More Than Just Rock, Paper, Scissors: Relationship Skills to Support Mathematical Partnerships
Carla, an English learner student who was in the Spanish bilingual program the year before, is working with Jerome, a fairly confident math student. Carla has written down an answer, 783 and explains to Jerome how she got her answer. Jerome, has a different answer on his page: 837. He explains his answer, and here is where an interesting thing happens: Although Carla is correct, she erases her answer, writes down his answer, and they continue working on the second part of the problem.
For my inquiry last school year, I chose to explore math partnerships because our math curriculum required students to work together in partners on tasks to solve word problems. At the beginning of the year, I noticed that when I told the students to work together, almost all of them worked on the task individually and hardly talked to or looked at their partner at all. A few students would get into small arguments and then refuse to work together. By mid-year, students seemed to be working together well, but the video data of Carla and Jerome, which I collected to look at with colleagues in our February Mills Teacher Scholars inquiry session, helped me see the complexity of what it really means to help students develop the Social and Emotional skills they need to grapple with content and construct new understandings together.
Introducing and Practicing Relationship Skills
In order to support students’ ability to work together collaboratively, we spent the first few months of the school year talking about relationship skills: what they are, what they look like, and how we can use them throughout the school day to work with one another. During our morning circle I elicited ideas from the class and organized all of their ideas into three main groups:
- looking at and listening to our partners
- offering help when someone needs it
- solving problems in a healthy way
We referenced this poster frequently, at various times throughout the day. Students would choose one way they would try to listen to their partner, help someone, or solve a conflict in a healthy way during a particular lesson or activity. They would share their idea with a partner before starting the lesson and after the lesson or activity they would self-reflect on how they did and what they wanted to work on next time.
After a few months, I could look around the room during a math task and see all of my partnerships working together, talking to one another and getting along. I could hardly believe it– I was so proud of the work we had all done around relationship skills and their visible growth in this area.
Some Illuminating Video Data
In February, Aija Simmons from Mills Teacher Scholars helped me collect the video data of Jerome and Carla working in partnership on a math task about place value. The content of the video was eye-opening.
In the task, students were given three digits. They were asked to make the number with those digits that was the closest to 800, and then place and label the number on a number line.
When she sees Carla erase her (correct) answer, Aija, the videographer, prompts Carla about her first answer. She asks Carla if she wants to have a conversation with Jerome about the answer, and whether she thinks the answer is 783. Jerome waits patiently, looking at her, while Carla sits there silently, visibly uncomfortable.
“Is there a way you could tell your partner you think the answer is 783?” Aija asks.
“Did you want to do that?”
“Do you want to try it?”
She nods and smiles, but then begins fidgeting in her pencil box and continues to not say anything.
At this point Aija steps in to help scaffold the conversation, asking questions such as “Is there a way you could check or talk to each other about the two numbers?” She continues, “So we have two numbers, we have 837, and we also have your idea. How could we talk to each other and see?”
Jerome steps in at this point to suggest they could both agree on one. Aija asks how they could do that.
“Uh… the easiest way is to rock paper scissors and just figure it out,” Jerome says. “Or, we could look and see which one is the closest….” He then asks Carla what her number was, and she tells him. He compares the distance to 800 with his number, and proceeds to erase his answer and write Carla’s answer down, at which point Carla then also erases his answer from her paper and writes her own, original answer, once again.
Students had internalized the relationships skills we worked so hard on earlier in the year— they were listening to each other, being patient with one another, and trying to solve their disagreement in a healthy way— perhaps the only way they were comfortable and familiar with: rock, paper, scissors. Without Aija’s prompting, however, they would have simply moved on to the next task, with Jerome’s incorrect answer on the paper and Carla’s great mathematical thinking unacknowledged.
My next step was clearly to move deeper into supporting students to explain their thinking and negotiate meaning with diverse partners. We needed to engage in modeling, discussing, and practicing how to share our math thinking, respectfully disagree with each other and agree on a correct answer.
A Plethora of Ongoing Implications
This video, and the accompanying conversations with colleagues, left me with dozens of ongoing implications for my teaching practice with which I continue to grapple a year later. One implication is around grouping partners. I had grouped my partners partially based on how well the students would work together, and also in a sort of high/medium or medium/less-practiced partnership. Teachers often pair students this way, thinking that the “higher” student will help the one that needs more support; but this data helped me see that it often turns into that student dominating the partnership while the other one goes along with whatever they say. Neither partner is getting the sort of challenge that they need. I want to put a lot more thought into the way I group partners, taking into account their culture, language, gender, and students’ own perception of their math ability in order to support students like Carla to find their voice.
A second implication is around considering the social and emotional skills and strategies students need to constructively address academic disagreements: themes that came up for me included trusting yourself, self-advocacy, speaking up, not being afraid to make mistakes, and working together to find the correct answer by trying out one student’s way and then the other student’s and comparing the two. I found that these two students did not necessarily have the language (and/or confidence, in Carla’s case) to negotiate their two different answers– I had not yet provided them with the explicit tools to do this. As a class, we had practiced sentence frames such as “I agree/disagree with _____ because…” but they were obviously not yet at the point where they were using these sentences on their own, without being prompted.
I’ve also been thinking deeply about the discomfort that comes with disagreement, whether it is something big like a belief or value, or something smaller, like an answer to a math problem. Disagreement is uncomfortable by nature– how can I as a teacher, help my students experience it in a way that feels productive and non-threatening– safe? One idea is that I have started to think about alternatives to the language of “agree/disagree.”
The Value of Inquiry
The inquiry process, in particular data collection and analysis, helped me see many things I may not have seen otherwise. Simply looking at my class and observing them as a whole as they worked, it would have appeared as though they had all mastered relationship skills. They were talking to one another, completing their work, and getting along with one another. Sitting down and looking at their papers would have also made it appear as though they had agreed on their answers. But looking at the video data gave me a whole new lens with which to see how my students were interacting and solving disagreements with one another. Five minutes of video data has given me many next steps as I continue to go deeper in exploring my students’ — and my own — understanding of relationship skills.
SEL Teacher Scholar Ruanna Owens is a third grade teacher at Garfield Elementary in Oakland Unified, where she is part of the SEL lead team responsible for supporting staff with the integration of SEL into academic content areas. She received her credential and MA in Education from UC Berkeley’s Developmental Teacher Education program. In December 2016, she had the opportunity to share her inquiry work and data with educational leaders from throughout California at the California Collaborative on District Reform.