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HTH/MAIC Public Lesson Study #2 - 8th Grade

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 second of the series - an 8th grade lesson on exponents.

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 an 8th grade research lesson on exponents.

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. It should be noted that for this lesson one person, Dr. Libby Butler served as both expert content and equity commentator.

The Research Team

The cross-site and cross-grade level research team included:

  • Katie Pond Waters, 8th grade math, High Tech Middle

  • 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

The Pre-Brief

Memorializing Document (adopted from SFUSD & Mills College)

This lesson took place March 5th, 2019 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

The team developed a research question based on observations of student behavior and content knowledge from their contexts. How can we create a classroom environment in which being lost, making mistakes, and questioning for understanding are seen as a normal part of doing math?

The Theory of Action

Once the research team settled on a pressing problem of practice, they generated a theory of action to guide their inquiry.

Determining the Mathematical Goal

Learning from a previous research lesson highlighted the importance of having 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 meet the content goal for the lesson.

The Context for the Problem

The team provided the context for the chosen lesson and how it relates to the research question and the lesson equity goal.

Group Roles

Group roles provide a structure for supporting students in productive group work and were used in this lesson. The video below describes the different roles. Additional information about group roles can be found here.

Anticipating Student Thinking

The research team anticipated what kinds of student thinking they might see during the research lesson.

Mathematical Practices

The Common Core outlines key mathematical practices that students should be developing to build their mathematical identities. The research team outlined the practices focused on during this research lesson.

Data Collection & Assessing Student Thinking

The team shared their data collection plan and tools.

The Research Lesson & Observation


The lesson followed a 'launch, explore, discuss' lesson structure. This video shows the lesson launch.


During the explore phase of the lesson the students first worked independently and then worked in groups to make sense of the problem together.


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. This lesson stopped short of a full class discussion, ending with student sharing their preliminary strategies. One of the key learnings for the team was the importance of discussing the student ideas as a whole class to evaluate the merits of different problem solving strategies.

The Debrief

After the lesson observation the research team engaged in a discussion about how well they met their mathematical and equity goals and what they learned 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 debriefs about what they learned about their research question, "How can we create a classroom environment in which being lost, making mistakes, and questioning for understanding are seen as a normal part of doing math?" and their theory of action, "If we use well constructed problems, anticipate student thinking/problem solving strategies, focus our lessons on student discussion, and use ‘why’ questions to push students to articulate their understanding, then we will create a class culture where students will feel more comfortable sharing their mathematical ideas with each other resulting in a deeper mathematical understanding."

Katie's Reflection

Katie reflected on a key takeaway around the importance of whole class discussion and identified it as an area of growth.

Team Debrief

The team shared their lesson observations in relation to the equity/culture goal and the next steps they might take in relation to the mathematical content goal.

The Expert Commentary & Key Learnings

The team identified two key learnings about teaching and learning from the research lesson:

  • The importance of developing concrete questioning strategies to guide the whole class discussion

  • The importance and continual work of attending to language used during the lesson and it's impact on student mathematical identity development

Dr. Libby Butler engaged the audience in some reflection about the research lesson and the degree to which the team met their content and equity goals.

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