Observing a student working on a whiteboard is the best way that I’ve found to get immediate insight into his or her thought processes. Perhaps because of the impermanence of the medium, students act much more freely than when working on paper. They are more willing to take risks and to potentially make mistakes. Even when writing in pencil on paper, the act of erasing is slower than it is on a whiteboard – it seems like they can think more quickly and freely on the whiteboard, which leads to a more fluid thought process, and less barriers between their thinking and their writing.
I’ve been a huge advocate of students’ use of whiteboards since I began teaching. One of the very first things I do when I move to a new classroom, is to cover as many surfaces as possible with whiteboards. Asking students to stand up and work in a visible way has the immediate effect of increasing sharing of ideas and showing thinking in a public way. And it’s fun and they just really like it.
John Orr’s whiteboarding protocol in his recent “My Favorite” post (Week 2 of the MTBoS 2016 blogging initiative), has filled in a piece that was missing from the work in my classroom. When he groups kids at the whiteboard, he gives each group only one marker. Every few minutes, he calls “marker switch” and whoever has the marker has to give it up to someone else in their group. Sounds simple, and I know that I have read about this somewhere before (I think maybe in Henri Picciotto‘s blog but I couldn’t find the reference), but I never thought that it would have the profound effect that I observed when we tried this. When the kids all had markers, some would inevitably be drawing instead of mathing, most would be doing their own thing, and they would occasionally talk to each other. Providing only one marker forced communication and collaboration in a way that I just hadn’t anticipated. If they wanted to express their idea but it wasn’t their turn to draw, they had to argue for it verbally. I can’t recommend this strategy highly enough, and it has had a very positive effect in my class.
A related, but maybe non-mathy aside: I was an art teacher, both at the college and the community level for years before I got into math teaching, and have continued that work along with teaching math. Most of my life as an artist has been focused on making sculpture, but I did some animation and installation work for a couple of years, which involved a technique I learned from studying the South African artist, William Kentridge. The process involved making a charcoal drawing and taking a photograph of the drawing. The drawing would then be erased and/or altered slightly, and then photographed again. This process was iterated again and again and again (this must be related to my interest in fractals…). The photographs could be played in a sequence, which gave the illusion of motion. Here is an example of an animation of some flying bats, which I used as a projected component of an installation piece.
For me, this process of animation was extremely freeing. I was not afraid to make marks on the page because I knew that whatever I did would be erased soon. There would be a record of the act of making the drawing, and all of the pieces would come together to form a whole, but each individual drawing would only be seen for fraction of a second. I think that kids experience something similar to this when white-boarding. They are more inclined to take risks and just try things because there is no danger of permanence.
Try giving them only one marker! And let me know how it goes.