bansho: board writing and collective knowledge production

One of my math instructors mottos, nay, mantras at the Brock Faculty of Ed is “no fear”. She wants to instill in us aspiring math teachers a positive view of math and to leave any math anxiety scars from our own educational experiences (bells and cells) behind so as not to spread that contagion to our future students.

One of the ways we are taught to do this is to entice and challenge students to love math by engaging them in rich learning tasks and meaningful problem-solving based lessons. Another way to leave the fear behind? Creating a “safe math-talk community”.

 A recent strategy we learned does just that, its called bansho.

Bansho is a Japanese teaching strategy which asks students to solve problems and illustrate their thinking, solve problems in a variety of ways and to identify and explain theirs and others’ strategies used during the problem solving process. The teacher has a central role in organizing the student work to show variety and commonality - the entire “range of student thinking” and to facilitate discourse that guides student reflection and learning about the procedures and concepts used in the problem solving context.

 Last math class we learned by doing a “bansho” by solving the area of an L-shaped geometric shape. We were told to take the “worksheet” (I know what you’re thinking and no, we were not supposed to do a mad minute or drill worksheet quietly in our desks for the remainder of the math class). No indeed. We were told to work cooperatively in groups and to produce as many ways to solve the area problem as we could. For a group of pre-service teacher candidates this was a seemingly easy problem. Everyone knows how to calculate the area of a rectangle, right? Not so. We had to be producers of a variety of ways to solve the problem. This was harder than it sounds. Each time we were solving the problem differently we were to document our work on a new worksheet. As we produced our solutions we were to hand them over to the teacher and she worked hard to review and sort them for the bansho. As we worked, the teacher created “types” or “ways of solving” categories and spread them out across the back wall gallery as “headings” or “titles” (in this case she numbered the ways 1-9). To do this she had to have done some pre-work and thought through the variety of anticipated student responses she’d receive.

 As we (rather factory like, actually) produced our solutions, we naturally glanced around the room, seeing what others were doing (not stealing their strategies, just seeing the volume they were coming up with, this pushed us on in a somewhat competitive, game-like challenge). When we petered out, we gathered at the back where our instructor had sorted our work and was finishing taping up the last examples. She then facilitated a rich discussion of our work, by asking students to explain why they had solved it the way they had. We saw the most “popular ways” and the ways which really expanded our minds as we hadn’t thought of that!

We were able to see commonalities and rarities and everything in between. We started to see neat work, good ways to organize, efficient strategies. We were analyzing work like real mathematicians and this was extremely empowering and engaging on many levels.

I am eager to try bansho with my students in math and in other subjects which require solutions to a problem. This is an innovative, collaborative and creative task that engages the students to think in different ways, to talk about their work (explaining and justifying) and to internalize and understand the work of others in a rich learning community.

Furthermore, as a future teacher, I feel it is important that we teach the 21st century fluencies.  I believe that bansho is a wonderful method of teaching that touches on 3 21st century fluencies: solution, collaboration and information fluency. I am keen to adapt bansho so that it can be carried out digitally and across a broader learning network not just within the 4 walls of a traditional classroom.

For more information on bansho: http://professionallyspeaking.oct.ca/march_2010/features/lesson_study/bansho.aspx http://alibull.edublogs.org/files/2010/01/Ontario-Bansho.pdf http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_bansho.pdf http://southeast1math.blogspot.com/2010/04/what-is-bansho.html