Updating an alternative grading system after a 6 year break

What's changed, and why I'm changing it

Photo by Markus Winkler on Unsplash

I teach a lot of calculus. Or at least, I used to: From 2014 to 2018, I taught Calculus 1 or 2 almost every semester. Along the way I created and refined an alternative grading system to use in those classes that I was very happy with. But then I started focusing on other classes and haven’t taught calculus for the past 6 years.

I recently learned that I’ll be teaching Calculus 2 again in Fall 2024. So I dug out my old Calculus 2 syllabus and read through it, planning to see how I might update the grading system. Turns out, I’ll be throwing it out and starting over from scratch.

Let’s take a look at what I used to do, what I’m planning to do instead, and why I’m changing so much.

What I used to do in Calculus 2, and why I don’t like it any more

My previous Calculus 2 system, which I’d used for (pauses to count) 7 semesters, is basically Standards-Based Grading. In retrospect, one of its biggest flaws was that I tried really hard to wedge everything into a Standards-Based Grading format, even when some of those parts really didn’t play to SBG’s strengths.

I had a list of standards (which I called “learning targets”) and then aligned every assignment to one or more standards. I most recently had 34 standards. In retrospect, that’s way too many, which in turn drove some of the poor choices that I’m now throwing by the wayside. The standards were divided into two categories: “core” (21 standards) and “supplementary” (13 standards). The idea was that “core” targets were the main class topics – the things required by our syllabus of record, for example – while “supplementary” standards were extensions or stretch topics.

To earn credit for a standard, students needed to show “mastery” (a word that I’ve moved away from) two times on different assignments. To show a higher level of understanding – and to earn a higher grade – students could choose to show mastery one additional time (three total), with the 3rd time coming at least one week later than the previous attempts. I referred to this as “continuing mastery,” and it was really hard to keep track of that one week requirement – in practice I often ignored it.

Where could students show “mastery” of a standard? Here’s the core of what I’m going to change when I teach Calculus 2 this fall. The short answer is that students could show “mastery” almost anywhere: on all kinds of assignments, all over the place.

Here’s an outline of the main assignments in this old version of my class:

Checkpoints: A fancy name for midterm exams. I had four of these spaced throughout our 14-week semester. Each Checkpoint had many questions, each aligned with one or more recently studied standards. Students could show mastery of each standard by having consistently correct work across all problems aligned with that standard (which might appear on multiple pages within the exam, er, Checkpoint). There was also a final Checkpoint which was one last chance to show mastery of each standard. Something I noticed right away is that since I last taught Calculus 2, I’ve moved towards focusing each page of an exam on just one main standard, regardless of whether others might apply – it’s much simpler for both students and for me. If multiple standards apply, perhaps that questions should go on more advanced assessments like Advanced Homework – see below.

Quizzes: Shorter exams with fewer standards. I found that these helped students focus on a few tricky topics. This took some pressure out of the bigger Checkpoints, and gave students more chances to meet each standard. Otherwise, these were graded just like Checkpoints.

Labs: One hour per week, each calculus class would meet in a computer lab. Most weeks, students would work in teams to complete hands-on labs that benefitted from having technology on hand. Teams would write up responses to a structured set of questions and list the standards they thought they’d met. I listed “likely” standards on each lab – in other words, “if you complete all questions correctly in the way I expect, your work will probably earn credit for these standards” – but depending on the approach students took, they might address more or less or just different standards. I’d write a list of which standards each student actually mastered on the returned lab, but if they didn’t tell me they were attempting a standard, they wouldn’t earn credit for it. This was, needless to say, confusing and often frustrating for students.

Advanced Homework: Advanced calculus problems with an additional focus on learning about professional communication. Unlike labs, they were done individually, and held to higher specifications for writing style. These suffered from most of the same problems as labs, but in addition I tried to wedge my writing specifications into a limited list of standards. Students could earn credit for meeting some writing-related standards and not others, just as they could also earn credit for meeting some content standards but not others. Here’s an example of what the standards looked like on one Advanced Homework (note that I called standards “learning targets”):

See that note at the bottom? Again, kind of confusing, and students often felt unsure about which standards they were supposed to be focused on.¹

Online homework (Webwork): Autograded homework for regular weekly practice. I created a homework set aligned with each of the main standards in the class and assigned them once we had covered that standard. These didn’t directly count in the final grade – I’ll say more when discussing reassessments, below.

