# Lesson Study and Teaching Mathematics Through Problem Solving: The Two Wheels of a Cart

## Abstract

The international education community has taken an interest in lesson study, the Japanese approach to school education. Lesson study first came to the attention of educators outside of Japan primarily through the publication of The Teaching Gap (Stigler and Hiebert in The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. The Free Press, New York, 1999) and the TIMSS video study, which showed the typical structure of Japanese mathematics instruction in the classroom. However, while there has been tremendous international interest in using lesson study as a model for professional development, there has been less of a focus on applying the method of Japanese mathematics instruction, which is teaching mathematics through problem solving. This paper discusses the interplay between lesson study and teaching mathematics through problem solving and outlines suggestions for educators seeking to improve both teaching and lesson study outside Japan.

## Keywords

Japanese lesson study Teaching mathematics through problem solving Structured problem-solving Designed tasks*Kikan*-

*jyunshi*

*Neriage*

*Matome*

*Kyozaikenkyu*

## References

- Becker, J. P., Silver, E. A., Kantowski, M. G., Travers, K. J., & Wilson, J. W. (1990). Some observations of mathematics teaching in Japanese elementary and junior high schools.
*Arithmetic Teacher,**38*(2), 12–21.Google Scholar - Department for Children, Schools and Families. (2008).
*Improving practice and progression through lesson study: Handbook for headteachers, leading teachers and subject leaders.*Nottingham: DCSF Publications. http://teachfind.com/national-strategies/improving-practice-and-progression-through-lesson-study-handbook-headteachers-le. Accessed September 27, 2011. - Doig, B., & Groves, S. (2011). Japanese lesson study: Teacher professional development through communities of inquiry.
*Mathematics Teacher Education and Development,**13*(1), 77–93.Google Scholar - Doig, B., Groves, S., & Fujii, T. (2011). The critical role of task development in lesson study. In L. C. Hart, A. S. Alston, & A. Murata (Eds.),
*Lesson study research and practice in mathematics education*(pp. 181–199). Dordrecht: Springer.CrossRefGoogle Scholar - Fernandez, C., & Yoshida, M. (2004).
*Lesson study: A case of a Japanese approach to improving instruction through school-based teacher development*. Mahwah, NJ, USA: Lawrence Erlbaum.Google Scholar - Fujii, T. (2014a). Theorizing lesson study in Mathematics education as an emerging research area: Identifying components and its structure of lesson study. In Japan Society of Science Education (JSSE) (Eds.),
*Proceedings of Second Annual Spring Conference of Japan Society of Mathematical Education*(Vol. X, pp. 111–118) (in Japanese).Google Scholar - Fujii, T. (2014b). Implementing Japanese lesson study in foreign countries: Misconceptions revealed.
*Mathematics Teacher Education and Development,**16*(1), 65–83.Google Scholar - Fujii, T. (2015). The critical role of task design in lesson study. In A. Watson & M. Ohtani (Eds.),
*ICMI study 22: Task design in mathematics education*. Switzerland: Springer.Google Scholar - Fujii, T. (2016). Designing and adapting tasks in lesson planning: A critical process of lesson study.
*ZDM Mathematics Education*. https://doi.org/10.1007/s11858-016-0770-3.Google Scholar - Fujii, T., & Stephens, M. (2001). Fostering an understanding of algebraic generalization through numerical expressions: The role of quasi-variables. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.),
*Proceedings of the 12th ICMI Study Conference: The Future of the Teaching and Learning of Algebra*(pp. 258–264). Melbourne: University of Melbourne.Google Scholar - Fujii, T., & Stephens, M. (2008). Using number sentences to introduce the idea of variable. In C. E. Greenes & R. Rubenstein (Eds.),
*Algebra and algebraic thinking in school mathematics*.*National Council of Teachers of Mathematics, Seventeenth Yearbook*(pp. 127–140). Reston, VA, USA: National Council of Teachers of Mathematics.Google Scholar - Fujii, T., & Iitaka, S. (Eds.). (2011).
*Shinpen Atarashii Sannsu (Elementary school mathematics)*. Tokyo: Tokyo Shoseki.Google Scholar - Fujii, T., Kumagai, K., Shimizu, S., & Sugiyama, S. (1998). A cross-cultural study of classroom practices based on a common topic.
*Tsukuba Journal of Educational Study in Mathematics,**17,*185–194.Google Scholar - Hart, L. C., Alston, A., & Murata, A. (2011).
