The Common Core Standards of Mathematical Practice (MPs) have been available for a while now. They lay out eight habits that mathematicians embody. They’ve been instructive in what to teach and how to teach. They’ve also been helpful in providing a comprehensive vision of what math classrooms can be.
|MP1. Make sense of problems and persevere in solving them.||MP2. Reason abstractly and quantitatively.||MP3. Construct viable arguments and critique the reasoning of others.||MP4. Model with mathematics.|
|MP5. Use appropriate tools strategically.||MP6. Attend to precision.||MP7. Look for and make use of structure.||MP8. Look for and express regularity in repeated reasoning.|
They’re also painfully challenging to interpret and assess. What does it mean for a student to “look for and make use of structure?” And how can we measure student achievement and growth in these areas?
To these questions, I offer a DRAFT rubric. The rubric is very VERY much in draft form. There’s a phrase I heard at a High Tech High PD once – “possibly incorrect and definitely incomplete.” I would apply that sentiment to this rubric. I drew upon a few individuals and a few books and other resources to guide its creation. When I worked for New Tech Network I was part of a team that created rubrics with Stanford’s Center for Assessment and Learning for Equity (SCALE) which helped me craft rubrics for non-content outcomes (while also teaching me just how hard it is to create a rubric).
I find rubrics eminently helpful in understanding what students know and can do and where to go next. Rubrics are as much a scaffolding tool as they are an assessment tool.While I was unable to find a CCSS MP rubric, it’s possible that another, better one exists. If that’s the case feel free to use that one, this one, a combination, or whatever you like. Personally the act of creating a rubric and doing the work helps clarify and challenge my own thinking. At the bottom of this post, I’ve listed some of my other blog posts on assessment and rubrics.
A rubric that accurately and equitably assesses the eight standards of mathematical practice could be a boon for schools and teachers desiring to develop a system of student portfolios, as I often advocate. I would absolutely consider using this DRAFT rubric throughout a school year for your portfolio problems.
I want to acknowledge that this rubric and assessment and teaching of the MPs is probably not top-of-mind for teachers. At the current writing, we’re figuring out how – if at all – we’ll be able to meet with students in person or virtually, whether it’s safe to teach in person during an unrestrained epidemic of COVID-19, while in the midst of a real reckoning with our systemic oppression of communities of color. Also, in education there’s a particular thorniness around assessment and race. Standardized tests are weaponized to prevent access to education and opportunity.
While this rubric is an attempt to move to a more equitable way of assessment, rubrics have also been tools of oppression, and it would be foolish to think that this particular rubric couldn’t be used in such a manner. This rubric is being dropped into an environment which did not ask for it.
Before we get to the rubric itself (which is a DRAFT), I’d like to submit a few principles for rubric use:
Rubric Assessment Principle 1: Approach any and all forms of assessment, particularly rubrics, with a great deal of humility. You, nor I, are the arbiter of student knowledge. My interpretation of student work can differ and be incorrect. Make sure you’re approaching student work with willingness to be convinced that your rubric score may not be the best rubric score.
Rubric Assessment Principle 2: Be aware of your own biases and be aware that you have biases you don’t know you have. Dovetailing from the previous principle, it’s crucial to understand that you have biases. You have racial biases, behavioral biases, and biases around what you value in students and student work. It’s important to acknowledge these biases while also acknowledging you have biases that you are unaware of.
Rubric Assessment Principle 3: Don’t try to assess every row on every problem. Large rubrics such as this one are not meant to be used wholesale. Also, most problems are ill suited to assess more than a handful of MPs effectively. Instead, take a couple of rows for a particular problem and assess those in laserlike fashion.
Rubric Assessment Principle 4: Assessing is not the same as grading. This rubric is not necessarily meant to have score totals afixed to each column. It’s meant to be a diagnostic as well as a pathway of improvement. Grades can stunt both of those goals.
There are many more tips, tricks, strategies, do’s, don’ts and best practices around rubrics, but I’ll leave it at those four principles for now.
I also want to acknowledge my instructional background is in secondary education. As such, I can’t truly say how useful this rubric is at the elementary (or even lower level junior high) level. I’m writing and crafting from a vantage point of a high school teacher. Also, one of the things I really struggle with when creating a rubric is that first column (in this case, I’ve dubbed it “Emerging.” I end up using more negative language than I would care to: “fails,” “does not,” etc. Right off the bat, I know that’s something I need to improve about the rubric.
At this point I’d like to state that I’m by no means an expert. Maybe I’ll be able to claim expertise when I complete my PhD program (which I’ve yet to start), but for now I’m just someone who’d like to have a good tool to assess and teach the MPs, and currently I’m not able to find a satisfactory one. It’s very possible (probable) I’ve misinterpreted the MPs and how they show up in student work. I genuinely struggle with differentiating between MP7 and MP8. It’s quite possible this rubric isn’t particularly useful in a virtual environment. It’s certainly not top of mind for most educators right now. However, I wanted to put it out into the world so that A) you’d have it for the following school year, particularly if you intend to use some sort of portfolio assessment system, and B) so that we can improve it. I hope you’ll offer the gift of constructive feedback so we can make this tool more useful, more instructive, and more edifying for a student and teacher.
Some of the MPs (and therefore, the rubric indicators) are as much behavioral as they are artifactual. For example, how do students demonstrate “perseverance?” Unless you have students journal about their problem solving experience (which is an entirely valid task) it is hard to measure “perseverance” based on the student work alone. You may have to assess that row based on conversations with students, evidence based observations, or other method.
Now let’s get to the DRAFT rubric. You’ll find a google doc and PDF version below.
- CCSS MP Rubric (Google Doc)
I’m certain I’ll write follow-up posts on how to use the rubric (which is a DRAFT): ways of assessing, potential problems, and the like, possibly even with some example calibration exercises. Also be sure to follow for any edits to the rubric (since it’s a DRAFT, after all), based on feedback. Here are a few of my posts on rubrics and assessment that may be instructive.
- Equalizing practice and assessment (Part 1)
- Equalizing Practice and Assessment (Part 2): What You Value Should Be What You Assess
- Specifics before Strategies (the creation of a rubric)
- Your Student Portfolio System Begins Now
- Portfolio Problems: Rebuilding Assessment with Rich Tasks
- Assessment via audibles