My Discovery-Based Math Elective: Grading and Feedback (Part 5)

This is part 5, of a 15-part series of posts detailing how I developed and piloted a discovery-based high school math elective. The first, introductory, blog post for this series can be found here [Introductions]. The goal of this post is to describe how I used the standards discussed in the previous post to guide grading, assessment, and feedback.

I have always tried to be as competency- and standards-based in my grading as possible. Standards-based grading is complicated, and I know that this grading/assessment system I'm describing below has some problematic features. This is the best version I've got so far, after a few different iterations, and it's functional, though far from ideal. I already wrote about where this rubric came from, so let's talk about how I used it for grades.

Link to the PSet Rubric Shown

• How it was used to generate grades
• I wanted grades to be as simple as possible. When I was in high school, I never had a particularly clear understanding of what my grades were. There were so many little assignments, of varying weights, all I could really do was try my best on each assignment, and hope for the best. This experience contrasts with that of my college grades. Especially in my math classes, how your grade was calculated was typically pretty clear. There were maybe a couple midterms, of a given weight, and a series of problem sets, each weighted equally. That's it. So that's what I wanted to recreate.
• I graded each student's notebook once a week. I grade each PSet individually, using the above rubric. The evidence I used to base my assessment on was the work that was done in the notebook, as well as notes that I had taken on my circulation notes tracker. I would grade the PSet on a scale of 0-4 for each of the four sections, for a maximum grade of 16 for the whole PSet. Each PSet had the same weight.
• I would print the rubric out on a half-sheet of paper, and then tape it onto the next blank page of their notebook, right after the last page of their work for that PSet. I did this because I wanted the grades to be kept in the notebook, right next to the work itself. I also didn't want to write out the same thing over and over, and figured it was easier to just print out a blank rubric and tape it in. 
• The one thing I will say is that it felt especially important to keep up with the PSets, and grade them every week, since they were basically the ONLY thing I graded. Students at my school are used to having multiple things go into the grade book each week, and missing one PSet means that a kid is going two full weeks without any grade development. Some students cared about that more than others, and I probably cared about keeping up more than they did. A weekly routine felt nice.
• Having to grade physical notebooks meant that it was hard to take things home to grade, for better or worse.
• How it was used to facilitate feedback
• I tried to use the rubric to provide efficient feedback. I would check off the items they did really well, and then circle the items I wanted them to focus on for the next PSet. When I had some extra time, I'd try to circle and check something in each of the four sections. But usually I would just circle and check one thing each on the whole rubric.
• With an unnatural level of resources, ideally a teacher would have the capacity to leave written feedback in most students notebooks multiple times per week, in addition to the end-of-PSet assessment. Or maybe if a teacher had teaching assistants, they could spend a lot of time doing this? Let me know if you figure out a great way to do this! Definitely another area of improvement for this class. A little bit of good feedback can go a long way, especially in such a open class like this one.
• The primary source of direct teacher feedback that students received came verbally, during our conferences during circulation. I would also provide a little bit of written feedback in their notebook when I graded them. Writing in the notebook after the PSet felt like a "meh" use of time, since there wasn't a really strong culture or system around revising old PSets. As far as I could tell students rarely regarded my feedback. The only time written feedback really seemed to help was when I gave them written feedback on a PSet that they were in the middle of working on. This only ever happened after the first day of a PSet, because I would grade notebooks Mondays after school. So it was easy enough to peek ahead to the work they'd done that morning on the new PSet.

Link to full-sized image.

• You could also choose to wait until the middle of the week to grade the last week's PSet. This has the benefit of taking making it feasible to provide mid-week feedback in students' notebooks. Since you're already going to be flipping through each student's notebook, it wouldn't add too much time to review the PSet they're currently in the middle of, and provide some feedback. Honestly, I wish now that I had done this instead of grading on Mondays. It certainly would have been more interesting to see two or three days of math in the notebooks I was checking.
• If I had a student helper, I could ask them to take each notebook, tape a blank rubric in the correct place in each student's notebook, and then leave it open to the first page of the PSet. That way I don't have to worry about flipping through pages. If you have this available to you, I recommend you do it! Or maybe you can build up the routine that all students tape in the blank rubric, and leave it open to the first page of the PSet. The goal here would be to minimize the amount of time you spend shuffling papers, pages, and notebooks.
• Revisions
• I got nothing for you here. I had an alright system, when I was using Google Slides to compile PSets, but that was seated deep within a largely dysfunctional system of compiling PSets (which I'll talk about later). Officially, the revision policy was that students could revise a PSet at any time before the end of the semester, for up to full credit. They just had to go back, and keep working on it, and circle their revisions, or otherwise indicate what the revisions were.
• Unsurprisingly, no student did this. This is likely because it was really only a token system at best, and I didn't encourage students to use it because I was too aware of its flaws. Circling revisions is an unreliable way of indicating revised work. Students would have already started to do work on the next few pages on their notebook, so the revisions would have had to go somewhere else, which would have disrupted the continuity of PSets in the notebook.
• I'm sure there's a good system out there for revisions. I think the system we had when we transitioned the class to distance learning was alright for revision, which I've written about here [Modifying the Class for Distance Learning]. Let me know if you come up with something though!
• Tests and Quizzes
• Nope. Maybe it makes sense to test content knowledge during tests and quizzes (maybe). But I didn't really care too much about specific content knowledge. And assessing student performance, from a practice perspective, is so difficult on tasks that are supposed to be miniature representatives of a whole chunk of content. I watched Joey Kelly teach the first half of this course as an elective, and two years later I taught the first half, before teaching it again this year. With every iteration there were fewer and smaller tests and quizzes.
• This year's commitment to do away with them was honestly a relief, and I haven't missed them for a second. Moreover, tests and quizzes were pretty unnecessary. Students are doing graded work in their notebook every single day, which culminates in a much more authentic and representative representation of their understanding.
• PROMYS had an interesting practice of having a midterm and final, which were scored, but not graded. Their reasoning was that it was helpful to have students pause every once in a while, and try to review, consolidate, and defragment all the knowledge they had accumulated over the first half of the course. Which makes sense, I suppose. But the actual performance of taking an exam, and then having it scored, feels unnecessary. I'd rather have students just spend a week doing another interesting PSet.
• Projects ("Exhibitions")
• PSets made up 75% of a student's grade. The other 25% was Exhibitions. I talk in depth about exhibitions here: Exhibitions.