This is Part 4 of a mini-series on a rubric masterclass. Be sure to check out the Intro post and subsequent posts.

Before we get to it today, I want to offer a bit of a warning: this piece of rubric-land gets very sticky, very fast. It represents the tension between our aspirations as growth-minded educators and the lived systems in which our classrooms sit. It’s an attempt at minding both of those realities, which can tie one’s self into knots. The technicalness of this blog post stems directly from the fact we want to achieve something with our rubric – accurately assessing students across a spectrum of mathematical skills and habits and using that data to improve instruction – that is in direct conflict with our system of awarding singular numerical grades. By weaving these two forces together we create a technical mishmash. This conversation works better when I can respond to clarifying questions, such as in a workshop or conference session, but this medium doesn’t allow that. So feel free to toss questions and ideas in the comments!

In the last post, I stated that our rubric is complete. That was a bit of a lie though because there’s one more sticky addition we need to consider: turning our beautiful, growth-encouraging rubric into a cold numerical grade. It’s an unpleasant aspect of teaching within a system that requires numerical grades. More and more schools utilize Standards Based Grading, which certainly makes our task easier, but there’s still an inherent, singular number to which our students get distilled.

Which is the exact opposite of the point of developing multi-dimensional rubrics with common indicators. So in this post, we’ll address the aspiration of assessing students in full color in tandem with the lived black and white reality of The Gradebook.

Scoring vs. Grading

I’d like to make a distinction between scoring and grading. A score is the mark you give on a rubric; you identify the most appropriate column for each row. A grade is the number we assign to our score. It’s an important distinction when discussing what exactly we are communicating and how we talk about student assessment. The score represents our best attempt at interpreting student work against our rubric. The grade is the oft-necessary numerical manifestation of that score. The former is an attempt at neutral, evidence based assessment; the latter heaps on value in the form of credit, pass-fail, and grade point average. 

So how do we maintain this distinction and be clear about our commitment to student growth? 

First, we need to retain the category-specific scores somehow, some way.  Maybe our Learning Management System (LMS) gradebook offers a way to us to keep that rubric specific data. Maybe we just keep these rubrics in a physical folder that we can revisit from time to time. Maybe we keep them in a google spreadsheet such as the following. 

This google spreadsheet is an example of how you can record students’ score on a rubric, particularly those common outcomes. 

We now have another decision to make: we need to decide if we want to grade (not just score) the common outcomes along with the specific indicators. We’ve scored the common outcomes. Do you want to assign a grade to them as well? There’s good arguments on both sides. If you do want to grade them, you need to be mindful that we’re going to use these common outcomes again in future tasks and in future rubrics. How are you going to grade on a common indicator in September versus March? If you don’t want to grade common outcomes, how are you going to package the information for students in a meaningful way? 

One split-the-difference approach is to award points to common outcomes, but in a relatively “soft” way. For example, create a grading category in your gradebook entitled “Habits of a Mathematician” or straight up “Mathematical Practices” and assign it 20% alongside whatever other grading categories you have. Be generous with the actual points awarded for this category (more on that in a second). 

Now we come to assigning points for however many outcomes we wish to assign points to. If we are using SBG this becomes relatively straightforward: 

Advanced = 4
Proficient = 3
Developing = 2
Emerging = 1 or “redo”

If we’re using a four column rubric alongside traditional grading schemes, we naturally want the top end to be full (or extra) credit. From there we can work our way backwards to the bottom end. At the risk of inviting hot takes about grading zeroes, I’ll state that I don’t put zeroes at the bottom of my rubrics, I put “redo.” If a student obtains a “redo” I will note the scores, hand them back the rubric and work and ask them individually to redo it. In a traditional grading system, a zero is an invitation for students to give up. It wrecks a grade. I don’t need to tell math teachers that a gradebook with a zero plopped in it can be the death knell for a student. And even if you’re like “you can make it up though” that wrecked grade conveys a uselessness in trying to make it up. So I leave it as “redo” and the assignment as “incomplete” in the gradebook for as long as possible. 

Defining the numerical grade “proficient” and “developing” is a personal preference. You may also wish to assign in-between categories: between, say, developing and proficient. Here’s my example. 

You can check out the fully formatted rubric document here

As I warned at the outset of this post, this process is tricky. I’ll also add this: it should be tricky. We need to wrestle mightily with the system as it is and our hopes for students. It requires extra intentionality, effort, and clarity to convey to students that they are welcome to the discipline of math, while unpacking all of the things they experience that tell them the exact opposite. 

It’s also challenging to get specific when we all have such different backgrounds and systems when it comes to assigning numerical grades. That’s why this series ends with a post on being humble and flexible with your grades. Grades are qualitative data, not quantitative data. So treat them as such. 

Be sure to subscribe to Emergent Math if you’d like to receive every new post in your inbox. If you’re new here, you can check out my featured posts page or other mini-series (Routines, Lessons, Problems, and Projects & Your Math Syllabus Boot Camp).

Additional posts in this mini-series:
Intro: A Rubric Masterclass
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 Grading

3 thoughts on “Part 4: Scores, scoring, grades, and grading

  1. Geoff, thank you! These are great ideas and resources. I’ve been spending part of my summer coming up with rubrics around content, but also with grading. I will be incorporating some of these ideas for sure. I created rubrics for a couple of projects and I’ve found that students do so much better with a rubric. Just reading the rubric and discussing/assessing student progress by referring to the rubric increases student mastery of content and vocabulary.
    I’ve started one for factoring polynomials, from binomials and trinomials to higher-order polys. There’s so much to factoring and I think students struggle with knowing how to approach a problem. I think factoring is pretty skills-based and gets easier with practice, for most students. But to be able to condense it down to one page that serves as part rubric part cheatsheet and hand it out to students to use as a reference as they work, should be helpful for most. Organizing it into a grid was pretty straightforward and I’m hoping it will help students make connections between strategy and problem type. It’s different than just a ‘how-to’ sheet because it’s tied to grades and level of proficiency. It clarifies what I’m looking for when grading and gives us a reference point when we discuss it. When it’s ready, I’ll share it on my blog. 🙂

    1. Totally concur about letting student process the rubric. That’s actually the thrust of the next Part in this miniseries. I can’t wait to see your finished rubric! Be sure to toss me a link!

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