Throughout the lesson study organizing and executing timeline, my team and I kept a log of our process, research, and idea testing.  We began by recognizing that a challenge we all faced was finding a way to help students organically stay engaged with the material we teach in our classrooms.  Our goal was to establish an equity-based research theme that spoke to our problem of practice and allowed us to try different ideas in our classroom to impact student behavior.  We designed and implemented multiple ideas into our classrooms and considered their impact, specifically through the lens of a handful of focal students.  Through observations, idea implementation, and consulting with outside experts, we came up with the research theme:  How do we foster a community that is curious about topics and collaborate with one another?

After completing our PDSA, my team and I looked through our data and were pleased with the results we saw from having students craft norms and then using them as they had discussions.  Our PDSA focused on non-content related tasks, and we wanted to bring this strategy into our content area and also implement another technique for increasing collaboration and curiosity.  Could we use technology, along with our prior work in our PDSA, to create an environment where students had to communicate and collaborate in order to succeed?

My team and I determined that the strategy we wanted to use with a class was to have two students share a single computer and work on a digital activity (Desmos Polynomials Activity) as they started learning about polynomials.  We had originally though to use this strategy to close out a unit on logarithms, but could not find a suitable lesson that felt like it authentically used this computer swapping idea and encouraged discussion among students.  The team worked together to combine two Desmos teacher lessons into one to craft an experience where students would be invited to revisit what they already knew about quadratics (a 10th grade standard) and see how they could apply these ideas to a new area, polynomials (an 11th grade standard).  The 11th grade teacher member of our group hosted the lesson, and I and the other teachers served as observers - focused on noting and observing student interaction and conversations.  The content understanding goal was that students would be able to understand the relationship between zeroes and factors of a polynomial and understand the relationship of polynomials to quadratics.

During the lesson, as an observer I was able to listen in to conversations of 5 different groups of students and took notes about the questions they asked each other, the questions they asked the class, and the conversations they had about the topic.  Both of the focus students for the host teacher were in my observation group, and I paid particular attention to them and how our lesson choices (the activity, sharing computers, and established norms) affected their ability to access the lesson and benefit.

Throughout this process, students eagerly chatted about the task and asked questions of each other, though not as many to the full class as my team had hoped.  To the left, you can see a few examples of their work and way they were interpreting what they were seeing as they were introduced to a new idea, cubic functions, with their partner.

(Note:  All data from lesson study observer team was digitally aggregated to compare, but not shown here due to having identifying student information)

From the very beginning, our lesson study group was focused on increasing students interdependence and their ability to rely on each other to drive their mathematical thought and questions.  Our discussion norms helped students identify strategies that would make them more effective discussion partners, and they felt that it did help in the exit survey.  The implementation of the single computer between two students had mixed results across the host teacher's class.  To the left, I have included my observation log for the five pairs that I observed.

While my data is broadly interesting, I was paying particular attention to pair 3 and the bottom pair 1, which were the pairs that included the two focal students for the host teacher.  

For pair 3, the focal student left class for over 20 minutes during the meat of the activity.  He was in class for the warm-up as students recollected their understanding of quadratics, but he missed the opportunity to engage with the lesson in the way we intended, as his partner wound up doing the work and he did not have many opportunities to engage with it.  However, there was one point where he had the computer and asked multiple questions to his partner to work through the activity.  To me, this says that the strategy we implemented could be effective for this student but we need to address an underlying concern regarding the student's attendance in class.

For bottom pair 1, the focal student was paired with another student that did not say anything during the entire class.  It was evident that some of the more successful pairings in class were either those where the two students were friends / frequent collaborators or pairings with one strong, help-oriented student.  The focal student in this pairing worked on the activity but never asked questions or shared thoughts with her partner, thus I never got to hear her explain her thought process or work through these new ideas with a peer.  I think that our technique would have worked better for the focal student if we had more thoughtfully grouped them with either a friend or a peer that is more communicative.

Broadly, it was clear that having established norms and inviting students to collaborate through an exploratory Desmos activity benefited students by allowing them to ask questions of their partner in a safer low-stakes environment and then it encouraged more students to respond to group questions (anecdotal verification of this by host teacher).  For future lesson studies, I would want to work with my team to establish benchmarks for certain other observational data (for example, total number of questions asked / hands raised during a class) so that we could have a baseline for better analysis of the impact of the changes we implemented.