Lesson Study Cycle 3
As a lesson study group, we had the opportunity to design and complete our final lesson study cycle on social justice teaching. Teaching for social justice can be multidimensional, requires intentional work, and can take time to observe any form of result. Some ways we can promote social justice teaching is by having high expectations for our students, fostering learning communities, spending more time on specific content, building depth in a lesson, using multiple forms of assessment, and teaching about activism and inequity. We decided to focus on a lesson that would increase student engagement and critical thinking skills by designing and implementing socioculturally relevant math tasks. In preparation for a year long exhibition project, my lesson study team member worked closely with an environmental studies instructor to be able to deliver the lesson and project. The students were successful in their critical thinking and engagement as they reflected on what their rate of change lines and integrals mean in context of their topography map.
Teaching Partners:
Sabelle O. - Math - 12th grade
Samantha M. - Math - 10th grade
Gemma R. - Math and Science - 6th grade
Goals
Part 1: Planning
Equity Goal:
We will increase student engagement and critical thinking skills by designing and implementing socioculturally relevant math tasks.
Content Goal:
Students will discuss and better their comprehension of the meaning of theirs and others rates of change and integrals, using their topographic maps as reference.
Students will connect their analysis of contextualized math products (topographic maps) to the data-based equations that they created to describe them (rate of change, integrals).
Overall Goal:
This lesson will act as a summative lesson to help students condense the ideas they have on their own socio-culturally relevant math project and think critically about what the different components mean collectively, as they prepare to discuss them at exhibition.
Research Base
Throughout our lesson study planning phase, we did research on: social justice teaching, explored individual questions about culturally responsive teaching and how they can be solved, connected our students needs with our equity theme, and implemented lessons that would engage our students in critical thinking.
In order to build on our equity theme we first wanted to try a lesson (change idea) that would allow our students to explore, assess, question, and make connections. We wanted our students to make connections and dig deeper when bringing in real world problems. A prediction we had was that our warm up would initiate great discussion and engagement. We also predicted that we would have various results in our student examples and that we would struggle with having students come up with their own questions throughout the lesson.
For example, in my research I had students look at a would you rather graphic and engage in a discussion. I followed the lesson with the Penny Problem (Exponential Functions) and had students ask questions half way through the delivery of the lesson. We were able to engage in a productive discussion; however, most of our students responses (questions) were very common. We decided to adapt the lesson and practice another PDSA in order to allow our students to deepen their understanding and ask more specific and unique questions.
PDSA Cycle:
The Penny Problem
Focal Student #1
FS1 is social and interested in communicating with their peers. They rarely share with the class, instead deferring to a tablemate to share instead of them. FS1 participates in class activities and tasks sporadically, but often talks off-task with their peers or watches videos during work time instead of completing the assignment. FS1 will occasionally raise their hand to ask for assistance, and will pay attention somewhat to explanations at their table. At the beginning of the semester, two of FS1's friends who had previously encouraged them academically left the school, which may have had an impact on their academic performance and focus.
When asked their thoughts on math at the beginning of the semester, they commented, "I wanna say that our relationship dynamic we have had together over the years were good and that we had a fun time together having good memories but it wouldn't be true. We always started off on a rocky start after suddenly transferring into a different school during middle school in the 5th grade, and getting called out and embarrassed by teachers for never being taught a course. I felt at a young age to not even bother to try or ask for help because it would have led to more embarrassment. It left me behind on my understanding of you, it took me longer to understand you then suddenly changed into the next course leaving me back a square one again. It wasn't until freshman year that I felt like I could give it my all even if I never understood and knew and that was when I had my first A in your class, where I felt that I can actually be a better student if I tried even if I was wrong or confused. When I received my first positive feedback from my freshman year teacher that I did good and that I shouldn't have lowered my worth as a mathematician and person just for not understanding you... Even when I wouldn't understand clearly from his lessons I would go home and study online and take notes to better help me so I wouldn't feel like I'm behind or last in place on understanding it did work. I hope we both can get along this semester and that I have the confidence to ask questions about you and grow a better understanding of each other. I hope we start off this year together on a good note."
Focal Student's Assets and Needs
Focal Student #2
FS2 is a student who engages minimally in group tasks or activities in the classroom, and rarely speaks or participates. FS2 has a group of friends they are close to and occasionally collaborates with, but often prefers to work alone after initially understanding an assignment. Past assignments have shown that FS2 meets expectations for assignments the majority of the time, and in a timely manner. FS2 almost always focuses silently on the task at hand, occasionally talking to a table mate, until the math task is complete before promptly turning to a personal project. FS2 is interested in computer games and computer game development, and plans on attending college as a Computer Science major.
When asked their thoughts on math at the beginning of the semester, they commented, "my past experiences in math have been very different ... For a couple of years I was doing very well in math and was always on the honor roll in my school up until seventh and eighth grade. In this school where I had the same teacher for both years, I had bad experiences with this teacher which I'm not going to talk about because it would make this letter too long. Other than that when I got to highschool I felt far more confident up until now and I think I will still feel pretty good in this class. I think the break that we had from math last semester was actually good for me and I will be able to come into this semester with a fresh mind."
Part 2: The Focus Study
Content Goal:
Students will discuss and better their comprehension of the meaning of theirs and others rates of change and integrals, using their topographic maps as reference.
Students will connect their analysis of contextualized math products (topographic maps) to the data-based equations that they created to describe them (rate of change, integrals).
Equity Goal:
We will increase student engagement and critical thinking skills by designing and implementing socioculturally relevant math tasks.
Lesson Hypothesis:
If we as teachers, incorporate a purposeful and relevant warm up that allows for discourse and personal connection, then students will be engaged and deepen their critical thinking skills, interact comfortably and respectfully with all people whether they are similar to or different from them, and use rate of change and integrals to understand the impact of change, resulting in student participation in small group and class conversations and the utilization of their resources and funds of knowledge in understanding the lesson activities (i.e., talking with group members, recording thoughts on their note catchers, reflecting on their project resources, and listening to others).
Lesson Goals Flow:
1. Students will learn about rate of change and apply it to real-world problems.
2. Students will learn how to construct lines of best fit by using data on Desmos.
3. Students will learn how integrals can find the area of real-world functions.
4. Students will learn how to find the area between two lines.
5. Students will construct integrals on Desmos using lines of best fit and find the change in area of their topographic maps.
Lesson Flow:
1.) Introduction: This semester, you’ve made 2 topographic maps. On your worksheet, write down one of the map locations you chose, and why that location was meaningful to you.
2.) Warm-up and Discussion: What do you think the images with maps and graphs were telling us? What were some noticings (facts and data) vs. wonderings (analysis and stories). At your tables, decide which statements are facts vs. analysis. Write an analysis on the following three topics:
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The story of your rate of change project.
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The story of your integral project.
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The impact on your map location.
3.) Peer Feedback:
Get at least 2 people to write down their analysis of your data.
They must each attempt to explain:
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Your rate of change story
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Your integral story
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The impact on your map.