make assignments more manageable for both students and instructors.
In my Calculus 2 class, we had “interleaved” deadlines: An in-class quiz or exam every two weeks, with take-home homework due during the other weeks, each having a consistent deadline during the week.2 Near the end of the semester, I surveyed my students about the timing of our assignments. I suggested other options and tried to spell out their benefits, for example: “A shorter quiz every week with occasional homeworks” or “Exams every 3 weeks, giving you more time to prepare, with homework in between”.
Students overwhelmingly preferred the interleaved approach that we had actually used this semester. Maybe that’s not surprising – it’s what they were used to – but their reasoning was enlightening. Students said:
Having one big thing due every week was convenient and consistent.
Having an exam every two weeks felt like enough time to absorb previous material without rushing.
Having homework and a quiz due in the same week, even if the quiz was relatively small, would increase anxiety and decrease their ability to focus on one thing at a time.
Exams that were spaced out by 3 weeks or more would give more of an incentive to put off studying, whereas the interleaved system kept them on top of recent material.
Of course, I scheduled assignments this way because it is a good idea from both a learning and teaching perspective, and I told students this at the start of the semester – but what surprised me is how much they agreed by the end! With confirmation that students find this interleaving beneficial, you can bet I’ll keep using it in the future.
3. My students are starting to read and learn about alternative grading. My department is a hotbed of alternative grading. Our students are absolutely used to it and I’ve often heard them comparing different professors’ approaches.
Nonetheless, I didn’t expect to walk into our student study lounge one day and see a copy of Grading for Growth sitting on a bench! It turns out that one student had bought a copy. A few days later, a different student had borrowed it, and it’s been making the rounds ever since. A few students even subscribed to this blog.3
I’ve had some interesting student discussions as a result. The book has prompted students to think about the bigger picture purpose of grades and grading. With many of these students going on to grad school, I’m excited to think about how their experiences at GVSU might affect their future teaching.
Three things I learned
1. The importance of positive feedback. We talk a lot about helpful feedback. Often, that feedback is meant to correct and guide a student who is still working on learning something new. But helpful feedback can – and should! – also highlight things that a student does well.
I had two experiences this semester that drove home just how impactful positive feedback can be. First, I overheard a few students talking in our student study space. They were expressing surprise – and joy! – at how one of my colleagues gave them detailed positive feedback on an assignment. They were going over it carefully, thinking about what it meant, and very clearly appreciating the fact that this colleague took the time to write about their strengths (while also being a bit baffled by the fact that he’d taken time to do this at all). It’s easy to forget positive feedback as we try to finish a pile of grading, but this overheard conversation reminded me of its importance.
The second experience was a bit more dramatic. At the end of each semester, my department sends “recognition emails” to students who have done noteworthy work. These are meant to recognize those who show significant growth, perseverance, or sense-making, and help us identify students who may benefit from encouragement. Faculty can write a sentence about why they nominated a student, which is included in an email sent just before the start of exams (students are also invited to come to our main office to pick up a pin and a candy bar).
This year, I nominated several students who had shown real dedication to improving their learning. I wrote a brief note to each, essentially “I really appreciated your hard work, questions, and great use of office hours.” During exam week, each one of these students found me and told me how meaningful that nomination was. Each one had a different reason why it was especially impactful – academic difficulties, personal struggles, etc. – none of which I knew about when I nominated them. There’s a lot going on in my students’ lives that is invisible to me.
Going forward, I’m going to make sure that I don’t skip over positive feedback during the semester, on student work, and especially making sure that I take time to recognize and appreciate what students are doing well.
An added bonus: I’m prone to exasperation when I’m grading a stack of work that has a lot of repeated errors in it. While grading exams, I found myself remembering these positive experiences, which improved my mood and helped focusing on giving more helpful feedback of all types.
2. Giving students options can open new doors. This sounds obvious when I write it down. But several times in the past year, giving students options has opened up opportunities for students to really shine in their learning, in ways I didn’t expect.
This was highlighted for me in my Communicating in Math class, in which students assemble a written portfolio of proofs. I grade these proofs using specifications that are focused on both logical correctness and discipline-based writing conventions.
I offer an Excellent mark on these portfolio proofs. There are baseline writing specifications required to earn Successful, and an extra set that must be met to earn Excellent – the extra specifications have to do with finer, polish-your-writing details that are not as essential for students who are just beginning to learn about mathematical writing (but are definitely worth encouraging students to practice with once they have the basics down).
