Teaching Through Problem Solving (Mondai Kaiketsu Gakushu) in Japan

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

Abstract

Objectives
This presentation:
1. Highlights how Japanese lesson study networks have drawn on Western ideas about mathematical problem-solving;
2. Describes Mondai Kaiketsu Gakushu (Teaching Through Problem-Solving);
3. Examines TIMSS data on mastery of non-taught curriculum; and
4. Presents a case study of a Japanese school-wide lesson study focused on students’ mathematical problem-solving.

Theoretical Framework
The AERA call for “public scholarship to educate diverse democracies” argues that “the research base itself needs advocates; it will not be used unless it is thoughtfully promoted” (p.1). Interacting local, regional and national lesson study systems in Japan provide testing grounds for research-based ideas and places for teachers to publicly examine teaching and to refine it. The process of lesson study epitomizes Dewey’s argument (AERA call p.2) that “science can best contribute to social progress (including educational progress) through a process of sustained public inquiry, rather than by being asserted or trickling down….” This presentation illuminates the Japanese process of “sustained public inquiry.”

Methods
This multi-method study includes (1) a case study of school-wide lesson study in a Japanese elementary school; (2) secondary analysis of TIMSS data; and (3) review of historical documents. The author taught elementary and lower secondary mathematics in Japan for two decades and was nationally active in lesson study, providing a first-hand vantage point on instructional changes toward problem-solving.

Data Sources
Data sources from the elementary school case include (1) observations of lesson study-related events (e.g., research lessons, post-lesson discussions, public open house); (2) interviews of key decision-makers; and (3) documents (e.g., lesson plans, planning documents, reports).

TIMSS 2003 (but not subsequent TIMSS studies) provide data on the average percentage of TIMSS mathematics topics taught at grade 4 and 8 in Japan and other participating countries, as well as the average achievement. These data allow us to look at achievement as it relates to curriculum coverage across countries.

Western and Japanese historical documents are also examined, including Young (1908), NCTM’s Agenda for Action (1980) and Principles and Standards (2005), and Japanese mathematics textbooks from various eras.

Results
Artifacts from the case study show how Japanese educators used lesson study to share and refine instructional knowledge to support students’ mathematical problem-solving. Figure A1 provides one example: an improvable framework for enacting and judging a high-quality discussion.

Analysis of TIMSS grade 4 achievement by curriculum coverage suggests that Japan is unusual internationally in students’ capacity to answer correctly items that have not yet been taught; see Figure A2. This finding will be linked to instructional approaches that emphasize solution of novel problems, as well as curriculum that uses open-ended problems to have students derive new mathematical concepts.

Historical texts trace flow of mathematics problem-solving ideas between the West and Japan, and into classroom practice through Japanese lesson study.

Significance
This presentation (1) highlights lesson study, a structure for public examination and improvement of teaching and for enacting and refining research-based ideas that originated in another country; and (2) shows how Japanese-style Teaching Through Problem-Solving has been built and spread through lesson study.

Author

• Akihiko Takahashi, De Paul University, College of Education