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HTH/MAIC Public Lesson Study #3 - 3rd Grade

Updated: Jun 24, 2020

The cross-site elementary lesson study research team visits the presenting teacher's classroom to get to know focus students better prior to the public lesson study

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 third of the series – a 3rd grade lesson on comparing fractions.

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 student thinking 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 3rd grade research lesson on comparing fractions.

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 understanding 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:

  • Karen Underwood, 3rd grade, High Tech Elementary North County

  • Alli Kucia, 3rd grade, High Tech Elementary

  • Josh Benedick, 2nd grade, High Tech Elementary

  • Marissa Adams , 2nd grade, High Tech Elementary Explorer

  • Matt Sheelen, 2nd grade, High Tech Elementary Chula Vista

  • Ruth Smith, 4th grade, High Tech Elementary Chula Vista

  • Yekaterina Milvidskaia, Improvement Facilitator/Math Coach, 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

This lesson took place June 10th, 2019 at High Tech Middle North County. The following videos document portions of the pre-brief, the actual research lesson, and the post-lesson debrief, including commentary from the equity and content experts.

The Research Question

The team developed a research question based on observations of student behavior and content knowledge from their contexts. How do we create a class culture where partial understandings and making mistakes are a normal part of mathematical learning?

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. If we implement routines around celebrating and valuing partial understandings then students will internalize that it is ok to make mistakes when learning math, resulting in a class culture where mistakes are seen as an equally valuable part of mathematical learning.

Determining the Mathematical Goal

Learning from a previous research lesson highlighted the importance of having a concrete mathematical goal. The specificity of the content understanding 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 Equity Goal

The team also generated an equity goal for their lesson. Equity goals relate to the effectiveness of the classroom learning culture and patterns of student participation.

Anticipating Student Thinking

The research team anticipated how their focus students might approach the task and share the connections they hoped to spark during the 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 was a CGI story problem and followed a 'launch, explore, discuss' lesson structure. This video shows the lesson launch.


During the explore phase of the lesson the students worked independently to make sense of the problem. While students grappled with the task, Karen circulated and conferred with students to better understand their thinking and to select students to share their strategies for the discussion phase.


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.

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. Susan Nickerson from San Diego State University served as the content commentator and Mari Jones from the Center for Equity and Innovation served as the equity commentator.

What Did We Learn About our Research Question & Theory of Action?

The team debriefs about what they learned about their research question, and their theory of action.

Karen's Reflection

The presenting teacher has the opportunity to reflect first.

Team Debrief

The team shared their lesson observations in relation to the equity/culture goal and the mathematical content goal.

Equity Goal Reflection:

Content Understanding Goal Reflection:

The Expert Commentary & Key Learnings

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

  • The importance of using turn and talks throughout the discourse so all students have multiple opportunities to process their thinking out loud

  • The importance of language in the math classroom and how it can set up students to learn additional/advanced concepts later on in their academic careers - this learning came through the content commentary

Dr. Susan Nickerson's Content Commentary

Mari Jones' Equity Commentary


Daisy Sharrock works at the Center for Research on Equity and Innovation at the High Tech High Graduate School of Education, and is part of a Student-Centered Learning Research Collaborative-sponsored research team that is currently engaged in the following study: Leveraging the Power of Improvement Networks to Spread Lesson Study. Read more about their current study here. We are grateful to JFF, KnowledgeWorks’, and the Student-Centered Learning Research Collaborative and its funders for their support. Learn more at

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