Using Lesson Study to Build Japanese-Style Teaching Through Problem Solving in U.S. Schools: Student Mathematical Impact

• In Event: Using Lesson Study to Build Mathematical Problem Solving in Three National Contexts

Abstract

Objectives
U.S. mathematics frameworks have emphasized problem-solving for several decades (NCTM, 1980), without major success (e.g., OECD, 2007). Our research provided U.S. educators with Japanese resources on Teaching Through Problem-Solving and a live lesson study process, and studied the impact on instruction and students.

Theoretical Framework
Our theoretical framework assumes that mathematical problem-solving is multi-faceted (Ho & Hedberg, 2005), entailing: mathematical knowledge; problem-solving strategies (e.g., organizing data); metacognition (e.g., capacity to monitor one’s own strategies); and beliefs (e.g., that effort matters).

Our framework treats instructional improvement as a complex interaction among teachers, students, and curriculum that requires iterative cycles of feedback from students and colleagues. Lesson study (Lewis & Hurd, 2011) engages teachers in ongoing, collaborative study of live instruction, incorporates feedback from colleagues and students, and supports teachers’ motivation as researchers of practice. Hence it was chosen as the intervention method.

Methods
U.S. elementary educators were randomly assigned to 2 conditions after providing baseline videos. In the experimental condition, educators took part in a 4-day summer lesson study workshop with daily research lessons that allowed observation and discussion of Japanese-style Teaching Through Problem-Solving as a way to build the students mathematical practices of the Common Core State Standards-Mathematics (CCSS-M; CCSSI, 2010). Control group educators conducted independent study of CCSS-M, using online materials widely available in the U.S. During the subsequent school-year, both groups continued study of their respective online materials (Japanese or U.S. materials) and applied them to their teaching of two topics: polygon area (a brief assignment), fractions (a longer assignment entailing planning and teaching of 4 classroom lessons).

Data Sources
Data included baseline and end-of-study assessments of students’: knowledge of area and fractions; mathematical attitudes (growth mindset, belonging, perseverance); and actual perseverance on open-ended mathematics problems; most items were drawn from available assessments and research studies. Teachers submitted pre- and post-intervention classroom video portfolios.

Results
HLM analysis accounted for nesting of students within teachers within conditions and indicated no significant treatment impact on either student knowledge measure (area or fractions). However, further analyses show teachers in the experimental group who participated in school-year lesson study produced a significant increase in students’ fractions knowledge (but not area knowledge) (Table 1, Figure 2).

ANCOVA analyses of student attitudes, using pre-scores as a covariate, and grouping of experimental vs. control as the fixed effect, found significantly higher scores on perseverance (p < 0.01) in the experimental group, but no significant differences in mindset or belonging. Experimental group students also showed significantly greater effort on the open-ended mathematics items (measured by number and elaboration of responses; p < 0.001), providing behavioral evidence of increased perseverance. Figure 3 illustrates one student’s elaborate post-response.

Analyses of pre- and post-intervention classroom video suggest that teachers’ redistribution of classroom time to allow more student presentation and explanation of ideas may be the mechanism of change.

Significance
This study suggests that U.S. teachers can effectively use problem-solving approaches developed in Japan if opportunities for collaborative practice-based learning (such as lesson study) are provided.

Authors

• Kevin Lai

• Catherine C. Lewis, Mills College