Grading for Growth in Geometry: Part 2

Reflections on my gradeless system

Photo by John Macdonald on Unsplash

Last week, I introduced a feedback-focused assessment system that I used in my upper-level Euclidean Geometry class for future teachers. I put only feedback – no grades¹ – on assignments during the semester. In Part 1, I described the structure of the class, what students did, and how final grades were set. 

This week, I’ll reflect on that system and how it played out, and offer bigger thoughts on going feedback-only as a goal and a philosophy. Make sure to read Part 1 first, since most of this won’t make sense without it!

What does gradeless class time look like?

First, and most importantly: I think that I almost managed to remove students’ focus on grades and really dive into learning and growth for its own sake. Almost. This isn’t to say that I failed, but rather that for almost the entire semester, almost all of my students seemed to be truly committed to learning and growth, without worrying about grades. I’m going to begin by describing what that felt like.

To set up a class where I wasn’t at the center, I worked hard to establish a routine. Students quickly learned how things worked: Each day I wrote an agenda of presenters on the board. Those students presented, took questions, and then there was class discussion until we were satisfied with their work. When all presentations were done, I put our textbook under the document camera, and students read and discussed the next few ideas in small groups. When everybody was satisfied with the new ideas, they worked in groups on the next problem in the textbook. When a group thought they had a solution, they volunteered to present, and the process repeated until the end of class.

It took a few weeks for students to get used to this process, but once they did, class began to almost run itself. One of my undergraduate instructors once described this process of establishing routine in an inquiry-based class as “launching the Queen Mary”: At the start, you work and work and work to get the ship moving in the direction you want. Once it’s moving, inertia keeps it going in that same direction, and it’s very hard to change course. Whether through experience or luck, this time our ship was set on a very productive, learning-focused, grade-free direction.

I’m not kidding about the class running itself. One day in late February, I had an unavoidable event during class time.² Rather than canceling class, I asked two students if they would be the “coordinators” for the day. Students were excited about running class “all on their own”. I provided the coordinators with a list of presenters and a basic outline (mostly, which parts of the book to read and problems to attempt), and they took care of the rest. I later assigned that day’s main in-class proof as a homework problem, which from experience I know is one of the hardest in the class. Students did as well or better at showing their individual understanding on that homework than in past years.

Overall, class time was productive, interesting, and filled with “aha!” moments for students. Grades had nothing to do with it, and their absence helped make that atmosphere possible.

A direction for growth

If you paid close attention to the final grade criteria that I posted last time, you might have noticed something unusual: To earn an A, students needed to show “significant growth in a new direction (presenting or writing).” In the past, students have often commented about how useful it was to practice both presenting and professional-quality writing in this class. I wanted to help students intentionally work on one of those areas where they were less confident, and the “direction for growth” was my attempt at doing so. I previously wrote about it in my New Year’s Resolutions.

For the first few weeks, I mentioned the “direction for growth” occasionally, especially how students could choose between presenting or writing. On the first homework, I asked students to choose a direction for growth and explain why this direction would be a stretch for them. I also had them set a specific short-term goal, and a general long-term goal (“At the end of the semester, how will you know that you’ve made significant growth in this direction? What are some ways you will be able to recognized you’ve grown?”) About three-quarters of the class chose to focus on presenting, often citing their future careers as K-12 teachers. Those who chose writing often indicated that they felt confident in presenting already and wanted to work in a new direction.

Every two to four weeks after that, I asked students to do a quick check-in about their short term goal, and sometimes to set a new one. I also asked them to describe progress on their long-term goal. I gave detailed written or verbal feedback on their goals and progress, including specific suggestions for new things to try. Students had one chance to change their direction for growth, around five weeks into our 14 week semester. Only one student changed, with my support.

There were some real benefits to this direction for growth. It gave students individualized goals to work on, and I noticed them doing exactly that. It also gave me specific things to focus on during presentations and when reading written work, which helped me give more tailored and immediately useful feedback.

