Meggie Gonzalez
Secondary life science teacher Digital Portfolio
Lesson Study Cycle 1
For the lesson study focus of our coursework, I was grouped with Ella and Cliff, two other middle school teachers (one math, one math and science). Early in our meetings, we discussed the desire to cultivate an inquisitive mindset among our students. As STEM teachers, we feel we could measure success as having classes full of independent (and interdependent) learners with a desire to keep learning. Our experiences at this point of the school year had been students who are very dependent on their teachers for guided instruction, full of "how do I . . ." questions, even needed reassurance in their note-taking. When our students feel uncertain of their knowledge, they become silent and hesitant to put pencil to paper.
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Our first shared activity we took to our classes was a Venn Diagram. We presented each class with a comparison query relevant to a recent lesson and asked them to complete the diagram. We noticed organized thoughts and effort on the part of our students. However, many of our artifacts seemed very brief. As a lesson study group, we discussed how there is a difference between show me what you know and what do I have to do to meet the activity requirement. This led back to our idea of wanting our students to feel confident sharing their ideas and feeling a drive to keep trying. Ultimately we landed on the idea of student agency and how we might increase it in our classrooms.
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The equity-based research question for our first lesson study was: How do we support students in developing their agency as mathematical and scientific thinkers?
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Plan-Do-Study-Act Implementation (PDSA)
When considering a problem of practice that we would like to address, we expressed our observations that, for some, school has become a place to conform and not a place to speak your ideas or alternative ways of thinking. In an effort to encourage the sharing of ideas, we thought it might be beneficial to implement what Cliff wittingly named the "Snap Back". With this protocol, a student was asked to restate or ask a question about the line of thinking of the student before them, prior to stating their own idea. Overall, our students were receptive to this practice. In both classes where we tested out the "snap back", we had increased participation overall, and an increase in the breadth of students participating. A few students that are typically very quiet took the opportunity to express a thought. Another student used the opportunity to come up and show her thinking on the board for the first time. It was a mixed result as it seemed a portion of students were emboldened with this protocol knowing their thoughts would be given the consideration of their peers, while others felt intimidated by the need to comment on someone else's thinking. Overall, this protocol seemed to have potential in increasing student engagement, and we feel with some practice could be an excellent tool in our classrooms.
Through our literature search, we identified teacher neutrality as another practice that can increase student agency. We incorporated this in to our second PDSA plan. Over the course of a week, we actively made the effort to keep neutral during class discussions and noted student participation. Again, we noticed that by not giving an emotional response to a student's idea, or immediately accept it as correct/incorrect, the more students were prone to participate in the conversation. I noticed with my class that if the "right" answer was still out for grabs, students would continue raising their hands to contribute their thoughts. Students would even start to respond to their peers by considering an idea and then wanting to add their own twist to it. This practice of neutrality is one that we agreed we want to continue bringing into our classrooms as a way of aiding students in becoming more independent learners.
Our Lesson
This first cycle, our lesson was hosted by Cliff. The lesson, "The Price of One", was designed to be taught to his 6th grade math students. The students have been introduced to the concepts of ratios and proportions, and have discussed multiple methods for solving related problems.
The standards for the grade level are as follows:
6-RP-A:
Understand ratio concepts and use ratio reasoning to solve problems.
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed.
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
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The learning goal for this lesson was that students will understand that a unit rate a/b represents the amount of a per b (for example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each one cup of sugar.”) and be able to find a unit rate using a diagram such as a ratio table or double number line.
It was expected that students would struggle to apply methods that were learned to find equivalent ratios, and apply it specifically to finding a unit rate. Students have so far dealt with whole numbers for these concepts. In this lesson they will gain some experience with the fact that unit rates do not always result in even numbers. Students will have the cultural knowledge of using money with decimals. For this reason, it was felt an appropriate lesson frame for unit rates would be finding the price for a single item given a bulk quantity and price. Students can apply their previous learning of double number lines and ratio tables to solving these problems, and can use manipulatives and multiplication tables to explore numbers.
