Building a Knowledge Base for Teaching: Design and Test of Research-based Toolkits for Mathematics Lesson Study

Principal Investigator: 
Project Overview
Background & Purpose: 

The project developed and tested two “toolkits” (mathematics resource guides) designed to help practitioners working in lesson study (LS) groups use and build upon research-based knowledge. The toolkits provided resources on the teaching and learning of two content areas: proportional reasoning and area of polygons. The project studied impact of the toolkit-supported LS work on teachers’ knowledge and attitudes and on the development of a knowledge base for teaching that is shareable, verifiable, and improvable.


Volunteer lesson study groups from across the U.S. were recruited for the study, including groups from five states (CA, MA, MN, FL, and NY) and a range of different settings (urban, suburban, and rural). A total of 27 groups from 10 school districts were included in the study. Four sites in or near Oakland, CA were chosen as “intensive study sites” so that researchers could easily observe the intervention and conduct research.

Research Design: 

This project was comparative and was designed to generate evidence that is descriptive [case study and observational] and causal [experimental]. Original data were collected through diaries, assessments of learning, observation [personal observation and videography], and survey research [self-completion questionnaires and focus groups].

The study included two major types of data analysis: 1) hierarchical linear modeling to study the impact of experimental assignment on teachers’ mathematical knowledge for teaching and attitudes; and (2) descriptive and correlational analyses of the group processes associated with teachers’ use of the intervention.

A teacher pre- and post- assessment was developed to tap teachers’ mathematical knowledge for teaching of proportional reasoning and area of polygons. The assessment included 34 items focused on mathematics teaching and learning (out of a total of 53 survey items) and were drawn from established instruments (Learning Mathematics for Teaching Project at the University of Michigan, the University of Chicago School Mathematics Project and the student National Assessment of Educational Progress). Several additional items were constructed-response items developed by our project to tap particular knowledge related to the mathematics resource materials. The remaining items assessed teachers’ attitudes about mathematics and professional development, or gathered demographic information about respondents.


Our conceptual model of teachers’ development during lesson study predicts lesson study impact on three areas of teachers’ development: mathematical knowledge for teaching, teachers’ learning dispositions, and teacher learning community.

Development of Mathematical Knowledge for Teaching: Preliminary t-tests and HLM analyses show that the experimental condition (toolkit-supported lesson study) did not significantly impact teachers’ mathematical knowledge for teaching (MKT) as measured by items from standardized tests of MKT. Analysis of constructed-response mathematical items revealed a different picture of teachers’ knowledge. Items that required teachers to generate mathematical ideas (about the characteristics of a proportional relationship or about what students should know about area of rectangles or parallelograms) revealed significantly greater increases in the toolkit-supported lesson study groups than in the comparison teachers. Teachers’ self-reported knowledge of the proportional reasoning toolkit topic studied also increased significantly from pre-test to post-test and in relation to comparison teachers.

Development of Teachers’ Learning Dispositions: The second domain we posited would be influenced by lesson study is development of teachers’ disposition to learn mathematics and to improve their teaching. We derived three measures of this domain from survey data: interest and enjoyment in learning mathematics (6 item scale); expectations for student achievement (6 item scale); and teachers’ agreement with the statement “by trying a different teaching method, I can significantly affect a student’s achievement.” Preliminary t-tests indicate that teachers in toolkit-supported lesson study group significantly increased their agreement with the statement about changes in teaching method from pretest to posttest, whereas teachers in the comparison group did not. Further HLM analysis will describe the impact of toolkit group assignment on teachers’ learning dispositions.

Development of Teacher Learning Community: A 4-item Collegial Learning Effectiveness scale was developed to tap teachers’ perceptions of the effectiveness of the teacher learning community in building teachers’ mathematics knowledge for teaching. Preliminary t-tests indicate that the toolkit-supported lesson study teachers rated the collegial learning effectiveness in their group significantly higher at posttest than at pretest and also significantly higher than the comparison teachers at posttest.

Publications & Presentations: 

Perry, R., Lewis, C., Friedkin, S, and Baker, E. (2009). Teachers’ knowledge development during lesson study: Impact of toolkit-supported lesson study on teachers’ knowledge of mathematics for teaching. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.

Perry, R. & Lewis, C., with Burge, P. & Bombardier, J. (2009). Using a mathematical toolkit to support teachers’ learning. Paper presented at the research pre-session of the annual meeting of the National Council of Teachers of Mathematics, Washington, DC.

Lewis, C., Friedkin, S., Baker, E., and Perry, R. (Forthcoming). Learning from the key tasks of lesson study. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching elementary mathematics: Tasks to enhance prospective and practicing teacher learning. Springer Science + Business Media, B.V., Dordrecht, The Netherlands.