This is fine, although it sometimes makes for mechanical feedback when students ask how to earn Excellent. (“Look carefully at every variable – is it italicized? Are you sure?”)
At one point last semester, while examining a student’s revision of a portfolio problem, I realized that it was definitely excellent work – but it wasn’t Excellent based on those specifications. I had asked students to include some examples illustrating a result, and while doing those examples, this student noticed some patterns and actually generalized the result and extended their proof in a new direction.
This was a perfect example of the curiosity and inquiry that is central to mathematics. While it wasn’t how I had intended for a student to earn Excellent, it was definitely excellent work. Once I realized this, I assigned the Excellent mark and didn’t think twice about it.
One takeaway I have from this is that in future semesters, I’m going to add options for how students can demonstrate excellence. I’ll begin by offering extension problems and open-ended questions that they could optionally choose to answer – not required for Successful, but one possible way to qualify for Excellent. The excellent writing specifications will still be available as another option. Students can take different approaches to earn Excellent, and I want to recognize that!
3. Nothing beats building relationships. If you follow this blog regularly, you might reasonably think that I’ve run out of ideas. That’s because I just wrote at some length about the importance of building relationships with students. There, I wrote about how building solid relationships with students is the best way to deal with the ever-shifting issues that face our profession:
Nothing beats having solid relationships with students. Not the best slides, the most innovative activities, the most alternative of grading systems. If students don’t trust you, none of the rest matters.
Right now, I’m thinking about something related. While reflecting on my recent classes, I was uncomfortable with the atmosphere in one particular class, particularly that students seemed unusually resistant to helping each other during class work times.
In most classes, early in the semester I assign students to work together in semi-permanent “base groups”. These groups sit together in class and I usually encourage them to form a study team outside of class (sometimes going so far as to assign them so that they have some open study time in common). That helps students build a small, friendly, and supportive group within the larger class.
But due to the physical setup of this particular classroom — desks fixed in place in awkward rows — I never got base groups going. To try to approximate these groups, some days I had students choose cards that randomly assigned them to seats, and on other days let them choose where to sit. Neither of these seemed to work particularly well.
What I realized was that, because of this constant scrambling and lack of consistency, students didn’t build new relationships with other students in the class. When they were randomized, they made only transient relationships, and when they could choose where to sit, they chose to sit alone or with existing friends. My role in helping them build new and productive longer-term study relationships was missing.
My takeaway is that I need to find a way to assign at least semi-permanent groups, even in a classroom where the physical setup discourages it, and help students use those groups more productively. I’m thinking of randomizing groups for a few weeks at the start of the semester, then assigning groups for 4 or 5 week, before randomizing again. I’ll have to make a bigger deal than usual about how these teams should work together, both in terms of their physical arrangement, and in how they help each other.
This also reminded me of a bigger lesson: If something isn’t working, rather than tinkering around the edges or blowing up my entire approach to teaching, the place to look is at how I build relationships with and between students.
Three questions I have
1. How do I make take-home assignments more impactful to student learning, especially in the face of AI? Sure, I’ve made some changes to my assessments to try to better confirm what students actually know, but that mostly means rearranging things to make sure students have an in-class check-in on each topic.
I still have take-home assignments in each class. I keep them around because I believe that the work students could do on those assignments could be much more meaningful than anything they do in a timed, in-class setting. This is based on years of experience, helping students struggle and learn as they work on large-scale projects, proofs that take days to discover and polish, and more – all of which can, practically, only happen outside of class.
Many students do get that experience, largely through their own choice to truly do the work and not use AI tools on it. Others, I am pretty much certain, don’t. The solution here is not to move more assignments in-class. That limits the type of assessments that are available to me and cuts out some valuable experiences for students.
I am also pretty sure that the real answer here is basically what I said in the previous item: Establishing trusting relationships with students. Building those relationships takes time, and can be really hard to do in larger classes. But it’s absolutely worth it.
Nonetheless, the pull of AI (and its pull on students’ minds and study habits) is strong. What is my best approach to helping students understand the unavoidably human benefit of taking the time to deeply learn something new? One suggestion by a recent commenter is to co-construct an AI policy with students, to help build trust and buy-in. I’m considering that as a real possibility that aligns with other things I co-construct with students, such as in-class norms and some rubrics.
2. How can I make day-to-day practice more meaningful for students? Here, I’m thinking about assignments that are meant to encourage the kind of regular (and deliberate) practice that helps students “do the reps”, as opposed to the larger and more in-depth assignments from the previous item.
