Lesson Study Cycle 3
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?
The theme of this third and final cycle of lesson study for our M.Ed. was teaching for social justice. Our team of sixth- through twelfth-grade mathematics educators researched and developed a lesson about local climate injustice and explored variations on the Graph Talk routine to support student access and sense-making.
Content Understanding Goal: 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 understanding how rising temperatures connect to the environmental injustices affecting the Pala Band of Mission Indians.
Key Research
“Teaching for social justice” is a comprehensive blend of content and process that sits at the union of pedagogical theories including Democratic Education, Critical Pedagogy, Multicultural Education, Culturally Responsive Education, and Social Justice Education, with an additional emphasis on specific academic content and K-12 pedagogy.
Six guiding principles are:
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Assume all students are participants in knowledge construction, have high expectations for students and themselves, and foster learning communities;
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Acknowledge, value, and build upon students' existing knowledge, interests, cultural and linguistic resources;
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Teach specific academic skills and bridge gaps in students' learning;
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Work in reciprocal partnership with students' families and communities;
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Critique and employ multiple forms of assessment;
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Explicitly teach about activism, power, and inequity in schools and society
Dover, A. G. (2009). Teaching for social justice and k-12 student outcomes: A conceptual framework and research review. Equity and Excellence Education, 42(4), 507-525
Climate change poses a threat to the ecological, social, spiritual, and economic health of the Pala Band of Mission Indians in northern San Diego County. Rising temperatures are interrelated with drought severity, storms and flooding, wildfires, air quality, food and water insecurity, and more. In order to address the impacts of climate change on community psychosocial health, and to further protect and steward the land, the Pala community is actively working to understand, adapt to, and mitigate the effects of climate change, including through The Climate-Ready Tribes Initiative.
Pala Band of Mission Indians (2022). Impacts of climate change on the Pala Band of Mission Indians. California Office of Environmental Health Hazard Assessment. https://oehha.ca.gov/media/epic/downloads/06pala.pdf
Schramm, P. J., Al Janabi, A. L., Campbell, L. W., Donatuto, J. L., Gaughen, S. C. (2020). How indigenous communities are adapting to climate change: Insights from the Climate-Ready Tribes Initiative. Health Affairs 39:12, 2153-2159. https://doi.org/10.1377/hlthaff.2020.00997
Research Base
(Problem of Practice, Research Theme)
Plan - Do - Study - Act
Continuous improvement through the PDSA Cycle
Hinnant-Crawford, B. N. (2020). Improvement science in education: A primer. Myers Education Press.
In this routine, students view a graph and respond to the questions:
- What do you notice?
- What do you wonder?
- How does this graph make you feel?
This routine provides a low-floor, high ceiling entry to data analysis; gives students opportunities to apply their funds of knowledge; and introduces real, relevant data to the classroom.
Building on the Graph Talk routine, annotation offers more options for action and expression. Students can still write sentences as they would in a notice/wonder, but they can also highlight important features, add arrows to connect related items, sketch lines of best fit, add drawings or dialogue, and more. With diverse options for responding to real-world data, we attend to students’ diverse communication practices and their use of mathematics to understand and investigate meaningful situations
Showcase Lesson:
Snow and Acorn Speak through Data
Content Understanding Goal
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 understanding how rising temperatures connect to the environmental injustices affecting the Pala Band of Mission Indians.
Standards Addressed
HS.F-IF.B.4: Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
HS.F-TF.B.5: Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
JU.9-12.12: I can recognize, describe and distinguish unfairness and injustice at different levels of society.
The Pala Band of Mission Indians is a federally recognized Native American Indian tribe that has lived since time immemorial in the lands now known as northern San Diego County. The Pala region is near Bonsall High School, where Cassilyn Peetz, a member of our lesson study group, teaches Math 3. Many of Cassie’s students have Luiseño and/or Cupeño ancestry and feel a connection to the native land practices and culture. In this lesson, students apply their understanding of periodic functions to analyze temperature graphs, connect data to traditional wisdom, and learn about ongoing climate efforts by the Pala Environmental Department.
Pala Band of Mission Indians (2022). Impacts of climate change on the Pala Band of Mission Indians. California Office of Environmental Health Hazard Assessment. https://oehha.ca.gov/media/epic/downloads/06pala.pdf
Student Work
Focus Student Spotlight
Focus Student 1 had a tough start to the school year but has come around and taken on a whole new work ethic. He is often very quiet in class, but has been opening up more and more.
During this lesson, FS1 engaged with the task in depth. He saw in his graph the temperature patterns characteristic of his community and correctly guessed that this was data for Pala. He also quickly noticed that the midline for each year was not consistent, and asked whether he should label the midline for the five year data set or for the individual years. In the whole class discussion, he voluntarily shared what he noticed about the rising temperatures and their potential impact.
Reflection
This cycle began with a lot of questions: what does it look and feel like to teach math with a social justice perspective? What are the philosophical foundations and implications? Which mathematics ideas are our students struggling with the most, and how can justice-oriented strategies help bridge gaps in understanding? As a white teacher of Latine students in a low-income neighborhood, questions of culture and systemic liberation are especially salient. Teaching for justice is a lifelong process, but I walk away from this lesson study cycle with a clearer vision of authentic student learning through authentic, meaningful data.
Our PDSA cycles focused on improving one particular routine: the Graph Talk. Graph Talks, also called Data Talks, are open-ended mathematical tasks that illuminate student thinking and provide opportunities for students to make sense of real-world data, thereby developing their data literacy. With each PDSA cycle, we refined the routine a little bit more. We found that annotation, rather than written responses on a sticky note or Google form, allowed for different forms of expression and helped us access our students' thinking more effectively. We also found that the graph itself matters a lot. Engagement was low when students felt only a tepid interest or connection with the data on-screen. In contrast, when students work with a data set that is both personal and significant, like the Pala temperature data, engagement is high. During our showcase lesson, Cassie's class started working immediately when the graphs were handed out, and after ten minutes of intensive, dedicated annotation, they asked for another five minutes to record more notes and dig into the significance of the data. The students made discoveries by contrasting their graphs with their peers', co-constructing a story of rising temperatures and threats to traditional ways of life. In previous lesson study cycles, my team tried different strategies for different PDSAs, but I found the iterative improvement of one routine through PDSA to be very effective. I think our students also benefited from the repeated exposure to and practice with real data.
Another takeaway from this cycle was the power of integrating feedback from other educators in the lesson planning process. After our demo lesson, our team received specific feedback about the order of activities for maximum accessibility, and for building a clear narrative through the lesson. We implemented the feedback for our live showcase to great effect. I wish there were more day-to-day opportunities to discuss lesson plans and collaboratively build instruction! As a first year teacher of three different grade levels, everything I teach is for the first time. I'm looking forward to making improvements next year, and involving my colleagues as team members in future lesson studies.