Over the 2018-2019 school year High Tech High teacher teams from the Mathematical Agency Improvement Community (MAIC) conducted three research lessons culminating in three public lesson study events. This post documents and memorializes the first of the series - a 10th grade lesson on quadratics.
Why Lesson Study?
“Knowledge for teaching is embodied in instruction and is spread and refined as teachers watch and discuss practice”
~ Lewis & Hurd, 2011
In order to improve student learning, teachers need opportunities to observe and discuss teaching. Lesson study provides a structure for teachers to collaborate around pressing problems of practice and to engage in cycles of inquiry to explore the intersection of pedagogy and student learning. Engaging in lesson study supports educators in:
Developing pedagogical skills necessary to enact ambitious instruction in classrooms
Building the mathematical knowledge necessary to teach for student understanding
Crafting a communal vision of ambitious student-centered teaching for equity
What is a Research Lesson?
Lesson study can take many forms – quick lesson study cycles lasting 1-2 days to test a particular practice/hack/change idea, or longer more in depth research lessons that explore more complex problems of practice. This post memorializes a 10th grade research lesson.
A research lesson is driven by a pressing problem of practice such as "how can we develop students' ability to engage in rich mathematical discussions, including listening to, building on, and challenging each other's ideas?" To explore the problem, the research team develops a mathematical content goal, an equity related teaching goal, and a theory of action to guide their inquiry. The team then designs a research lesson by researching best practices, exploring the standards and situating the lesson within the common core conceptual progressions, choosing focal students and anticipating student thinking.
During a research lesson, a teaching team introduces students to new learning, and tests out a new lesson structure, pedagogical move, or task, and collects data to determine how it impacted student learning and the development of an equitable learning environment. The lesson is observed by two outside individuals: a content commentator, and an equity commentator. The commentators provide feedback to the team about the degree to which the lesson achieved the research team’s content and equity goals.
The Research Team
The cross-site and cross-grade level research team included:
Sarah Strong, 10th & 11th grade math, High Tech High School
Aurmon Harchegani, 11th & 12th grade math, High Tech High Chula Vista
Leandra Fernandez, 8th grade math and science, High Tech Middle Chula Vista
Cate Challen, 10th & 11th grade math, High Tech High Media Arts
Curtis Taylor, 6th grade math and science, High Tech Middle North County
Kristin Komatsubara, Coach, High Tech Middle
Yekaterina Milvidskaia, Improvement Facilitator, High Tech High Graduate School of Education
Daisy Sharrock, facilitator, High Tech High Graduate School of Education
The team met for one hour a week for eight weeks to research and design the research lesson.
Public Lesson Study Event
This lesson took place November 7th, 2018 in the Forum at the High Tech High Graduate School of Education. The following videos document portions of the pre-brief, the actual research lesson, and the post-lesson debrief, as well as lessons the team learned about teaching and learning.
The Research Question
Each research lesson is guided by a research question that the team is interested in exploring. The richest learning comes from choosing research questions that the team is truly grappling with.
The Theory of Action
Once the team settles on a pressing problem of practice, they generate a theory of action to guide their inquiry.
The Lesson & Mathematical Goal
It is important to anchor each lesson study around a concrete mathematical goal. The specificity of the content goal has an impact on what can be learned from the research lesson. The more specific the content understanding goal, the easier it is to determine whether students met the content goal for the lesson. This was a key learning for the research team that came out in the team's debrief (see final section of this post).
The Mathematical Practices
The Common Core outlines key mathematical practices that students should be developing to build their mathematical identities. The research team outlines the practices focused on during this research lesson.
Anticipating Student Thinking
The research team shares what student thinking they anticipate might occur during the research lesson.
The team shares their data collection plan and tools.
The Research Lesson
The Lesson Launch
The lesson followed a 'launch, explore, discuss' lesson structure. This video shows the lesson launch.
The Explore Phase
During the explore phase of the lesson the students first worked independently and then worked in groups to make sense of the problem together.
The Discuss Phase of the Lesson
During the discuss phase of the lesson students engage in a whole class discussion about the different strategies, and make sense of the problem as a group. In this discussion, connections were made and questions were raised to be explored in the next lesson.
After the lesson observation the research team engages in a discussion about how well they met their mathematical and equity goals and what they are learning about their research question and theory of action based on the observations and data collected from focal students. A research lesson debrief also includes commentary by an outside expert content commentator and equity commentator. In this lesson Dr. Libby Butler served as both content and equity commentator. However, common practice is for these roles to be separate.
What Did We Learn About Our Theory of Action?
The team debrief about what they were learning about their research question, "How can we help students see each other as co-constructors of mathematical ideas and help them find value in collaborating with others?" and their theory of action, "If we as teachers anticipate student thinking in order to be a skeptic, and show students how to be skeptics of one another then students will challenge and build on each other’s ideas resulting in students developing stronger mathematical reasoning skills that support their co-construction of mathematical ideas."
On Student Thinking Over the Course of the Lesson
Cate reflects on the trajectory of student thinking over the course of the lesson and the importance of having students share their ideas publicly with their peers.
On the Evidence of Productive Struggle
Curtis and Kristin share evidence from their focus students and their group members of the students engaged in productive struggle.
The team discusses next steps for their practice.
The Research Team's Reflections & Key Learnings
The team identified three key learnings about teaching and learning from the research lesson:
The importance of having a concrete and focused mathematical goal
The importance of timing and bringing the whole class together to discuss partial understandings throughout the lesson
The importance and continual work of attending to group dynamics
A Focused Mathematical Goal
Sarah reflects on the key learning for the research team. The importance of having a concrete mathematical goal. A focused mathematical goal establishes what you hope all students understand from a lesson and helps to focus questioning strategies for the class discussion.
Discussing Partial Understandings Throughout the Lesson
The full lesson was an hour and a half long (whew!). Sarah reflects how the timing could have been improved by bringing the class together to discuss partial understandings more frequently throughout the lesson.
Attending to Group Dynamics
Sarah reflects on the ongoing work of Complex Instruction - fostering positive group dynamics in order to disrupt traditional patterns of social behavior that can show up in classrooms and lead to inequitable learning outcomes.