Guided Practice: Part of the flipped learning model that I used (and which I will keep using), in which students encounter new ideas before class, usually reading the book, watching videos, and attempting a few carefully chosen practice questions to get their hands on the new ideas. I only graded Guided Practices for completion and making a genuine effort, which I recorded as a simple 1 or 0 in my gradebook. While I named the standards that students were learning about on each Guided Practice assignment, they couldn’t earn credit for those standards – the idea is that I wanted students to feel free to struggle, make mistakes, and learn from them without any kind of grade pressure. I still very much like this approach and use it in all of my classes.

Just in reviewing all of these assignments, I’m feeling a bit overwhelmed. There was a lot going on – no question about that.

Reassessments were also handled in a multiplicity of ways. One form of reassessment was simply to offer many new attempts: As you can imagine from above, standards appeared on many different assignments, including Checkpoints, Labs, and Advanced Homeworks, giving students many chances to show their understanding. The marks that students earned on each of these all counted equally: As long as they collected two “M”s (for “mastered”), they had earned credit for that standard. Notice a bit of terminology confusion, too: Students needed to earn two “mastered” marks on a standard in order to “master” it. Um… what does “mastered” mean again?

But there was another option: Once per week, a student could come to an office hour and request a new problem on any one previous standard. To do this, they first needed to complete the corresponding online homework that covered that same standard. This was a (very useful) way to ensure that students had completed relevant practice. Then I would give them a new question from a stack of problems that I had prepared (pre-writing all of those questions was a real pain), and they either worked it out on paper or completed it live on my office whiteboard. I would grade it on the fly and record it as a brand new assessment of that standard. If they didn’t reach the “mastered” level, I could quickly pivot into helping them improve their understanding.

Oh, wait, there was one more option: Once per week, instead of an office hour reassessment, a student could instead revise their previous work on any one standard, from any assignment. I would review their changes, and if it showed sufficient evidence of understanding, I would update their mark on that standard. This was a very popular option that also led to a lot of confusion, since individual problems often covered more than one standard. In addition, I was never really happy with students revising Checkpoint work: What I really wanted to see was them handling those ideas correctly from scratch (this should have been a hint that I needed different kinds of reassessments for different kinds of assignments). Revising a lab was even more confusing: Did a revision count for all students in the group that wrote the lab? Or did they have to revise separately – and if so, was I really learning what they individually understood?

The plethora of assignments and reassessments also meant that students could earn both “M”s on more basic assignments like Checkpoints and quizzes, especially with reassessments. These “M”s counted exactly the same as more advanced labs and Advanced Homework. Or they might focus on group assignments (labs) more than individual ones. This made it hard to be certain about where each individual student’s level of understanding actually stood.

As you can see, there was a lot going on. I was solidly committed to the idea that every skill in the class should be assessed, and that students should be able to earn credit for each skill in a consistent way (mastering it twice, or three times for continuing mastery). That meant that I had to offer a lot of opportunities to master all 34 standards!

Final grades were also complex, requiring a mix of “core” and “supplementary” standards, each at “mastered” vs. “continuing mastery” level, plus completing a certain number of Guided Practices. There were lots of ways for students to miss one small requirement out of many, and thus not earn the grade they thought they’d achieved.

But that’s not to say that this was a bad system. I used it for many years and saw most of the usual benefits of alternative grading, especially the way that it encouraged students to try, struggle, keep learning, and eventually succeed. Many students loved it, and I got lots of great comments. Especially 6 years ago, very few people (even here at GVSU) were using alternative grading, and students saw the system as incredibly beneficial.

But when I picked up my old syllabus and started reading it again, I realized there was no way I could use it next fall. It felt a bit like the phenomenon of “bit rot” in computer science, in which code stops working after being ignored for a long time, even if nothing else has changed. As a colleague kindly put it, the real issue is growth: In the past 6 years, my philosophy and approach to alternative grading has grown and changed in some important ways, but this old syllabus hasn’t changed with them.

The central problem with this system was that it was much too complex, largely in a misguided attempt to add many knobs and levers that would show me exactly what students knew and when they knew it. So, I set out to simplify every part of it. Let’s take a look at the new system that came out of that process.

What I’ve changed for next year’s Calculus 2

The first thing I did was reach out to colleagues who have taught Calculus 2 more recently than me. Alternative grading has spread like wildfire in GVSU’s math department (and beyond), and in short order I had 5 different models for inspiration. I’ve been working to distill them into a system that works for me. Lesson: There’s a great community of alternative graders out there — lean on it! (Here’s a link to a bunch of resources I put together for alternative grading in general.)