*Lesson study research and practice in mathematics education*. New York: Springer.CrossRefGoogle Scholar - Hino, K. (2003). Meaning of “Jiriki Kaiketu” (solving problems by students) situation in the mathematics lessons in Japan and Australia: Analysis of two classrooms (in Japanese). In Y. Shimizu (Ed.), Research on cross cultural of comparison of teaching and learning process in mathematics lessons (in Japanese) (Report on collaborative research between Japan and Australia by the Japan Society for the Promotion of Science (in Japanese), pp. 51–79). Tokyo: Tokyo Gakugei University.Google Scholar
- International Math-teacher Professionalization Using Lesson Study (IMPULS). (Eds.). (2017).
*Essential mathematics for the next generation: What and how students should learn.*Tokyo, Japan: Tokyo Gakugei University Press. Google Scholar - Lewis, C. (2002).
*Lesson study: A handbook of teacher-led instructional change*. Philadelphia, PA, USA: Research for Better Schools Inc.Google Scholar - Lewis, C., & Hurd, J. (2011).
*Lesson study step by step: How teacher learning communities improve instruction*. Portsmouth, NH: Heinneman.Google Scholar - Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river.
*American Educator, 22*(4), 12–17 & 50–52.Google Scholar - Lewis, C., Perry, R., & Hurd, J. (2009). Improving mathematics instruction through lesson study: A theoretical model and North American case.
*Journal of Mathematics teacher Education*,*12*, 285–304.Google Scholar - Makinae, N. (2010). The origin of lesson study in Japan. In
*Proceedings of the 5th East Asia Regional Conference on Mathematics Education: In Search of Excellence in Mathematics Education, Tokyo*(Vol. 2, pp. 140–147).Google Scholar - Matsuzawa Elementary School. (Eds.). (2011).
*Matsuzawa elementary school research report*. This school research report is originally written in Japanese and translated into English by the Project IMPULS for the International Seminar on Lesson Study, Nov 30–Dec 1, 2011. http://www.impuls-tgu.org/. Accessed September 13, 2017. - National Course of Study (in Japanese). (2008).
*Ministry of education, culture, sports, science and technology*. http://www.mext.go.jp/a_menu/shotou/cs/index.htm. Accessed April 30, 2015. - Ohtani, M. (2014). Construction zone for the understanding of simultaneous equations: An analysis of one Japanese teacher’s strategy of reflection on a task in a lesson sequence. In F. K. S. Leung, K. Park, D. Holton, & D. Clarke (Eds.),
*Algebra teaching around the world*(pp. 113–128). Rotterdam, The Netherlands: Sense Publishers.Google Scholar - Ono, Y., & Ferreira, J. (2010). A case study of continuing teacher professional development through lesson study in South Africa.
*South African Journal of Education,**30*(1), 59–74.Google Scholar - Soma, K. (2000).
*Mondaikaiketsu no jyugyou ni ikiru mondai shu*. Tokyo, Japan: Meijitosho Shuppan Coporation.Google Scholar - Stigler, J., & Hiebert, J. (1999).
*The teaching gap: Best ideas from the world’s teachers for improving education in the classroom*. New York, NY, USA: The Free Press.Google Scholar - Takahashi, A. (2008).
*Beyond show and tell: Neriage for teaching through problem-solving–Ideas from Japanese problem-solving approaches for teaching mathematics*. Paper presented at the 11th International Congress on Mathematics Education in Mexico (Section TSG 19: Research and Development in Problem Solving in Mathematics Education), Monterrey, Mexico.Google Scholar - Takahashi, A. (2013). Investigation of the mechanism of lesson study as the core of the Mathematics teacher professional development. In Japan Society of Mathematical Education (Eds.),
*Proceedings of First Annual Spring Conference of Japan Society of Mathematical Education, Tokyo, Japan*(pp. 83–87) (in Japanese).Google Scholar - The TIMSS 1995 Video Study. http://www.timssvideo.com/videos/mathematics/Japan. Accessed September 13, 2017.
- Tokyo Shoseki Co., Ltd. (2011). (Eds.),
*Mathematics 1–6*.*Japanese mathematics textbook*(Vol. X) (A. Takahashi, T. Waranabe, M. Yoshida, B. Jacson, & R. Tieff, Trans.). Tokyo, Japan: Tokyo Shoseki.Google Scholar - Watanabe, T., Takahashi, A., & Yoshida, M. (2008). Kyozaikenkyu: A critical step for conducting effective lesson study and beyond. In F. Arbaugh & P. M. Taylor (Eds.),
*Inquiry into mathematics teacher education*(Vol. 5, pp. 131–142). Monograph Series. San Diego, CA, USA: Association of Mathematics Teacher Educators (AMTE).Google Scholar - White, A. L., & Lim, C. S. (2008). Lesson study in Asia Pacific classrooms: Local responses to a global movement.
*ZDM Mathematics Education,**40*(6), 915–925.CrossRefGoogle Scholar - Yoshida, M. (1999).
*Lesson study: A case study of a Japanese approach to improving instruction through school-based teacher development.*Unpublished doctoral dissertation, University of Chicago, Department of Education.Google Scholar