Okay so I’m using this idea of having a portfolio. So far it’s useful because it’s getting students to think about the mathematician’s habits that I try to emphasize in class. What it’s not doing is building too much of a sense of pride into my students regarding their work. But that’s because it’s missing a big thing, aka what’s going to be the point of it at the end? I have completed two portfolios in my day — one at the end of grad school that was basically a bunch of reflections supported by ‘evidence,’ and the other in my senior year of high school, which was a writing portfolio. I haven’t thought much about portfolios in general and have never even seen one used in math classes.
Luckily my principal gave me a book about portfolios the other day when I told him I was planning to use them in my class, so I’m getting a little bit of direction from that. And then I hopefully will expand my reading on it when I’m done with this. (The book is Power and Portfolios by Jim Mahoney.) It’s definitely about writing portfolios, not math. But I do like pulling from other disciplines. TA-ing a choreography class was one of the things that most influenced the way that I now think about running a math class. (In art classes, we really respect kids as ARTISTS, rather than as some dumb kids who have to do some dumb art.)
I’ve only read about 40 pages of this book so far, but already I’m having some thoughts about what I want to do with my class so I thought I’d record them here.
The final product:
The book describes a portfolio with 5 pieces of writing. The students select them, I’m guessing, from the things that they’ve worked on throughout the year, and then put finishing touches on them. This is so hugely different from math class. We don’t write papers. I do have my students make projects throughout the year, and several of them could certainly produce candidates for the portfolio. But I want to also get into the idea that the problems we work on in class — the good ones that you spend half an hour on — can also go into the portfolio. Otherwise, everybody will be choosing from amongst the same 8 or so projects.
Every Friday, I have been asking students to select something that they’ve worked on to put into their portfolio binder. Even though our final portfolio won’t bear any resemblance to these, I think it’s actually going to be very useful to do this. When students are deciding which 5 or so (I’ll decide that … later) things to put into their portfolio, they’ll have a nice selection of work to start from. Obviously they’ll need to do some serious polishing on it, as it’s mostly messy work from class that was not prepared with an audience in mind. They’ll need to not only make it legible but also flesh out their reasoning. The work currently does involve some lovely little bits of thinking.
Of course, this means that I need to continuously ensure that I’m giving students questions that could end up in their portfolios. And also giving them the space to create and investigate their own questions.
I like the idea of each piece also being accompanied by a reflection as well. This again will be so very different from a reflection about a piece of writing. I do want to continue using the mathematician’s habits in this part of the process. As in, part of the reflection would be explaining in what ways the student was thinking as a mathematician. I would prefer not to require them to use the specific habits that I’ve been hyping, as some sort of checklist, even a checklist with explanation. We’ll see if that can work.
Oh also they definitely have to write a cover letter sort of thing and make up a sweet title. And make the whole thing really cute if they’re into that.
The more pertinent bit right now: The quarterly work
I already knew that I wanted this to be graded by the student, a classmate, a family member, and myself. But I didn’t really know what I wanted it to look like. Of course now I’m reading what Mahoney has written about his quarterly assessment, and that helps. I like the idea of writing a reflection over what has happened.
But also they should take a stab at fleshing out one of the things that they have done so far, as I described above. I guess this means that by the end of the year, they’ll already have 3 things that they have worked on (and of course I’ll expect them to make these things even more spectacular after a few more months of developing as mathematicians) in addition to the projects that they work so hard on.
I guess .. the question is how we’ll get the time for it all. I think this can become very important. But I don’t want all the work to be done at home, and already there’s a lot of Stuff that I’m supposed to cram into their brains. Generally speaking I don’t worry too much about the time question, so surely I’m going to charge ahead and do this all anyway, but it’s certainly come into my head.