I'm worried about my career in math education. I'm worried because I'm starting to wonder if it is a fool's errand to attempt to teach math in a way that goes against the mainstream. It's tiring...and I haven't even been doing it long. Our society has a clear, and in my opinion misguided, perception about the nature of mathematics and particularly about the way that mathematics should be taught in schools. I gave a year-end survey last week and, while there were many things to celebrate, students clearly echo the thoughts/opinions of the masses. Generally, I read a lot of things like:
       
        - We didn't cover enough math topics
        - We should have prepared for the STAR Test
        - We didn't do Algebra II (or whatever math we were supposed to be doing)
        - I didn't like when there wasn't a clear/right answer

As you might guess, I try to create a class in which students are doing math. We have worked on some interesting problems this year (How many combinations are there at Chipotle, What is the area of the Koch Snowflake, How can we predict global population, What is the best strategy for the game of Pig, etc) and students have done some really interesting mathematics as a result. Unfortunately, our society views mathematics as a thing and not an act of creating. Our national content standards, for many, serve as a definition of what mathematics is (and, by comparison, what it is not). In schools, society dictates, math should be compartmentalized and taught by transmission; if you perform well on the STAR/SAT/Whatever then you are good at math and if you don't then you're not.

I have tried really hard to open up this narrow definition of mathematics and to provide all students the opportunity to be mathematical every day, yet some of my students don't even recognize what we do in class as mathematics. It's difficult to be a part of a system while simultaneously doing things that run against it. You can't, and I don't, blame students for their outlook on things. I'm not sure my writing here captures the drama of all this, but I find it really alarming that this is what our educational system is teaching students about mathematics and about themselves. As I reminded my students today, the root of "educate" is "educe," or "to draw out." My job with them has been to teach by offering them an opportunity to express what was already a part of them, the ability to create mathematics, to create powerful ideas.
 
 
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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