Discourse and Debate

As a teacher, I have spent many years developing my understanding of children in the 7-9 year old range. Now that I have my own child, I find it infinitely fascinating to watch him grow from the ground up. I suppose that was the great interest of Piaget, and in watching my son, I realize he is a unique individual with unique experiences like all children. However, watching him make mathematical sense of our world is both delightful and entertaining at times. He was a late bloomer when it comes to speaking. It wasn’t until shortly after age two that he began really expressing himself verbally, and that we could gain some insight into how he processed his world. We had spent much time counting, especially the 13 stairsteps in our house. Counting to 13 seem to come easily to him, learning three numbers at a time. What was especially interesting was when he first began speaking in 2-3 word phrases and he noticed that both of his grandmas were in the kitchen with him. He looked back and forth out them, and said with delight, “Two gras!” Since then, he has shown how he explores our world mathematically by choosing to count different objects and people. Although he may not really understand the concepts, it is fascinating to hear him use mathematical terms in his daily conversation. He has expressed numbers such as 20 1/2, 100, and 1000, and looked at objects and said, “I’m trying to find how many inches,” as he demonstrates his own form of measuring. His learning is certainly not linear, and he is absorbing far more than what I intentionally work on with him.

So how does this relate to my topic? It is through conversation that I gain insights into my son’t thinking. As a toddler, these discussions are rather short, however, questioning still plays a role. How many do you see? Which is more? How much do you want? The importance of dialogue does not change as children get older. Unfortunately, we don’t have the leisure of much one-on-one time with a classroom full of students, and it is easy to fall into the pattern of teacher talking and students “listening.” However, learning is not a passive role, and without discourse, we don’t really know what students are thinking. Conversations play a central role to eliciting student misconceptions, conjectures, and big ideas. Conversations can allow for us to probe student thinking, scratch away the surface, and develop enduring understanding. Conversations will tell us more than any test alone.

So how do we give students more time to talk? Put them in the driver’s seat. Instead of leading the lesson, pose problem situations that students can grapple with and debate. Be the facilitator, rather than the leader of the classroom conversation. And when kids really don’t agree, then organize a debate. Students love this opportunity to defend their thinking, and it forces them to analyze the nuances of the problem to develop a greater understanding. It is also memorable, which has a lasting effect.

Other tools for giving students more talk time include pair-share thinking frequently throughout a lesson, conferring with students one-on-one, in pairs, or small groups during independent work time, and strategic student share outs. When students are ready to support each other in their learning, I put them in collaborative groups to discuss their strategies and efficiency with concepts. I call these small group  activities “Math Chats.” They are differentiated cards that groups of 3-4 work with to discuss their thinking behind a concept. Students are encouraged to offer different perspectives and analyze how their strategies make the problem friendlier.