MS. PEETZ'S TEACHER
DIGITAL PORTFOLIO
SDTR Trimester 3
Capstone Project
Indians & Mathematics:
A Culturally Responsive Lesson Study
How do we empower students to create and interpret visual representations of data to better understand and act in their world?
For our third and final lesson study cycle of the SDTR Year 2 program, my group and I wanted to focus on improving students' critical consciousness about real-world data through cultural connections and using visual aids such as graphs. My class at Bonsall High School was chosen as the 'test subjects' due to a few factors: 1) the proximity to the Pala Indian reservation and fact that Bonsall High School has a wide variety of represented backgrounds and cultures and 2) students would be learning about a particular visually-focused mathematical topic that has rich and tangible real-world connections to their personal lives.
PDSA Cycle 1
When wanting to improve a particular skill with students, it's helpful to first find a baseline for the students' fonts of knowledge - that is, what do they already know? What are they already good at and what is a struggle for students? As such, we started our PDSA cycles by finding baselines: each team member asked their students to analyze a data-connected graph out of it's article context and use it to think about the prompts on the graph itself.
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Since this was a baseline across all of our classes, which represents a large range of ages from sixth grade to twelfth grade, we made sure to use the same image that had a low skill floor. We also asked the same questions of the students.
Students were asked about
this graph:
1. What do you notice?
2. What do you wonder?
3. How would YOU respond to the graphs' prompts?
4. What would you change about this graph?
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PDSA 1 Findings and Conclusion
Overall, we were pleased with the engagement of our students regarding this graph. Many students wondered why the topics seemed so broad, when my students could come up with much more detailed reasons - something we later realized was because this graph was inspired by the responses of a fourth grade class!
Because there is no x- and y- axis, students were given something less reliant on skills regarding the 2D plane, and thus for our next cycle, we wanted to see how well students would do when looking at visuals such as line graphs and scatter plots, and how well they would do with 'closed' questions - that is, questions with distinctly correct and incorrect responses. We decided we would adjust our PDSA set-up for cycle 2, while implementing the aformentioned changes.
PDSA Cycle 2
For cycle 2, we introduced an x- and y- axis to the graph, adding some complexity to reading and interpreting the graph. This time, students were asked again to notice and wonder about the graph, but were also asked a question with a correct answer and were encouraged to annotate their graphs in a Desmos Activity Deck. Since we were looking to compare data across multiple sets of students of different ages, we used the same graph for all our students once again and then compared responses.
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PDSA 2 Findings and Conclusion
For my students, they seemingly were very capable of finding points given number lines in an (x,y) plane. However, students struggled with interpreting the meaning of the axis themselves, indicating that they’ve had practice finding points on graphs, but have not had as much practice having to interpret data or graphs or the design of the graph itself. For question 3, many of the incorrect 21 responses were close to correct. Just like my research partners, I had students correctly answer question 1 and then miss question 2, oftentimes thinking that the y-axis was just the reverse of the x-axis. It’s also possible students misinterpreted the y-axis label as the title of the graph, therefore extrapolating the wrong conclusions from the graph.
Read-Ask-Reflect
After the two PDSA cycles, we were confident that for our lesson we would continue this idea of annotating graphs with the cultural relevancy requirement of the lesson. It was here that we reached out to colleagues and read a few articles regarding social justice pedagogy in mathematics in order to better inform the lesson activities and structures.
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Formal Lesson Study
At this point, my research group and I were confident in what we wanted to do for the formal Lesson Study. After doing some research into Pala's environmental group, we decided that we wanted the lesson to speak to students directly. As such, we chose to look at the temperature data for the Pala reservation, home to many of students at BHS and only 10 miles to the northeast of the school itself. Nearly all of my students, whether or not they lived on the reservation, could relate to the temperatures of the local climate and quite literally feel the increasing temperatures in their own backyards year to year. Pala's Environmental Department notes a data-collection tool called Prism, and we used that same tool to create periodic looking graphs of minimum temperatures over 5 year increments.
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In this lesson, students were introduced to a video giving them some context of the lesson: the video clip features an interview from 2002 in which people on the reservation were interviewed about their lives, the school, and their culture. The clip mentions that the people used to regularly see snow on the nearby mountain range, but nowadays snow appears more rarely. To make use of this statement, we wanted students to think about why a mountain range that would normally host snow can no longer do so. As such, we warmed students up with a graph depicting some unknown location's maximum, average, and minimum temperatures over a given year. The shape of such a graph is a wave, peaking in the summer months and dropping at it's lowest in January to February. We had students think about the meanings of the graph, in particular, what can the average minimums and average maximums mean? How is it different to the daily averages? Which average is connected to snowfall?