I've written about this "Habits of a Mathematician" Portfolio system before, but I have done some work on it and wanted to post on my updated version. I really want the Habits of a Mathematician to be the centerpiece of ALL that we do in class next year. In my opinion, they really get at what it means to be "doing mathematics" and are useful in helping reinvest in students a sense of agency and authority that is sometimes lost in the mathematics classroom. Of course, some content "knowledge" (I write that with some hesitation) will be an outgrowth of our work on problem-based units, but I'm leaning (heavily) towards not testing or hoping for "mastery" of any of that (the content knowledge piece is a bigger philosophical argument, which you can read about in a previous post).

The Portfolio System

At the beginning of the year, each student will purchase a 3-ring binder with 12 dividers. Each divider will represent one of the 11 "Habits" and the last section will be for "Unit Packets" (all of the other work). Students will have requirements weekly, at the end of each unit, and at every third of the semester. Here is what I am thinking for each:

Weekly

At the end of each week, students will select one piece of work that they feel best demonstrates one of the "Habits of a Mathematician." They will fill out this reflection sheet (see below) and will submit it to me. I will provide short feedback on the sheet and hand it back to them. After reviewing the feedback, the student will submit that work to the appropriate section in their portfolio.

End of Unit

At the end of each unit, students will put together all of their work from that unit (excluding the work that has been submitted as "habit" exemplars). They will complete a unit checklist and write a cover letter for their packet that summarizes the mathematical themes for that unit.

Three Times a Semester

Each student will have a "critical friend;" someone who they work closely with in evaluating their work and their progress. At each 1/3 mark in the semester, students will have their portfolio reviewed by their critical friend, by their parent, by me, and by themselves. With all of this in mind, students evaluate where they are at with the "habits" and set specific goals about how they want to progress.

Grading

I would love for this to be a grade-less system. My students tell me "the world is not ready for that yet." I can't see how it could be done any other way. My thoughts at this point are that grades would only be given at the end of each semester. Student grades would be decided on by the individual student based on feedback from their critical friend, their parent, and me. Mostly, I imagine their grade to be a representation of their progress toward their specific goals set for themselves.


I'm beginning to like this system a lot. What we assess in our classes says a lot to students about what is valued and I think this system more clearly shows students that math is about "doing" and not about "knowing." I worry a little bit about parent concerns but I'm not sure that should stop us from pushing the boundaries and redefining grading. The system is still evolving and I would love any feedback or suggestions you have.
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Comments

05/07/2012 10:47am

Ambitious! Have you tried a mini-pilot of this system yet? It might not be a bad idea to do something small-scale in the time left this year. You could learn about the time it takes, how students take in what you're trying to do, what you're looking at in terms of workload and grading.

Sounds like you need a rubric. Speaking from experience, there's nothing worse that staring at a pile of juicy student work and having no idea how to give them credit for it. Are there 4 or 5 key things that need to happen for you to feel comfortable giving students a grade or incorporating a score for the portfolio into their grade? This would be another good thing to pilot and revise.

I know you've worked hard on your list of habits, but could you use or incorporate the Common Core Standards for Mathematical Practices? There may be people working on activities or suggestions for those (I have a couple of blog posts about them), and that might help lighten the load for you.

Good luck, and I look forward to reading about the implementation.

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Robert Gordon
05/07/2012 8:38pm

Bryan,

I am stoked on this system idea you have because of the fact that it allows all students, regardless of their status in the class at entry point, to be able to set goals, reflect on their goals, and to continue progressing as a learner and "doer" of mathematics.

For some reason I think you do not plan to have a rubric, am I right?..Or if you do, maybe you plan to keep it well hidden from the students.

I, like Belinda, am also interested in your ideas on implementing the Common Core into your classroom. Please forward me to literature you've written on the subject already

Take care and talk to you soon,
-Robert

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05/08/2012 8:36am

@Belinda Thanks for your feedback! I appreciate your push back on implementing a smaller version as well as grounding the grading or "credit" in something tangible to the students. I have tried similar portfolio systems with good success. It can be a lot of work, but valuable in my opinion. The real change with this is that it is entirely focused on the "habits" and relatively grade-less. I really don't think I'm concerned with a rubric in regards to this. I think we often underestimate just how subjective grading truly is. A rubric may create the illusion of objectivity, but we (teacher/student/class) are still assigning value based on what we decide to measure. I am, however, working on an evaluation and goal setting sheet that will guide students in their 1/3 semester checkpoints.

@Robert I know that there is a lot of talk about the Common Core and that this system would probably appeal to a wider audience if it was catered towards the practice standards. My focus is slightly different (although I think this could easily be adapted to reflect those standards by changing the sections in the portfolio). Mostly, the process standards SHOULD be happening in EVERY class already....they are indicators of rich tasks and opportunities for exploration and discussion. My hope is to help students see how they can engage more deeply with those tasks, to restore their (in my opinion) inherent ability to make sense of problems, and to believe in themselves as "doers" of mathematics.

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05/08/2012 11:41am

I love this, Bryan, not only because kids are selecting work by HoM, but the teacher is charged with assigning various rich tasks that allow these HoMs to flourish. (Not easy, but I try!) I think if HoMs are happening, then the 8 Practices are already in them. This portfolio provides a mainstay for the curriculum so that "doing math" is not home decor, it's the foundation/plumbing/electrical of the house itself.

We started electronic portfolios two months ago in my class. You gave me a lot to think about and tweak to something I can manage and follow through. Thank you!

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05/09/2012 7:59am

@Fawn You wrote, "this portfolio provides a mainstay for the curriculum so that 'doing math' is not home decor, it's the foundation/plumbing/electrical of the house itself." I'm so glad that this came across because it is something that I am working hard towards. It has been interesting for me to think about lesson design as I play with this new assessment system. If I am asking to students to develop and reflect on HoM, then it follows that EVERY lesson must offer them an opportunity to engage in them. People often make the case that students learn problem solving through math instruction. It wasn't until I started thinking about this system that I realized just how little problem solving, thinking, and "doing" was actually present in math instruction.

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Rachel
07/27/2012 11:25pm

I absolutely love this idea - the habits you've developed, the reflection questions you've posed, even the look/feel of the reflection sheet. I like - and am intimidated by - how incorporating something like this will force me to rethink my instruction.

I love this idea so much that I shared the idea it with some colleagues, and we're looking to launch a version of this in which kids post their reflections to personal blogs / e-portfolios that they will create specifically for math class. We're borrowing and adapting your reflection Qs - so thanks for getting the ball rolling for us. (Will certainly share with you what we develop, once it's a bit further along, if you're interested.)

Our dilemma: We *do* want to structure this portfolio around the Common Core Standards for Mathematical Practice, as Belinda suggested. (Our administration is into that idea, too. Go figure.) The language of the CC Standards, however, is dense and inaccessible, and we're struggling to pare it down to something that will be meaningful to our kids. I wish those Standards were as concise, and felt as relevant, as the 'habits' that you've developed. Despite all our edits and revisions, we're struggling to come up with something so solid.

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