There was an unexpected highlight for me. It’s easy for me to feel frustrated if I notice students struggling or not performing as well as I’d hope, especially on written homework. “Why are they doing this, we’ve talked about it already!” runs through my mind. This semester, when I noticed students struggling on written work, the direction for growth was a helpful reminder that they were intentionally working on something that was tough for them. Rather than feeling frustrated, I felt excited to be able to give tailored, useful feedback. It was also good to be able to celebrate small successes (like meeting a short-term goal) along with them.

Part of the final portfolio asked students to reflect on their progress in their direction for growth, especially in terms of their long-term goal. This is where I ran into some trouble: While short-term goals were specific and observable, the long-term goals weren’t. Students often observed their long-term growth in internal ways that I couldn’t easily see, like reduced anxiety, increased confidence, and mental organization and focus. These are absolutely positive qualities that students can work on in this class, but they were hard for me to observe.

In retrospect, I should have noticed these hard-to-observe goals early in the semester, but I didn’t think about it. For the most part, students did a good job supporting their conclusions about their growth with examples, such as presentations they’d given. But, I still felt uncomfortable, especially if the student was arguing that they showed growth in a way that I simply couldn’t confirm. I think it’s reasonable to trust students’ judgments about things they can observe in themselves, but nonetheless, this is one place where I worried about the results.

So the “direction for growth” wasn’t exactly an unqualified win, but it’s something I will definitely keep in future classes, with modifications. I’ll work with students to create observable goals from the beginning, especially long term goals. I’ll make it clear that my own observations will be a part of the assessment. But overall the “direction for growth” definitely achieved what I wanted:  to center, value, and support growing in ways beyond the content goals of the class.

General thoughts

Here are some more bite-sized reflections on this class and its feedback-focused grading system.

Things I liked:

• Students really did seem much more willing to stretch, try, fail, and generally do good work without worrying about grades.

• I also felt the differing incentives: It was a joy to be able to deeply engage with students about geometry and not worry about how that would need to be translated into a grade on an assignment, even a grade as simple as “successful” or “not yet”.

• Because students really were focused on learning rather than “playing the game”, there were some unexpected (but good!) results. Later in the semester, some students started to ask me if they could use a revision week to submit work that had never been assigned as homework, but which they wanted to include in their portfolio (e.g. a written-up version of a prep assignment, or a presentation that had never become homework). Yes, they were doing extra work! I didn’t expect this, so I fell back on one of my guiding principles: Let students show what they know!

Things I didn’t like:

• Most importantly, I found it exceptionally unpleasant to have to assign a final grade at the end of the semester. Final grades are never exactly a source of joy, and I felt that even more acutely this semester. It almost hurt to make the final judgments that these grades entailed. I wanted us to be able to keep learning and growing, without this final punctuation mark provided by a grade. It felt almost harmful after a full semester of gradeless growth.

• Students noticed this too. There was a definite change in attitudes at the very end of the semester, as students came back to the reality that they had to worry about a final grade. Questions became more grade-focused (“is this revision good enough?”) and students sounded more anxious about my role in grades in general (“so what do you want us to do for the second essay in the portfolio?”).

• It was a lot of work to carefully observe and take individual notes, even in a class of just 14 students. It was wonderful work, and helped me have great conversations with students. I’ve never been able to give such useful and targeted feedback. But if I’d had even 20 students, the amount of notes and feedback might have been overwhelming.

What did students think?

Throughout the semester, students told me informally how much they enjoyed the class and its reduced focus on grades. Students could also formally comment on the class and its assessments in their final portfolio, and in our SETs (student evaluations of teaching).

In portfolios, there were some extremely positive comments about the class as a whole. Very few said anything at all about grades. Here’s one quick example:

Dr. Clark was there to guide us along the way, but with the presentations of problems and any questions we had, we answered them and came to the understanding as a class rather than the professor just telling us the information. I really enjoyed this and feel like it helped me gain a better understanding of the content because of it.

