My best classroom has a ton of communication is going on: peer-to-peer; student-to-teacher: teacher-to-student; and students-with-themselves. Learning math means learning language, that is, in order to really claim new ideas, learners need to voice them and represent them to themselves and to each other, over and over again. For the first time, I have been able to line the walls of my classroom with whiteboards. The boards are facilitating learning in some surprising ways: Not only do students interact more, they revisit and revise ideas within a class period and from day-to-day.
When I put the boards up, I already knew that whiteboards make fixing mistakes easy. With a swipe, false starts and dead-ends disappear completely. Everyone in each group can see the whole process toward a solution and can be curious about each others’ ideas and help each other. They can also borrow ideas from across the room. All this demands communication and therefore using and learning language to describe what is happening.
What I didn’t realize was the way the boards in combination with cell phones and our on-line classroom management system would invite revision from one day to the next. As the school year started, students began assignments on whiteboards that they would later turn in digitally. At first I wondered how this would feel to them. Would they think they were being asked to do work all over again? As solutions began to appear around the room, I offered to take photographs and email them so that students could revisit their thinking the next day. I expected I might get in a lot of partially finished work in the form of photographed whiteboards. Instead, I am finding that the whiteboard work actually invites revision in some really powerful ways.
Sometimes student transfer photographed thinking to paper, in the process making changes as they learn. They also upload the whiteboard image to the classroom management system and then annotate on top of that, fixing errors or adding explanations to clarify their thinking for themselves and for me.
Recently Ella had painstakingly drawn a 3-D representation of a pattern built with cubes. When she came in the next day, it had been erased by students who had used the board later in the day. She hung her head, discouraged, and then remembered she’d photographed her work. She knew she’d have to draw one more stage of the pattern to illustrate that the algebraic expression she had written would work, but had to think through how she’d do that. I suggested she sketch instead of making a detailed drawing, and pointed to a few places in the room where students had done this. What she ended up turning in was an annotated photograph of her whiteboard work, to which she added sketches, labels and verbal clarifications. Her ideas got stronger and clearer with every revision.
Jason always seems to choose the board, even when working on paper or digitally might seem more efficient. When I asked why, he told me. “I can make my math bigger, and then I can redo it if it isn’t right.” I wondered if it bothered him to have to take a picture and start again the next day.
“Not at all,” he said, “ when I look again, I figure out my mistakes and my partner and I have more of a chance to think about it. Once it’s the way we want, we take a picture and turn it in.”
I remarked that sometimes he and his partner would add different ideas to their own photos before turning it in.
“Yea,” he said, “at the end we may both still see it differently.”
All this is happening without my having to require final drafts, explanations or revisions. Instead of demanding that students show their work or make corrections, I let the walls do the talking.
To learn more about classroom whiteboards and learning language in math class, see:
Liljedahl, P. (2016). Building Thinking Classrooms: Conditions for Problem-Solving. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and Solving Mathematical Problems (pp. 361–386). Springer International Publishing. https://doi.org/10.1007/978-3-319-28023-3_21
Zwiers, J., et. al. (2017). Stanford University Graduate School of Education. Understanding Language, 21. https://ul.stanford.edu/resource/principles-design-mathematics-curricula
I am appreciating the use of “vertical non-permanent surfaces” (VNPS’s) to promote with increased access and opportunity for math thinking, collaborative talking, language development and productive struggle with ideas. Two sentences stand out for me: “Instead (of partially finished work), I am finding that the whiteboard work actually invites revision in some really powerful ways,” and “Her ideas got stronger and clearer with every revision.”