My key goal in creating a new Calculus 2 alternative grading system was simplicity. Here are the key things I’ve done:

Simplify the list of standards: My current draft has just 14 standards, down from 34 earlier. These standards are a bit broader than my old ones, but more importantly, I cut out a bunch of unnecessary standards. There are plenty of topics² that we can discuss and practice in class, but that don’t need to be assessed individually. I also eliminated any standards that weren’t related to specific mathematical skills, such as writing-related standards (those are replaced with specifications, see below) and “attention to detail.” The idea of “core” standards lives on: The 6 core standards will be required to be reattempted on the final exam, which will lead to a “+” or “-” adjustment on the final grade. I threw out the idea of “continuing” mastery – students will just need to complete each standard twice to earn full credit for it. I’ve found that having students complete each standard twice, plus one extra time for the core standards on the final exam, does a good job of checking that they’ve retained the ideas, especially now that assessment opportunities are a bit more spaced out.

Simplify the types of assignments: With a smaller list of standards, I don’t need as many assignments to cover all of them. I’m simplifying my assignments down to just a few categories that also have nice, student-friendly descriptions:

• Put in the practice: Engagement will be a nearly ungraded category in which students aim to reach a certain number of “engagement credits” by completing (with genuine effort, but not necessarily correctness) activities such as pre-class preparation and online homework. This is based on Robert’s approach to engagement credits.

• Build the skills: Short every-other-week quizzes will be the only place where students complete standards. Each quiz will cover just a few standards, with a pre-planned schedule ensuring each standard appears on at least 3 quizzes before “falling off” (until the final exam, which will be one last quiz covering every standard). I’ll also focus questions on individual standards, rather than scattering many standards across multiple pages.

• Put it all together: Advanced Homework will be similar to what it used to be, focusing on advanced problem solving and communication that combines multiple skills. This will be graded holistically using specifications (not standards) and will be assigned in alternating weeks when we don’t have a quiz.

Labs remain as formative in-class practice only, giving us a chance to practice, fail, learn, and also address “stretch” topics without the pressure of a grade.

Separate standards from specifications: Standards will be focused entirely on discrete, lower-level skills such as computations that can be tested on quizzes. Advanced Homeworks, which address more advanced “put-it-all-together” problem-solving, won’t include standards at all. Instead, I’ll write a short list of specifications for writing and mathematics and grade the work for holistically meeting all of those specifications. Students will earn a single mark on the entire assignment.

This will, based on my experience in other classes, considerably improve students’ understanding of what is expected on each type of assignment and help focus them on productive goals. While it scratched a certain itch (for me) to have a consistent list of standards that applied to every assignment, the results were confusing, inconsistent, and bloated.

Simplify reassessments: Standards will be reassessed by making new attempts on a subsequent quiz – predictable and structured, with no need for special revision or reassessment rules and no office hour reassessments. Advanced Homeworks will be revisable using a token system. That’s it – nothing more is needed! While I loved having online homework “unlock” reassessments, I decided that it was much simpler to move online homework into the “engagement” category instead.

Simplify final grades: By simplifying everything else, my final grades get simplified along with them. Each letter grade will require three specific things that align neatly with the assignment categories: A number of standards completed (on quizzes), a number of Advanced Homeworks passed, and a number of engagement credits (with levels set to ensure that students have multiple pathways to achieve that requirement).

Based on recent experience, this is also a lot easier to explain to students, especially when it comes to explaining why they need to meet all three requirements for each grade: “There are three critical things you need to do to pass this class: Put in the practice (engagement credits), build the skills (on quizzes), and show me that you can put them all together (on advanced homework).”

What’s next?

When I looked at my old Calculus 2 syllabus, I knew I couldn’t use it again. Was I wrong in what I did back then? No, not really. In the past 6 years, I’ve gained a lot of experience as a teacher and practitioner of alternative grading.

I’ve learned more about what works best for my students and for me, especially the value of simplifying and focusing in on what really matters. This gives students (and myself) more breathing room to focus on learning and growing, and less on “playing the game”. What I used to do worked then, but now I’m a different teacher, teaching different students.

So if you end up in a similar situation, don’t feel bad! Just as we tell students, struggle is part of growth and learning. How each of us is teaching today is a direct result of how we were teaching years ago, including the things we’ve learned and changes we’ve made along the way.

1. Plus, what’s up with “I attend to details…”? That was a pretty weird standard, and always one of the hardest to meet. The idea was that it could take up the slack for things like mis-copying a problem, making simple arithmetic errors, missing an instruction, etc. Nowadays, if errors like that happen, I assess the regular content standards directly, without an extra “details” standard like this. I try to decide whether the errors make enough of a difference that the student hasn’t shown appropriate evidence of learning. In many cases, the errors are irrelevant, the student’s work still shows the kind of learning I wanted to assess, and so they still meet the actual standard.

2. Partial fractions, anyone?