The Use of Lesson Study to Unpack Learning Trajectories and Deepen Teachers' Content Knowledge

• In Event: Poster Session 9
  In Poster Session: Understanding Lesson Study From Different Theoretical Perspectives (Part 1)

Abstract

Objective
The purpose of this session is to share a case study of one school team of kindergarten through sixth-grade teachers, their math coach, and university educators collaborating on Lesson Study focused on fraction understanding. We highlight a learning trajectory-based professional development (PD) routine and tools used during Lesson Study to deepen teachers’ and coaches’ understanding through the analysis of student work.

Theoretical Framework
Lesson Study empowers teachers and coaches and provides a collaborative structure that promotes reflection and critical dialogue about pedagogical content knowledge among colleagues (Lewis, 2002; Lewis, Perry, & Murata, 2006).  The focus on a single rich problem with teachers from multiple grade levels within a Lesson Study team  allowed for rich and meaningful vertical articulation and a deepening of the understanding of the mathematical learning progression (Suh & Seshaiyer, 2014).

Methods
Drawing from  the research base in mathematics education on learning trajectories, (LTs) (e.g., Clements & Sarama, 2004; Confrey, 2012; Simon, 1995; Sztajn, Confrey, Wilson, & Edgington, 2012), we asked teachers and coaches to  1) create a set of related tasks across the vertical grades that map a developmental progression within a specific mathematical domain; 2) collect and analyze evidence of students’ thinking and learning around a specific problem they posed during Lesson Study. Through these activities, teachers and coaches thought deeply how their students’ rational number thinking fit into an existing LT.

Research Questions:
1. What are the affordances of Lesson Study with vertical teams of teachers focused on understanding the learning progression of rational numbers?
2. How did the teachers adapt a benchmark problem using a relevant curricular learning progression?

Data Sources
The data sources included video clips from the research lesson debrief, student work, teacher reflections from the Lesson Study, transcription from a videotaped group presentation on the Lesson Study ,and researchers’ field notes written as memos.  We also asked teachers to reflect on Lesson Study process of developing and refining a research lesson.

Results
Our  PD routine was a Lesson Study focused on the Math Vertical Articulation to Unpack the Learning Trajectory to help teachers and coaches translate learning trajectories to practice. The teachers wanted to investigate how kindergarten students would divide six sandwiches among eight friends with the support of concrete tools such as fraction circles. The observers of the host teacher lesson were surprised by the quality of student rational number reasoning. The coach facilitated a productive debrief with the participating teachers to verify, validate and sometimes dispute the hypothetical learning trajectories based on their observations.
The second iteration of Lesson Study was in the fourth grade classroom. Teachers were surprised to see that fourth graders still struggled to name the fraction. They discussed the progression of equal sharing problems and the progression of learning from problems of sharing that results in whole numbers, unit fractions and non-unit fractions. The teachers realized that this problem involving non-unit fraction was challenging for many students.

Authors

• Jennifer M. Suh, George Mason University

• Padmanabhan Seshaiyer, George Mason University

• Terrie McLaughlin Galanti, University of North Florida

• Sara Birkhead, George Mason University

• Rachelle Farmer