Last week, I was working with some second graders. We were doing a number talk and one of the students asked if he could use a hundreds chart. I said, “sure”.  All of a sudden, five kids got up and headed to the envelope of available hundreds charts. I watched the onslaught for a minute, wondering how it would work out. The first two students grabbed a chart and went back to their space on the carpet.  Then, two different students grabbed the envelope at the same time, each maintaining a fierce grip while glaring at the other. A third student stood quietly and watched.

“I had it first!” Elise said as she tugged the envelope towards her.

“No. I was waiting here. It’s my turn.” Joseph shoved his hand into the envelope and tried to wrestle one of the hundreds charts free while Elise simultaneously used her free hand to pinch the envelope closed.

I focussed my attention on Charlie, the boy who stood watching. “Charlie,” I said, “Thank you so much for waiting so patiently. It must be really hard to wait when you are anxious to get your hundreds chart and go back to your seat. I really appreciate how careful you are being.”

Elise and Joseph froze. Joseph dropped his hands from the envelope. Elise carefully took one of the hundreds charts out of the envelope and handed it to Joseph. I said, “Elise that was really thoughtful. I know how much you wanted that hundreds chart and you just gave it to someone else. Thank you for taking care of your friends.”  Joseph passed the hundreds chart to Charlie. I continued, “Wow, Joseph. You are also being really thoughtful and taking care of your friends. Thank you.”  Joseph took out a hundreds chart and handed it to Elise. Then, he took one out for himself and they all sat down.

You might be thinking, “well that only worked because Joseph and Elise don’t really have a lot of ‘behavior problems;'” Nope. Joseph and Elise have a really hard time relating to and communicating with their peers.  It is not easy for them to slow down and consider how their actions are impacting the people around them. You also might be thinking, “Well, it takes forever to establish that kind of relationship with kids. You’ve probably been working one on one with them all year.” Nope. I am only in their math class two or three days a week and I just started working with them in March.

I think my response to these students “worked” because I focussed on what the students were doing “right”. I held up a mirror for them. In the mirror, they saw who they want to be. The “reward” for their behavior wasn’t a sticker, a point, or a card. The rewards were feelings: pride, purpose, and gratitude.

Later, during the Number Talk, a different student was sharing his thinking.  Several students turned their bodies around to face that student. I took a moment to recognize their gesture. I said, “I notice you just turned around to face your friend. That shows them that you are really interested in what they are saying and you want to learn with them.” Simultaneously, three other students turned to face the speaker.

After our Number Talk, we  worked on a Same But Different Math problem that I created. As I anticipated, there was some disagreement about which numbers belonged in the blanks. We spent the remainder of class trying to prove whether or not the same number would make these two different equations true.

Some students didn’t get to finish their work before class ended. I decided to continue the problem on Monday. For the lesson close, I asked if anyone wanted to share anything  they had learned so far. Greg was anxious to share. He couldn’t hold it in anymore. He shouted, “I learned I was wrong!”.

“Wow,” I replied, “Tell us more about that.”

He continued, “I thought the answer was 22 and Riley did too, but then Riley thought maybe he was wrong, but he couldn’t figure out why he was wrong. He asked me to prove to him how I knew it was 22. When I started to try to prove it, I realized I was wrong! Riley helped me figure out I had made a mistake!”

“That is really cool,” I said. “That is what mathematicians do. They share their thinking and make mistakes. When Riley asked you to prove it, he helped you figure out what you did wrong.”

Greg grinned, “Yeah! He really helped me.”

Riley chimed in, “Its a good thing because I thought it was 22 too.”

As math educators, we talk all the time about how important it is to get students to ask questions, justify their thinking, and critique the reasoning of others.  If we really want to make this happen, I think we need to pay attention to the mirrors we hold up for our students.  If we use extrinsic rewards and punishments are we building agency or promoting compliance?

I’m not sharing anything new, here. I’m not claiming to be doing anything new and amazing.  I just wanted to take a minute to share Friday’s math class because I’m so proud of these students. In our world at large, where adults are rarely listening to each other with the intention of understanding, I feel an urgent sense of purpose to help young people experience  a respectful community of learners.