Building Modern Algebra: The grading system

Building Modern Algebra: The grading system

In the previous posts about my Modern Algebra course this semester, I've given an overview, written about how the learning objectives are different than other courses, and laid out a map of the assessments in the class. In the process of building the course, at this point we would want to work on the learning activities – both in and outside of the class meeting – and ensure there's direct alignment between the learning objectives, to the assessments (which measure the learning objectives), to the learning activities (which give practice and opportunities for growth in the things measured by the assessments) and then finally to the learning tools and course materials.

But actually I am going to skip to a later part of the process and talk about the grading system in the course. Building the grading system, chronologically, is one of the last things we do in building a course, but since we just looked at assessments, it makes sense to describe it now.

I approached the grading system for this course with many of the same assumptions that I used in building the Calculus grading system and all the other grading systems I've used since adopting specifications grading several years ago:

  1. The grading system should be internally valid, i.e. it should actually measure what it intends to measure. We do this by aligning the grading system with the assessments, which are aligned with the learning objectives.
  2. A student's grade in the course should convey information about what the student knows and doesn't know. I think of it like this: A third-party observer (like an employer or a graduate school) should be able to take the syllabus for the course and the student's transcript, and from that information alone be able to reconstruct a reasonable picture of what the student can do.
  3. The grading system should minimize false negatives and false positives. It should be hard, in other words, for a person to get a bad grade in the course if they actually have mastered the learning objectives; and it should be equally hard to get a good grade in the course if they haven't.
  4. The grading system should be based on the concept that humans learn through feedback loops, and the student's grade in the course should represent what they are eventually able to do after a period of revision and resubmission.
  5. The whole thing should be as simple as possible, but no simpler, balancing simplicity with validity. That last part means that some complexity has to be found in the system in order to ensure valid measurements; having a system where the entire course grade is the result of a 5-question quiz is simple, but you don't want it. But having a highly accurate system that is impossible to understand isn't great either.

As with past courses I've taught recently, I devised a mastery grading system for the course that I think hits all the notes. Here's how it works. Most of this is taken directly from the course syllabus.

First of all, there are no points or percentages on any items. Instead, student work is evaluated against quality standards that are made clear on each assignment. If the work meets the standard, then the student receives full credit for it. Otherwise, they will get helpful feedback and, on most items, the chance to reflect on the feedback, revise the work, and then resubmit it for regrading.

The individual types of assignments are marked as follows:

Assignment How it's marked
Weekly Practice E (Excellent), M (Meets Expectations), P (Progressing), or X (Not Assessable)
Problem Sets E (Excellent), M (Meets Expectations), P (Progressing), or X (Not Assessable)
Daily Prep Pass or No Pass
Workshops Pass or No Pass
Startup/Review Assignments Pass or No Pass
Proof Portfolio High Pass, Pass, or No Pass
Project High Pass, Pass, or No Pass

I use this rubric for Weekly Practices and Problem Sets. It's the same as my former "EMRN" rubric which was "EMRF" before that. I just changed the letter designations.

EMPX rubric
EMPX rubric

The three middle assessments that are graded Pass/No Pass earn marks as follows:

  • Daily Prep: Pass if the submission is complete and done with a good-faith effort to be correct, and turned in on time; No Pass otherwise, for example if an item is left blank or has a response like "I don't know". Mistakes aren't penalized; anything less than a real effort is.
  • Workshops: Pass if the discussion thread reply is clear and substantive, No Pass otherwise. I indicate this on Campuswire by upvoting the response.
  • Startup and Review Assignments: The criteria for Pass vary; most of these are in the form of Blackboard quizzes that require a 90% or higher to Pass.

As for the Portfolio and Project... confession time, I have not figured out how I am going to implement these yet. I've done them both before in different classes, so don't worry. In general, Pass means reasonable standards of professional quality are met; High Pass means all that plus the work is really impressive; No Pass means Pass wasn't achieved. And yeah, I'll get to work on these soon.

A student's final grade in the course is determined by the following table. Each grade has a requirement specified in its row in the table. To earn a grade, the student needs to meet all the requirements in the row for that grade. Put differently, the grade is the highest grade level for which all the requirements in a row of the table have been met or exceeded.

Grade Weekly Practice (M or E) Problem Sets (M or E) Daily Prep passed Workshops passed Proof Portfolio + Project Startup/Review passed
A 10 (out of 12) 5 (out of 6) 20 (out of 24) 10 (out of 12) Pass on one; High Pass on the other 6 (out of 6)
B 9 4 18 8 Pass on both 6
C 8 3 16 6 Pass on Proof Portfolio 6
D 4 1 10 2 Pass on one n/a

A grade of F is given if none of the rows has been fully completed.

As for plus/minus grades, in the past, I set up a nuanced system for determining whether a base grade (A, B, C, or D) gets a plus or minus; if X happens and either Y or Z also happen, then you get a plus and so on. Last semester this became hopelessly complex, and made an already-too-complicated system almost impenetrable. This semester, the plus/minus policy is:

Plus/minus grades: Plus/minus grades will be assigned at my discretion based on how close you are to the next higher or lower grade level.

That's all. I stole this, like a lot of things, shamelessly from my colleague David Clark who has thought very deeply about mastery grading and done extremely great things with it in his teaching. But doesn't that make plus/minus grading kind of a judgment call? Well, yes, but remember that all grading in the end is a judgment call.

We are just at the beginning of the semester, so it remains to be seen if this grading system works as well as I think it's going to – but I have high hopes. It's a significant scaling back of the outright legal code I was using in my courses last semester, a lot simpler to navigate and it doesn't feel like it loses information for having been simplified.

Last semester, my students didn't know how to track their progress toward a course grade, and it resulted in widespread panic and lots of emails after grades were turned in. I thought it was easy to track — just write down the requirements for the grade you want, then write down what you've done, then work on anything that is different — and in a way it was, but the requirements themselves were so hard to parse that many students ended up blindsided. I am making a big push this semester to get students to be more proactive about this. So I brought back the grading checklist I'd used in earlier courses. The one for Modern Algebra looks like this:

MTH 350 Grading Checklist

When you look at it in this form, I think you really see the simplicity of the system and it makes me happy. But to make sure students get it, I made a video for them:

How-to video for MTH 350

It turns out that most students didn't need this because they had just come from courses, like David Clark's upper-level Geometry course, that use mastery grading and both understood and appreciated the gist of how it works. In fact a few of my students asked me before the semester began whether I would be using mastery grading in the course, with the tone You're using mastery grading, right? as if to say they are expecting it and would be pretty unhappy otherwise.

That expectation speaks to a cultural impact that mastery grading is making in our department: After just a few profs implementing it, the word has gotten around and students both want and expect to see this in their classes. And they're right.

Robert Talbert

Robert Talbert

Mathematics professor who writes and speaks about math, research and practice on teaching and learning, technology, productivity, and higher education.