Lesson Study Cycle 3
We will increase student engagement and critical thinking skills by designing and implementing socioculturally relevant math tasks.
Previous Goals
Reason abstractly & quantitatively (Used by students as they constructed models of rate of change for environmental factors, taking abstract ideas and quantifying them through collected data)
Model with mathematics (Used when students made graphs and predictions for rates of change, and estimated area change using integrals)
Use appropriate tools strategically (Used when students constructed their lines of best fit and Integrals on Desmos)
Current Goals
1. Make sense of problems & persevere in solving them (Used by students as they process and recall their math ideas and reflect on what they can say about each topic.
3. Construct viable arguments & critique the reasoning of others (Used by students as they reflect on what their rate of change lines and integrals mean in context of their topography map)
Future Goals
No future goals: As graduating seniors, students will apply what they learn in this lesson at exhibition as they explain their projects.
Our Focal Students
Focal Student 1:
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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 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 high school 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."
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Focal Student 3:
FS3 very rarely engages with group tasks or activities in the classroom. Their mood can be volatile, and they are not easily swayed from their focus on their electronic devices. When asked, they state that they are paying attention but don't feel interested or able to participate. Past assignments have shown that FS3 does pay attention to the information from lessons, and completes worksheets easily or asks for help during office hours or from an AC if needed. FS3 was chosen as a student who has the capability to engage, but has not done so this semester so far. FS3 is interested in memes, video games, detective work, detective noir movies, and film overall.
When asked their thoughts on math at the beginning of the semester, they commented, "Dear Math, Let me pass. Please for the love of god. I just wanna be done and move on. Please let me pass. I need this. I need to graduate please please please please."
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PDSA Cycles
This lesson study cycle started by sparking interest and curiosity from our students. We wanted them to be engaged and be curious about what they are learning, so we started by scaffolding ways to keep them interested and curious. We started with the initial equity theme: we will increase student engagement by engaging students in socioculturally relevant math tasks where they can deepen their critical thinking skills. PDSA Cycle 1 started with a notice and wondering about math pictures and real world connections to the current unit, then mid lesson students had to generate three questions in the middle of the lesson, and then the lesson ended with an exit ticket that prompted students to reflect on how they see the current unit being represented in everyday life. This task was very successful in my class in particular. Students were excited to see different contexts of what they were learning and were able to visualize trigonometry better. Most students had clarifying questions, but those who did not feel they had any wonderings posed questions that might be helpful to someone who does not understand. It felt like a very successful PDSA cycle, as students continued to be more engaged than past units.
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PDSA Cycle 2 was very similar to our first cycle since it was such a success! We kept our equity theme the same and just added minor changes to our lesson. To start the lesson, we had students do another notice and wonder by themselves, with a partner, then with the entire class. We continued to implement these noticing and wonderings throughout the lesson so students kept their critical thinking caps on. Students had really great insight to what they were seeing and asked clarifying, thoughtful, and sometimes probing questions. Students had great discourse throughout the entire lesson.
Our Lesson
Our lesson was for a 12th grade calculus class that was finishing a project before their last exhibition for the year. This group of seniors had been working on a project involving their math and science class and this was the final lesson in the unit. In previous weeks, students had analyzed rate of change and apply it to the real world, and constructing lines of best fit for topography maps they researched. They also learned how integrals can find the area of real world functions, find the area between two lines, and finding lines of best fit and change in area of their topographic maps. Students had practiced asking questions and using math in real world situations during our PDSA cycles and they were heavily invested in their projects.
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Our lesson had two content understanding goals:
1. 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.
2. 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).
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Students spent a lot of time reflecting on their map location they chose for their project and shared why they picked it. After that, students spent time noticing and wondering different graphics that represented the change of water levels and predicted where they would be in a few years. Students shared their thinking and had a class discussion on what they saw.
Next, Sabelle taught the difference of analysis and facts. Students had a series of phrases that they would identify as either facts or analysis to practice their knew vocabulary. Students had individual think time, partner share, and a whole class discussion on whether the phrase was analysis or factual. Once the class was done discussing, students took turns critiquing their projects and they finished their write-ups on their exhibition project. We evaluated the students' understanding of analysis vs. fact and how well they were able to apply it through an exit ticket and initial activity. Focus students 1 and 2 had emerging understandings of the content goal- they were very close but not quite proficient.
Reflection
Since our lesson was the final lesson this senior class had, I was unsure of how our ultimate goal of engagement would play out. However, I think this lesson was implemented really well and we met our goal of having students be engaged in the lesson while it has a direct real world application. Students felt strong ties to their map and I think that was a really great buy in. They were excited to learn new calculus concepts because it helped them understand their favorite place more. Students were respectful in their discourse and listened with interest to their peer's ideas. Additionally, many students seemed to really understand the content of identifying facts versus analyses of statements.
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I think our PDSA cycles were very successful in not only pushing us out of our comfort zones to try new things, but also it got our students feeling curious and engaged. This lesson study cycle was a lot of fun, the research was interesting and it was great seeing students feel their work is important. I think part of the reason this particular study was so successful is because we had already done two cycles, the first one being with this same group. At this point of the year, we know our students better and we have a better understanding of what PDSA and lesson study cycles look like.
Moving forward, I would like to try to add more real world applications in our daily lessons. I have added more noticing and wonderings to our class' routines since it is so successful at getting students engaged and talking.
Student Work
