Lesson Study Cycle 1
Our lesson study group worked together to plan a sequence of lessons with the goal of supporting mathematical discussion.
A lesson study is a group of educators coming together to spend some time deeply crafting a lesson to answer a research question and test a theory of action. The results of the lesson are found through close observation of student experiences. Our lesson study group included four teachers, named Bailey, Lilly, Sandy, and Becca (me).
Our team reflected on some of the shared experiences seen in math discussions. With careful consideration of Bailey's students, we decided to focus on building academic language so students will have the tools to share their thinking and express connections. We believed that supporting language for more effective discourse will help students develop math agency. We also believe that the structures reinforced for math discourse will help students build community and value the thinking of each mathematician in the class.
Research Question
How can we help students use academic language to access mathematical discussion?
Theory Of Action
If we as teachers build upon students’ academic language, then students will be able to describe their math thinking, resulting in math agency and effective discourse.
Equity Goals
Students will hear, value, connect with, and build off of each other’s ideas.
Content Goals
Students will understand that a joint start unknown problem type can be solved with addition and/or subtraction.
Research
The host teacher, Bailey, shared some of her classes' goals around math and the math lesson structure, Cognitively Guided Instruction ( CGI) , used in her school. We discussed the strengths of CGI and some hopes she had for her students math discussions.
After carefully examining student work samples, we selected 4 students that would represent the skills and needs that can be found throughout her classroom. With Bailey's anecdotal notes and student work, we were able to develop personalized goals for each focus student.
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We brainstormed structures and scaffolds Bailey could build into her math instruction for lessons leading up to our observation. Based on research and group reflection, Bailey was able to add a turn and talk to the comprehension question, sentence starters, and math partners, while focusing on recording student conjectures and invented vocabulary. We kept track of all of our thinking on a memorialization document.
Planning
Work Sample for Focus Student 1
FS1 demonstrates a base 10 understanding with direct modeling. He feels comfortable using these strategies. FS1 is able to make connections to peer strategies.
We are hoping FS1 will be able to start experimenting with counting strategies, incrementing or invented algorithms. We also hope FS1 will feel confident sharing his thinking and expressing connections at discourse.
The Lesson
On the day of the lesson we each observed one focus student, recording low inference notes on a note catcher for use in our debrief later. I shadowed Focus Student 1. Our goals for FS1 were that he starts experimenting with invented algorithms and can share his thinking.
FS1 used direct modeling with base 10 evidence as a first strategy. He modeled 192 by drawing 10 sticks. He then crossed off 79, breaking apart the 8th 10 stick to complete the 9 ones. He then counted the remaining sticks.
After Bailey selecting his strategy to be shared, he attempted to use an incrementing strategy on the back. He was interrupted by discourse but continued working on his strategy through his peers share-out. Despite working on his second strategy at an unexpected time, FS1 was able to make connections to peers strategies during the discussion. He was not able to complete the second strategy, incrementing by 2s. He will soon find that larger increments are more efficient.
The group had a rich discussion and was able to reference shared vocabulary, even identifying and describing thee vocabulary invented by peers. The discussion did linger on one strategy for a bit longer than the rest, but the students were able to refocus themselves and engage with peer strategies at the end.
​Low Inference Observations of Focus Student 1
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FS1 was able to retell correctly
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Got distracted about who his partner was during the comprehension question
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Counted down from 179 by tens
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When I came close he stopped writing
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When Bailey drew a star on his paper he showed the person next to him and they said “so what?” but he still looked pleased
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Added date & tidied up his name
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He tried another strategy - counting down in increments of two, then switched to increments of 10
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I leaned in and he erased it all.
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He was excited to share and shared first
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Described his strategy and could explain it.
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Stayed standing and tried to complete his second strategy while the other two students shared their strategies.
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When FS2 shared, he noticed connections but couldn’t get into the conversation.
Lesson Artifact for
Focus Student 1
Findings
The team identified two big takeaways from the lesson:
1. The importance of a student created vocabulary wall that can be referred back to frequently between the teacher and the students.
2. Consistently built in structures for students to discuss mathematics (turn and talk, sentence starters, math partners, and past charts) are essential in effective discourse.
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Team Member Debrief Reflections
Bailey
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Ways to connect strategies with previous knowledge building.
Sandy
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Beautiful pattern from beginning to end in the CGI story structure.
Lilly
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First time with a 3 digit number - would have loved to see a discourse with an easier number - what does it look like?
Becca
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What does engagement look like in discourse? Sometimes students made connections even when they looked disengaged, or were able to be pulled back in.
Reflection
The opportunity to reflect deeply about student thinking helped me see how carefully we must balance the needs of the group and the needs of the individuals in the group. We were so focused on focus student needs, we did not necessarily choose the best shared strategies for all students to make the connections needed to deeply meet the content goal. The social emotional needs of individual students must be met in ways that also support the engagement of the group. This finding only deepens my understanding of educator's obligation to deepen their content knowledge to best meet the careful facilitation to balance and meet the needs of the learners in the room. In the future I will spend more time reflecting on the possible misconceptions and developing questions to push thinking of all my students.