A Rubric Masterclass

This blog post introduces a new mini-series from Emergent Math: A Rubric Masterclass. Be sure to check out Geoff’s previous mini-series: Routines, Lessons, Problems, and Projects and Your Math Syllabus Boot Camp.

The past two summers I’ve created Emergent Math “miniseries”. They’re an opportunity to do a deep dive into crucial aspects of the math classroom. Spanning multiple blog posts, I’m able to work through complex ideas. I don’t know if this will be an annual thing, but the Summer break is a chance to do some more relaxed, longform thinking and writing. 

This summer, I’m tackling rubric design and scoring. How do you design a rubric from scratch? What items do we even include? How can we score using a rubric with any kind of accuracy? We’ll also interrogate some of the technical aspects of rubrics, including common vs. specific indicators and learn how to turn our beautiful spectrum of growth into an ugly numerical score that our schools require. Consider this miniseries a masterclass in rubric design and use. This mini-series will be both narrow and broad: narrow in the sense that we’re honing in on one aspect of classroom assessment; broad in the sense that we’ll naturally wander into larger concepts around teaching such as communicating high expectations for students, fostering a safe classroom environment, and building students’ mathematical identity. 

This post introduces the miniseries and offers motivation.

Designing and using a rubric takes time, much more time than merely grading for correctness. Depending on how large the rubric is and how robust the task is, it might take 30 minutes to an hour to design the rubric (possibly more), followed by a not-insignificant amount of time scoring student work against a rubric. In a profession where time is already limited, I’d better make a convincing case that rubrics are worth it. (Note: as part of this mini-series, we’ll also identify ways to streamline your work so over the course of the year, we’re spending less time designing rubrics and more time using them.)

To me, the motivation behind using a rubric orbits around two primary foci: clarity and growth. For students, a rubric offers a clear path to what you are asking of them as their teacher-evaluator. Typical requests for students to “explain” or “show your work” are insufficient at communicating what we actually want students to do. By providing a rubric, we can make our requirements for quality mathematical work plain. Students can review their own work before submitting a final draft to ensure that it meets the standards we have established. A rubric also helps clarify exactly what you, the teacher, are asking for. Most non-rubric scored assignments are scored on the following:

• Is the answer correct? (half-credit)
• Do I see some scratchwork? (half-credit)

Shucks, sometimes even lazier rubric designs are essentially drawn from these two questions. Here’s an example of a “rubric” that I found on a widely used math resource. 

This is a checklist pretending to be a rubric. It doesn’t offer a spectrum of work quality or proficiency. It’s essentially our model of correct-plus-scratchwork. And that’s fine for daily tasks, but it’s not truly a rubric. 

Designing a rubric imparts intentionality into your grading. You have to consider what makes a sufficient explanation. You have to consider what habits of a mathematician are important that we would like to communicate to students. Do you, as I, believe that clarity of argument is an essential mathematical habit? Then you should add that to your rubric. Do you value the writing of complete summative statements? Then add that to the rubric. The standard prompt dangler of “explain” doesn’t capture the specifics of what you want students to do; a rubric can.

The second motivation for rubric usage is growth. A rubric aligns better with the ethos of student growth. Certainly, by allowing, say, re-takes on a test, you’re tacitly encouraging growth; using a rubric makes that encouragement explicit. By design your assessment – and your students’ grade – is based on a spectrum on which students can continually improve. Later in this mini-series, when we’re discussing common outcomes, we’ll even have a tool to identify growth over time. When you pass back a scored rubric, you’re offering students a pathway to improve their work and their score. There’s no mystery on what a student needs to do to improve: it’s right there in the next column of the rubric. And if a student disagrees with a particular score they receive? Great! You have a tool around which you can have a discussion. 

And before we get too far into the weeds of rubric design, let’s acknowledge that it’s probably not practical to assess everything with a rubric. And sometimes, particularly when it comes to practicing skills, immediate, right/wrong feedback is more efficient than awaiting the teacher-rubric score. If I’m backlogged on my rubric grading, students may not get my feedback for a day or two. When students are working through problem-sets, that lag time thwarts my goal of having students hone their skills. 

I also want to acknowledge this is my approach to rubric design. It might not be yours, your school’s or your district’s. I prefer four-column rubrics; you might prefer a three column or single column rubric. The principles contained in this mini-series still apply, but I’ll be modeling the construction of a four-column rubric. This series embodies an approach I’ve codified over time and use with schools in rubric design workshops.

With our motivations understood, we now turn to the mini-series itself. The following are the 6 parts we’ll be diving into over the next couple weeks. 

Part 1: Selecting Rubric Worthy Tasks
Part 2: Establishing Common and Specific Outcomes
Part 3: Defining Proficiency and Moving Outward
Part 4: Scores, scoring, grades, and grading
Part 5: Teaching with a rubric; teaching the rubric
Part 6: Humility in Scoring

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