Assessing the 8 mathematical practices

Like Fawn, I’ve been thinking about how to assess the 8 mathematical practices. Eventually I will want to “grade” them, but at the start the students will need opportunities to practice the practices. In addition I can’t just let them practice without giving them feedback. So I’m going to use this ASCD resource to drive my formative assessments, It provides a great framework and walks through the entire process using the Boomerangs lesson, a high school MARS task.

As you can see the feedback is mostly through written questions. When I first read the section on suggested questions I was thinking, “They sound a lot like the 8 mathematical practices.” For example the issue of difficulty in getting started could fall under the math practice of making sense of problems.

questions

These questions and my comments will hopefully provide the necessary feedback for students to improve on the mathematical practices, but I’ll have to do it on a regular basis for the feedback to be effective. Plus I’ll have to provide them with a rubric. Our district created this rubric for students and teachers.

practice tool

In the fall I’m going to focus on only two or three practices to start with, then add other practices. I’m stealing that idea from language arts teachers who use Six Traits of Writing. From what I understand middle school language arts teachers only focus on a few traits at a time.

What I’m also planning on doing is using this recording tool for anecdotal, informal observations. Sometimes I feel like a mad scientist walking around with a clipboard and jotting down my observations but I’ll have to get over it. The tool and rubric were created last month so I have not had a chance to take them for a test drive.

Assessing the math practices will be new to me. If you have experience or see some red flags feel free to chime in.

Update

I’m beginning to get incredible feedback. Your comments deserve attention so I’m placing them within the post. Please continue to share your thoughts.

  • Assessing them is not about “can they” do a specific SMP, but “do they” and can they eventually do so habitually?–Just one of Jessica’s suggestions.
  • Reading their reflections not only gave me great insight into how the students believed they were using the practices but also how they were beginning to think about solving problems in general–Jennifer shared her blogged about journaling.
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16 thoughts on “Assessing the 8 mathematical practices

    1. Hi Kristin,

      Our director of assessment provided the rubric and it’s designed to include each of the eight mathematical practices. Did you have something in particular in mind?

  1. Hi, Mary.

    I had my students write journals this year about using the practices while they were learning mathematics. Reading their reflections not only gave me great insight into how the students believed they were using the practices but also how they were beginning to think about solving problems in general. I wrote a blog post this afternoon about some of the journals.

    http://easingthehurrysyndrome.wordpress.com/2013/06/19/standards-for-mathematical-practice-student-journals/

    Their reflections are only a start … your idea to provide students with a rubric is even more helpful. Thanks so much for sharing!

    Jennifer

    1. Jennifer,

      I love your journaling idea and I’m developing a crush on Franky, Hannah, Emilee and all of your students! I could incorporate reflection on a regular basis when we discuss the use of a particular mathematical practice. Thanks so much, Jennifer!

  2. I am literally sitting in a training right now that is talking about how to assess the 8 SMPs. 🙂 There’s a difference between teaching a lesson that provides students an opportunity to use the SMPs and teaching a lesson that shows students how to do it (i.e. attend to precision) and how to do it better. Instead of using more tasks to allow them to practice the SMPs, unpack a meaningful task and highlight the use of a specific SMP. There’s a level of meta cognition that happens with this approach that does not exist when the students do more tasks. Assessing them is not about “can they” do a specific SMP, but “do they” and can they eventually do so habitually? I’m still wrapping my head around how to do this and what these lessons will look like, but it has been a real eye-opener for me. Best of luck!

    1. Instead of using more tasks to allow them to practice the SMPs, unpack a meaningful task and highlight the use of a specific SMP. Your words ring so true. I need a better analogy than the six traits of writing. Certain writing forms/genres may be better suited to developing a particular trait just like certain math tasks are better suited for particular mathematical practices.

      Another statement you made really caught my eye: Assessing them is not about “can they” do a specific SMP, but “do they” and can they eventually do so habitually? I’m moving that to the main part of the post. That deserves attention.

      1. I agree that this is something that still deserves a lot of attention and discussion. I have been part of this grant that has been working on rolling out CCSS for the last two years and it wasn’t until today that this conversation came up. We actually spent some time writing a “SMP Target Lesson” which was a great experience! I would be happy to share the general lesson idea as well as the lesson that we wrote, but I have to admit that I am new to Edmoto and I don’t know how. 🙂 Let me know what method works for you. Thanks so much!

      2. I will send you directions on posting to the Edomodo community. If you would also like to share your lesson on the blog I would LOVE to feature it–obviously your call.

        Thanks for your interest in sharing.

  3. So much goodness here, and in the comments too, Mary. I think we’ve already engaged kids in the math practices, but not giving ourselves enough credit for them until Common Core comes along. The important piece, as you pointed it out in post, is to do this regularly — so it becomes part of classroom culture.

    My handwriting has become atrocious, so I give kids feedback so much better via typing. Just a personal quirk that I have to figure out. Thanks, Mary, for continuing the conversation!

  4. I would love to hear more about how you record observations on the student log. This is a great idea, but does it turn into you madly checking off boxes instead of interacting with the students and the math. I am guilty of this in so many of my classroom endeavors.

    1. I hope to have more to say about that in the fall. The log was just given to us this spring and I haven’t had a chance to use it. You bring up a good point about the likelihood it would take away from interacting with the students. If I observe over the course of several class periods that would free me up to interact. I want to do it in such as way that that the kids don’t feel like they’re a part of an experiment–if you know what I mean.

      I’m glad you stopped by.

  5. Great ideas here and thanks so much for sharing them 🙂

    In Alberta we have 7 process skills which is similar to what you are talking about here. They are communication, making connections, mental math & estimation, problem solving, reasoning, using technology and visualization. Last year I began assessing some of these formatively and giving students feedback but I this year I want them to be metacognitive about how they use these skills/competencies. Because 7 are too many at one time, I am emphasizing four for the year – problem solving & critical thinking, communication, making connections and collaborating. I feel that focusing on these four will have an impact on the other competencies and positively affect students’ achievement. I am using a checklist like you have created with shorthand codes for my part but this is what I have done to get the kids involved – Each student taped together two twin-pocket folders and labelled each of the 4 pockets with the categories I just listed. Throughout the year I will give students time to reflect on how they have demonstrated these skills and they provide evidence to support their growth in each area. So it is sort of like journal writing and I’ll have to see how it goes. The kids seem to like having this separate ‘evidence portfolio’ and have the chance to explain what they have done and what they think about it.

    1. Trying to assess all of those at one time would drive me bonkers too! I think some problems lend themselves to certain practices more so than others, but I LOVE your idea about focusing on problem solving and critical thinking. Equally important is having the student involved and your idea for students to reflect is wonderful.
      I could always do more reflection. I need to find a better balance.

      Thanks for your thoughtful response!

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