The lesson began with a warm-up activity to prime students with their previous knowledge. After some work time as a table group, the activity was reviewed as a class. The host teacher spent the work time looking for different examples, and later warm-called selected students to share their thinking on the board. Additional volunteers were also accepted. After it seemed the warm-up activity had been sufficiently discussed, the students were then given a worksheet with additional problems aimed at helping students reach our lesson goal. The worksheet was intended to provide students with additional practice in calculating ratios and proportions. Students were encouraged to use any of the previously taught strategies, such as a diagram or double number line, as tools for this activity. Students were seated in table groups of 3-4 and permitted to work as a group and share ideas among their table mates. After about 15 minutes of work time, the teacher team became clearly aware that students were struggling with the task. Several of the students had stopped their attempts and begun talking about other things. Other students who had attempted the front side of the worksheet and cooperated to put something on their paper had become frustrated and were then hopping between questions on the backside expressing defeat. Our host teacher decided to bring math class to an end and begin prepping the sutdents for their science period.
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Observations and Debrief
The following week, our team met to debrief our lesson study experience. We took turns sharing our thoughts, celebrations, and challenges. One discussion point that came up was that the physical distance between the lesson study team and the focus students made it difficult to hear, in general, what the students were saying. We also expressed the wish that we had staged our positions more strategically to directly observe our focus students. Some more intentionality in our placements in the classroom would be beneficial in our next lesson study. With this in mind, we believe a data collection sheet that is more customized to our specific lesson and students could help with more successful data collection, and later analysis.
Of the observations we were able to collect on our focus students, we noted that Student #1 was inattentive during the warm up. She waited until the teacher was at the board to begin copying on her own paper. She did continue to copy as the second student came up to the board. When it came time for the worksheet, she wrote her name on her paper right away and spoke well with her table mates. The questions did seem to puzzle her as she wrote a few things down and then erased them. She take out her notes for some assistance when prompted. Student #1 is classified as an ESL student and is often reliant on her Spanish-speaking friend. The two of them conversed and Student #1 was compelled to draw a double number line. Our second focus student attempted to rally her table and was the one to get the conversation going during the group work portion of the lesson.
Student #2 was observed prompting across-table communication, which resulted in new ideas emerging. However, the table did not seem to come to a consensus as far as how best to approach the first problem on the worksheet. They eventually decided to skip the front and attempt the backside. Considering the class as a whole, we did observe some engagement from various students. A few asked about rights and wrongs, while another expressed deep frustration to a peer. A couple of table groups were seen getting notebooks out to check their notes from previous days.
During our debrief session, Cliff mentioned that some of the students have since called this lesson their "boss battle" and that they are going to work to eventually defeat it. Hearing this analogy, full of camaraderie and drive, was definitely a silver lining to our lesson study experience. Reflecting on the lesson design, we concluded that the chosen worksheet was probably not the best choice. The worksheet presented as a fill-in-the-blank for the answers. Looking back, it seems the students may have felt intimidated to only write if they believed they had a correct answer. It could have been more inviting to have the worksheet in the form of scaffolding thinking. Students may have felt more comfortable to get some initial ideas on paper and then we could gradually guide them where they needed to go. The worksheet also had some problems that dealt with not-whole numbers. This was another area to which students had not yet ventured with this material, and we believe they were put off by these new numbers while still grappling with the main concepts.
Reflection
This initial adventure in lesson study was very enlightening. It was rewarding to have time dedicated to sit and plan with other STEM middle school teachers. The sharing of our experiences, wishes, and struggles was extremely validating. It was inspiring to come up with some common goals for our practice. I appreciated through our literature search and class readings that lesson study is for the benefit of all involved. By examining our lessons and facilitation as a team, we can all grow from new perspectives and become better for our students. I am looking forward to further striving for student agency in my classrooms, with this lesson study as just the beginning.