A Randomized Trial of Lesson Study: Impact on Teachers’ and Students’ Knowledge of Fractions

• In Event: Lesson Study Supported by Mathematical Resources: A Theoretical Framework, Randomized Trial, and Implications for Reform

Abstract

Over the past decade, interest in lesson study has grown in the U.S. (e.g., Hart, Alston, & Murata, 2011), as have calls for rigorous research on the impact of professional development (e.g., U.S. Department of Education, 2002, 2009). To date, most research on lesson study has been small in scale and relied on qualitative methods. This paper expands on this foundational research by reporting a randomized controlled study of 39 lesson study groups that includes quantitative assessments of teachers’ and students’ mathematical knowledge.

Lesson study groups recruited from 27 school districts, in 11 states and the District of Columbia, were randomly assigned to one of three conditions: (1) lesson study on fractions, supported by mathematical resources; (2) lesson study on a group-chosen topic other than fractions; or (3) locally-chosen professional development other than lesson study. In all, the sample includes 213 educators and 1,059 elementary students from a broad range of socioeconomic backgrounds. Pre- and post assessments were administered to teachers and students in the fall and spring of the 2009-10 school year. Video-recordings of lesson study meetings and research lessons, related artifacts (e.g., lesson plans), and teacher reflection forms were mailed in by all sites.

Teacher assessment items were drawn mainly from existing instruments, including those developed by LMT (e.g., Hill, Rowan & Ball, 2005; Hill, Schilling & Ball, 2004) and by other research (e.g., Beckmann, 2005; Newton, 2008). Items were used to build three measures of teachers’ fractions knowledge: knowledge of fractions, frequency of mathematical errors and understanding of the whole. A fourth measure, teachers’ self-ratings of fractions knowledge, was created from ratings on the item “I have strong knowledge of fractions.”

Student assessment items were drawn from existing national and state assessments, curricula, and research studies (including Hironaka & Sugiyama, 2006; Institute of Education Sciences, 2007; Saxe, 2007). Three assessment forms for students’ fractions knowledge were developed, for students in grades 2/3, grade 4, and grade 5; the same core of items was used across all three forms, with additional items for the higher grade levels. Two subscales developed from the total item pool allowed assessment of students’ performance on items of both familiar and unfamiliar format.

Two-level HLM analyses indicate that the experimental treatment (lesson study with mathematical resources) had a positive, statistically significant effect on three of the four measures of teachers’ fraction knowledge, with effect sizes ranging from .14 to .37. Three-level HLM analyses indicate that the experimental treatment had a positive, statistically significant impact on the three student outcome measures, with effect sizes ranging from .45 to .53; experimental treatment effects held with both unfamiliar and familiar item types. This study, in which lesson study groups worked autonomously with carefully selected mathematical resources, suggests the potential of locally-led lesson study to improve both teachers’ mathematics knowledge and their capacity to support student learning. It also suggests the potential utility of the linear measurement model of fractions; connections between the study and the fractions content of Common Core State Standards will be discussed.

Authors

• Rebecca R. Perry, Mills College

• Catherine C. Lewis, Mills College