Why I Don’t Try to Assess the Mathematical Practices

[A grade is] an inadequate report of an inaccurate judgment by a biased and variable judge of the extent to which a student has attained an undefined level of mastery of an unknown proportion of an indefinite material.

-Paul Dressel

The Standards for Mathematical Practice articulate eight very important skills that I hope my students are better able to exercise as a result of their time in my class. They are the goals I care most about in a given course. But I choose not to assess them, in the sense of assigning any type of grade based on students’ mastery of the practices. A few reasons why:

I’m Unreliable
I have all kinds of shortcomings when I try to assess what students know. I’m not terrible at deciding whether a student knows how to graph rational functions. But that unreliability is exacerbated when I try to assess something like “reason abstractly and quantitatively”. I’m going to end up inconsistent, I’m going to miss important information, and my assessment is difficult to attach to an objective reference point.

They’re Context-Dependent
“Mathematical modeling” is not one skill; a student could be great at modeling with linear functions and terrible at modeling with exponentials. This creates two problems — first, I’m making arbitrary decisions about which areas I want to prioritize in my assessment; and second, I’m giving an assessment that may not transfer to a new context. Doesn’t seem fair or helpful for students.

Assessment Creates Incentives
Whenever a grade is attached to anything, it creates incentives. I can live with creating incentives around learning logarithm rules. And, at some point, we will be finished learning about logarithm rules in my class, and I will feel comfortable attaching a grade to that learning. But students are never finished learning how to “construct viable arguments and critique the reasoning of others”, and attaching incentives to the learning of something as nebulous and challenging as argument is likely to incentivize shortcuts and create motivation problems.

Assessing Soft Skills is Time-Consuming
This by itself isn’t a reason not to assess the mathematical practices, but given everything else I could be spending my time on, if I’m not sure of the value of something, I’d love to put that time into finding and sequencing great tasks for my students.

Kids Prior Experiences Vary Enormously
Let’s pretend that I can assess the practice standards accurately. Say kids’ skill in “look for and make use of structure” varies from 1-10. Some kids are coming into my class at a 1, while others may come in at a 7. It’s pretty hard to move the needle on something as broad as the mathematical practices. Maybe I can move some kids a point or two, but if I’m being honest with myself, those gaps are likely to be impossible to close in a short year.

What I Am Interested In Instead

I don’t want to attach any type of formal assessment to the mathematical practices, but that doesn’t mean I don’t value them. Here’s what I do want to do.

Narrate the Practices As They Come Up
I want to make explicit whenever I see the practices in action, both to clarify what they are, and to model or use students as models of what it looks like to “attend to precision”. I want to make this an ongoing part of the language in my class, so kids are as comfortable talking about the practices as they are talking about content.

Student Reflection
I make the practices explicit, and I want to ask students to reflect on areas they feel comfortable in, and areas they’d like to improve. I have a one-pager that is meant to translate the practice standards into more kid-friendly language. I want students to spend time thinking, in a low-stakes context, about what the practices are and what they look like in math class.

Get Assessment Out of the Way
I have to assess students on something, so I’ll assess them on concrete, context-specific skills that reduce my inherent unreliability and bias and create a more level playing field. I also restrict grades to assessments on these skills so that for the majority of class time we can focus on doing math — on putting the practice standards into practice, reasoning, finding patterns, arguing, and figuring things out. That’s the work of mathematics I want to prioritize in my class.

2 thoughts on “Why I Don’t Try to Assess the Mathematical Practices

  1. davidgriswoldhh

    This is basically what I do. My only problem with it is the student who is weak on skills but great at practices. I always have one or two. They improve the conversation of their groups and class, help us go deeper, then end up with low grades.

    Reply

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