Creating Communities of Discourse: Large Whiteboards

I have talked about individual whiteboards on this blog before. My school bought me supplies and I was loving the various classroom activities. While the grouping questions facilitated good mathematical talk between peers, I was still searching for a method to encourage more collegiality where my role could diminish to interested onlooker or curious participant. 

So I had this brilliant idea. 

Why don't we get group-sized whiteboards created where students could work collaboratively on tasks?

In my mind I had just stumbled upon something uniquely genius, but soon discovered that it had been done by Frank Noschese years previous. 

I set out to plan tasks around this methodology. I was nervous at first, but soon discovered that the students enjoyed the shift in culture. This post is not designed to give you a bunch of whiteboarding tasks, but rather share some of my experiences/revelations from the first two months of using them consistently.

How I Set Up a Whiteboard Task (Classroom Routine)

The class begins as normal. I have some kind of cue (either projected on the board, or spoken verbally) that students do not need to unpack. This saves getting things out and then repacking immediately. 

I use the app Triptico (see David Riley for information) to group the students randomly. Triptico has all kinds of other things, but I have found their timing and grouping apps the most beneficial. Students watch anxiously as their name is highlighted and the groups are created. I allow two minutes to get settled with the new groups. 

The first few times I handed each group a board and markers, but now they just nominate a member of the group. It doesn't take too many tasks until each student has worked with every other. This only strengthens class culture. 

I then have an introduction period where each student is expected to face the front to receive the task. When that is done, they go to work on the board. 

I circulate and question. Sometimes I connect groups together if they have similar thoughts. I have even make a group "trade" if I think some different thought or a leadership change is needed. 

I allow students to take pictures of their work as they go. Often times, students record audio of the discussion as well. I haven't formalized a place to collect these archives, but that seems to be the next natural step in the process. At the end, students erase and return their boards and supplies on their own. 

I always end a task with a discussion. Students are encouraged to present their strategies. During circulation, I always prepare them for this moment. I will say something like, 

"I really like your idea here, and I think the rest of the class needs to know. I am going to ask you to explain it during the discussion if it's okay with you."

If they are really uncomfortable, I will summarize but be sure to continually reaffirm that I am not skewing their thought. Phrases like, "Correct me if I'm wrong" or "I think this is what you meant when" engage the bashful student and they often end up taking over anyway. 

My Three Biggest Revelations Thus Far

• Tasks don't need to be complex for this to be effective

The strength is in the communication necessary to work within this framework. I have taken tasks that I consider to be "rich", but also used run-of-the-mill textbook problems. In each case it is the vibrant discourse created by the whiteboards that opens up avenues for creative and conceptual thought. The large whiteboards are what Di Teodoro et al. (2011) call an effective high-yield strategy. I do believe that good problems are often the basis of good lessons, but math teaching is not simply an archiving process of effective tasks. The structure in which a task is presented determines what type of learning is developed. Large whiteboards are an excellent way to encourage mathematical talk and cultivate deep, conceptual learning. 

• Students enjoy to see and interpret other ideas

I try as much as possible to have students view others' work. Most of the time this is accomplished through the group discussion at the end. There are other times when students will get into informal debates after one glances at another's board. I do not discourage this, but do mediate if it gets heated (which I have affectionately termed, "math beef"). Students will naturally move groups and assume the roles of tutor or participant. Others go out of their way to check work with their friends. I encourage all of these activities. I spark them with questions like, "How is this different?" and "Is this more efficient?" Again, the peer-to-peer discourse is the strength of the strategy. 

• It is always more effective to let a student talk about their thinking

This is the hardest for us teachers to admit, but we need to shut up a lot of the time. In the beginning, I led the summary of the strategies that I saw. I got so excited about the divergent thinking, that I lost track of the purpose of generating conceptual ideas. I now only revoice ideas after students have completed their thoughts. This has made a large difference in their stance as learners. They begin to see themselves as knowledge creators. They question what I do in class more and debate that they have easier ways to complete problems. I always tell them that communicating mathematics is often harder than the solutions themselves, but I insist that they practice it. 

Like any strategy, it needs to be tailored to your style. Whiteboards can be brought out every day or only once a unit. I began by using them as introductions, but now find them in my room about every three days. Their strength lies in the communication conduit they open between students and within students' own mind as the access the necessary metacognition to explain their thinking. Like everything, it is a work in progress and I would love to hear of ways others use them in their daily craft. 

NatBanting

References

Di Teodoro, S., Donders, S., Kemp-Davidson, J., Robertson, P., & Schuyler, L. (2011).      Asking good questions: Promoting greater understanding of mathematics through purposeful teacher and student questioning. Canadian Journal Of Action Research, 12(2), 18-29.