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 empower students to become data literate by interpreting visual representations like graphs in order to better understand and act in their world?

Anecdotally, we all felt that students struggled with graphs and had difficulty reasoning through graphed content or explaining how they could process them mathematically.  We needed to start with an activity that allowed us to get a feel for what students were able to get from graphs, as well as get them accustomed to routines through this cycle where they would consistently be asked to look at and process graphs.  We started with the graph to the right, The Biggest Problem, and in each of our respective classrooms we asked students to consider what they noticed, what they wondered, and how the results might differ from their own opinion.  After sharing with peers, students shared their thoughts in a whole group discussion where we documented what types of responses we heard.

We asked students to respond to a form noting what they specifically thought the biggest problem was, based on a list they created so that we could show them their own data.  The next day, we formed these responses into pie charts in our respective classrooms to compare to the original graph, allowing students to offer justifications and rationalizations for the differences.  While it led to interesting conversations in class, many of the responses were from high status students who often share, and little was heard from the majority of each class.  We knew we needed to find a method for getting a better perspective of all students' understanding.

Our lesson study process is composed of two Plan-Do-Study-Act Cycles (PDSAs described in Lesson Study Cycle 1) and are used to help hone in on a change idea.  After our initial Graph Talk to determine a baseline of student knowledge, we felt that it was possible students did not feel confident working with graphs and we simply needed to have activities like Graph Talks more prominently in our work.  After responses came in for The Biggest Problem, many students in my classroom challenged the validity and relevance of the topic because the responses were originally from 4th graders.  It was clear that they wanted something that felt more relevant to them.

After gathering data from PDSA1, we decided that having students annotate graphs would be the strategy that best reveals student thinking.  We saw mixed results in the type of responses we got when we each chose different graphs, so for this cycle we found a graph that we felt was understandable and relatable as much for 6th graders as it was for 12th graders.  Obviously, we expected different levels and quality of annotation across the grades, but felt this would be the best way to get students to share their thinking because it was academically safe (done on Desmos where only teacher sees results), offers ample thinking and work time, and focuses on an issue that students likely have opinions on.

Although we did not see more accuracy in the results we got after students annotated, we did get a lot more data about their thinking, opening up the door to a lot more conversation about graphs and a better understanding of where students are seeing success and where they need more work.  It appears that our topic did not strike a chord for many students, but now that we knew annotation would give us this clear picture we could focus on the social justice angle for our lesson to hopefully maximize engagement.

After deciding on our change idea and seeing some success with it, we turned our sights to the group lesson.  It made the most sense to have the IM3 teacher host the lesson and she was at the beginning of trigonometric functions with her students.  We spent a lot of time researching and trying to find various social justice causes to attach but ultimately decided on climate justice and the inequitable effects of a warming world on cultural traditions.  This seemed like a good fit, because the host teacher told us that she had recently seen a video in a professional development where a local Native American elder comments about the snow disappearing from the mountains and the way the community was still pushing through to follow their cultural traditions despite the changing world.

This seemed like a perfect connection.  Many of the students at the host teacher's school belonged to one of the local tribes (or were tribe affiliated), and it was likely that they too had heard about the impacts of climate change on their specific traditions.  After doing some research, our team found specific data for the Pala Band of Mission Indians that had been compiled in a report by the California Office of Environmental Health Hazard Assessment about the adverse impacts of climate change on the tribe's traditions and sovereignty.  We found the original source for their data and were able to compile a few graphs that had many similar characteristics to sine waves.  This would ultimately be the centerpiece of our lesson that allowed students to annotate their thinking, after being introduced to the elder's comments about the mountain and a refresher on trigonometric aspects.

As looked through the data, we began to form an idea for our content understanding goal that included both the curriculum content goals and a social justice goal.  We ultimately came up with the goal that for a periodic function that models a relationship between time and minimum daily temperature in Pala, students will be able to interpret and annotate key features including relative maximums and minimums, periodicity, and midline to support students in understanding how rising temperatures connects to the environmental injustices affecting the Pala Band of Luiseño Indians.

On the day of the lesson study, the students were introduced to it the same way our host teacher had been - with a short clip of the elder commenting about the snow on the mountains.  The class spent a brief amount of time reconnecting with what they new about sine functions (periodicity, amplitude, midline, etc.).  After being given the graphs with little additional context, students were asked to annotate everything they noticed and wondered, while specifically noting the aspects of the graph they understood.

Once the graphs were handed out, the entire class of students immediately started working.  There was only one who didn't jump right in begin annotation, and after a small redirection even he went into the data.  After 10 minutes of annotating, the host teacher offered more time if students wanted it, and they did.  For a total of 15 minutes, students annotated graphs with an outpouring of mathematical knowledge and spent time sharing it with their peers.  We found the right combination.

Causes that kids care about alone was not enough.  Having a tool to reveal thinking in annotation was not enough.  When we merged these two and presented them to students, we got great results.  While this process was challenging to find a lesson was so deeply connected to students lived experiences, it paid off.