I have rarely focused on “practice” homework in my classes. While I make practice material available, I also don’t make a big deal about it. Sometimes I’ve used free online auto-graded platforms (like WeBWorK), other times I’ve made lists of practice problems available. Generally I’ve counted these towards an “engagement” portion of the grade, with problems checked only for completion.
What I’ve noticed, though, is that I never really emphasize any of these practice problems, beyond talking about the value of regular practice. A few students take them seriously, but most others… well, they do the problems, or they don’t, but that’s all that I know.
What I’m looking for is a way to make these practice assignments more meaningful for students, while also not making them into a chore (and hence encouraging students to auto-complete them).
Here are a few ideas that have been knocking around my head:
Selecting exam questions from a pool of practice problems, with the practice problems assigned a week or two before the exam, but not otherwise graded. This incentivizes students to take the practice seriously, but could create high-anxiety situations that drive students to do unproductive things.
Keeping auto-graded homework, but using it to “unlock” access to certain reassessments. I used to do this in several classes: I had one problem set per standard, and in order to reassess that standard, students first had to show that they had attempted some practice. This worked well enough, but I’m not sure it would put incentives in the right place – I want students to do genuine pre-assessment practice, rather than attempting to patch things up afterwards.
My current best bet is to do something like Joshua Bowman’s homework reports, in which students self-select some practice problems and report which ones they tried, along with including one or more solutions on which they have questions or difficulties (and would like feedback). This gives students more agency, and really foregrounds the importance of asking questions, while minimizing the amount of additional grading for me. It might even encourage some more students to come to office hours—which is a great place to start building relationships.
This is a long-term project for me, and I’ll be experimenting next year when I teach several more sections of classes that use practice assignments. I’ll be sure to report back with my successes and failures.
3. How should I approach my next new class? Next year, I’m teaching a brand new (to me) class: Modern Algebra. This summer will, in part, be devoted to me getting my head wrapped around my fourth new prep in the last two years. I thought it might be interesting to talk through my current thought process about planning this new class.
Modern Algebra is a proof-based upper level class taken by juniors and seniors, but it fits a different niche than any other classes I’ve taught. It fits earlier in the curriculum than the also-proof-based Real Analysis 1, which I taught last fall. I need to be careful to choose an approach that’s flexible and gives lots of cushion to students who are still getting their proof-writing feet under them (and also gives me some flexibility as I navigate this new class).
What kind of alternative grading makes the most sense in this situation? This class has some very specific learning goals that could fit well with standards-based grading. But two things turn me off from that direction. First, SBG feels a little too mechanical, like something that’s more appropriate for introductory classes. Second, this is a proof-based class, and it’s hard to grade proofs using standards. Doing so risks dissecting proofs into a bunch of separate items while missing the big picture of the logical argument.4
Adding to all of this, Modern Algebra is a requirement for our secondary education math majors – a group of students who are often quite nervous about this especially difficult math requirement. But the class is also taken as an elective by many other math majors, some quite enthusiastic about it, so I’ll have students with a wide mixture of goals and career paths. That suggests that I should be looking at using projects and a portfolio, which can give students a lot of flexibility to choose a direction aligned with their interests.
All this makes me think that I should use these main elements in my grading:
Specifications graded homework, probably on a bi-weekly schedule. This lets me assign proofs, to be graded holistically with specifications, as I’ve done in many other upper-level classes. It also leaves the intervening weeks for revisions, my preferred form of reattempts without penalty in this kind of setup.
I’ll do a careful check of the core ideas using mastery exams.
I’ll have a final project that gives students flexibility in choosing a topic of interest.
All of this will turn into a final grade using some sort of bundling system, probably with some flexibility built in: “To earn an A, complete all assignments, earn Successful on all but one homework problems, earn Successful on three mastery exams, and earn Successful on the final portfolio.”
That’s my current thinking, here at the start of summer.
What’s next
As the last item suggested, I’m teaching (another) brand new class next semester. This is something I always enjoy (because it challenges me to grow as a teacher) and dread (because of the extra work, and, y’know, it would be nice to just have a quiet summer). I’ll spend time over the summer trying to integrate all of these lessons as I prepare to teach this class. I’ll be back next school year with more thoughts about it!
I had a luxurious 2-2 teaching load because I also had 5 credits worth of additional advising work for my department, including a portion from a colleague who was on leave.
You can see more about this system in My Go-To Alternative Grading Templates.
Hi!
Also called the “dead frog problem”, a term I first encountered in Beatty’s Standards-Based Grading in Introductory University Physics.