I’ll take that as a win!

SETs had almost no comments about grades or grading at all. Positive comments generally described the class structure, focus on learning, group work and presentations. Several students mentioned check-in meetings as a positive part of class.

Exactly one student left a negative comment, and it was entirely about grades. I’m genuinely not sure what to make of that comment: The student complained that the class had “optional” parts that, when they didn’t do them, reduced their grade (the student did cite some examples, such as revising past homework). I’m guessing that the confusion came from the fact that students needed to pick and choose what to do to support their final grade argument, but without interim grades as an incentive. While revisions were never required, if a student wanted to argue that they understood (for example) triangle congruences, they needed to identify a problem they’d worked on covering that topic, and revise it if the feedback indicated important issues.

Final reflections

Even with a fair amount of scaffolding and feedback on their grade progress (homework reflections, check-in meetings, portfolio instructions, all throughout the semester), it’s clear that this approach requires quite a lot of foresight and self-direction from students. Thinking ahead about what will be required fourteen weeks in the future, and making individual choices about what to do now, requires students to think differently than in most classes. It’s a different thought process than even in other forms of alternative grading. To help support this kind of self-direction, I’m considering how I could make a gradeless version of a “grade tracker sheet” – perhaps a structured sheet where students can keep track of the various aspects of their final grade, what artifacts might address them, and whether those artifacts need additional work. I’ll be thinking more about this as I plan to teach this class again next semester.

I have another, more fundamental, concern about going gradeless this way. Some students were definitely better at advocating for themselves, and/or were more willing to push back on my own observations during check-in meetings. Some students made strong arguments for a higher final grade than we had discussed during check-ins, and they supported their argument well. But others simply didn’t argue for a higher grade, and one portfolio in particular felt like the student had given up on advocating for themself by the end.

I had a plan to help students build self-reflection and self-advocacy skills: Students had many chances to practice describing their progress in terms of the grade criteria and their tailored goals, both during check-in meetings and in homework progress reflections. But, what I mainly brought up in those meetings were things that I could observe, which tended to focus on C and B grade criteria (which focused on geometric content especially). I think that some students became discouraged with the focus on how they needed to work on those lower-level grades, when they could feel – I think rightly! – how much progress they were making in other areas.

This brings me to another point, more of a self-critique. I took a lot of notes about homework and presentations, and recorded them in my “gradebook” (which was entirely these notes, since there were no grades!). By the end of the semester, I had a very detailed set of notes about a student’s growth over time in these specific, observable ways. I used these notes during “check-in” meetings with students, to give them some direction and feedback, and to compare to student arguments in their final portfolios. All of this was good.

But while I observed a lot of student work during class, I didn’t take notes on it. This would have been the time to notice how students were making sense of new ideas, sharing those ideas, and growing in their understanding. This could have helped support my understanding of student arguments about their overall growth. I should definitely have done this – I could have used the same note sheet that I used for presentations – and it would have helped me feel much better about end-of-semester grade issues. I’ll definitely work to take those notes next time, but as I mentioned above, the amount of note-taking I already did was quite a lot. I hope I’ll have a small class!

In the end, I loved almost all of how this class worked. I will definitely do something in this vein again. During the semester, students really did focus on learning. I could observe how they worked well together, had visible “aha” moments, and genuinely showed growth. It was, overall, the best in-class learning experience I’ve ever had the chance to facilitate.

I feel very similar to how I felt when I first used standards-based grading, many years ago: Despite many difficulties, there’s no way I want to go back. I will need to find a way to make “re-entry” at the end of the semester smoother, take more notes during class, and find better ways to help students practice self-advocacy and self-direction. It’s worth the work.

1. There sure are a lot of meanings of the word “grade”, aren’t they? In this class, I didn’t put any grades on individual assignments. But we did have final grades at the end of the semester.

2. Ironically, it was a university ceremony where I was presented with a teaching award.