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Activity systems analysis of classroom teaching and learning of mathematics: a case study of Japanese secondary schools

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Abstract

International comparative studies on mathematics teaching and learning often provide unitary and harmonious images of classroom practices. This paper aims to complement those studies by describing the complex aspects of those practices. Adopting activity theory as a framework, this paper considers classroom teaching and learning of mathematics as an activity system embedded in socio-historical contexts, analyzes its contradictions, and makes a comparative analysis of different practices of mathematics teaching and learning in the same country. As a case in point, mathematics lessons in Japanese secondary schools are considered. The initial activity system of mathematics lessons in Japanese modern schools came from the whole-class instruction system and then gradually evolved into the problem-solving style lesson. The latter has been facing challenges, and then a new activity system has emerged from a new paradigm of school education. It is argued that activity systems analysis enables us to understand the contradictions prevailing in mathematics education and that comparative analysis of more than one system in the same culture can provide valuable insights.

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Notes

  1. In traditional mathematics lessons in Japanese secondary schools, teachers may allow students to consult with nearby students, but do not organize small group work frequently. In either case, individual students are supposed to “struggle” alone first.

  2. In public secondary schools in Japan, the current standard class size has been determined as 40 by law.

  3. The Japanese word “jiriki” signifies doing by oneself.

  4. President of the International Network for School as Learning Community, Professor Emeritus at the Tokyo University, and Professor at Gakushuin University

  5. In Japanese, “hanashi” is a verb used to mean speaking, and attaching “-ai” after a verb X signifies doing X to each other.

References

  • Araki, Y. (1957). Hajimeni [Introduction]. In S. Nabeshima & K. Toda (Eds.), Chugakko sugaku kyozai kenkyu koza 6: Modai-kaiketsu [Teaching material study course for junior-high school mathematics No. 6: Problem-solving] (pp. 1–3). Kaneko Shobo.

  • 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. https://doi.org/10.5951/AT.38.2.0012

    Article  Google Scholar 

  • Clarke, D., Mesiti, C., Jablonka, E., & Shimizu, Y. (2006). Addressing the challenge of legitimate international comparisons: Lesson structure in the USA, Germany and Japan. In D. Clarke, J. Emanuelsson, E. Jablonka, & I. A. C. Mok (Eds.), Making connections: Comparing mathematics classrooms around the world (pp. 23–45). Sense Publishers. https://doi.org/10.1163/9789087901639_003

  • Duke, B. (1986). The Japanese school: Lessons for industrial America. Praeger.

  • Emori, I. (1990). "Benkyo" jidai no makuake [The start of the "Study" era]. Heibonsha.

  • Engeström, Y. (1993). Developmental studies of work as a testbench of activity theory: The case of primary care medical practice. In S. Chaiklin & J. Lave (Eds.), Understanding practice: Perspectives on activity and context (pp. 64–103). Cambridge University Press. https://doi.org/10.1017/CBO9780511625510.004

  • Engeström, Y. (1998). Reorganizing the motivational sphere of classroom culture: An activity-theoretical analysis of planning in a teacher team. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 76–103). Cambridge University Press. https://doi.org/10.1017/CBO9780511720406.004

  • Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen, & R.-L. Punamäki (Eds.), Perspectives on activity theory (pp. 19–38). Cambridge University Press. https://doi.org/10.1017/CBO9780511812774.003

  • Engeström, Y. (2001). Expansive learning at work: Toward an activity theoretical reconceptualization. Journal of Education and Work, 14(1), 133–156. https://doi.org/10.1080/13639080020028747

    Article  Google Scholar 

  • Engeström, Y. (2015). Learning by expanding: An activity-theoretical approach to developmental research (2nd ed.). Cambridge University Press. https://doi.org/10.1017/CBO9781139814744 (Original work published 1987).

  • Engeström, Y., & Sannino, A. (2011). Discursive manifestations of contradictions in organizational change efforts: A methodological framework. Journal of Organizational Change Management, 24(3), 368–387. https://doi.org/10.1108/09534811111132758

    Article  Google Scholar 

  • Fujii, T. (2018). Lesson study and teaching mathematics through problem solving: The two wheels of a cart. In M. Quaresma, C. Winsløw, S. Clivaz, J. P. da Ponte, A. N. Shúilleabháin, & A. Takahashi (Eds.), Mathematics lesson study around the world: Theoretical and methodological issues (pp. 1–22). Springer. https://doi.org/10.1007/978-3-319-75696-7_1

  • Fukuzawa, R. E. (1994). The path to adulthood according to Japanese middle schools. Journal of Japanese Studies, 20(1), 61–86. https://doi.org/10.2307/132784

    Article  Google Scholar 

  • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K., Hollingsworth, H., Jacobs, J., Chui, A., Wearne, D., Smith, M., Kersting, N., Manaster, A., Tseng, E., Etterbeek, W., Manaster, C., Gonzales, P., & Stigler, J. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study (NCES 2003-013). U.S. Department of Education, National Center for Education Statistics. https://nces.ed.gov/pubs2003/2003013.pdf

  • Hino, K. (2015). Comparing multiple solutions in the structured problem solving: Deconstructing Japanese lessons from learner's perspective. Educational Studies in Mathematics, 90, 121–141. https://doi.org/10.1007/s10649-015-9626-y

    Article  Google Scholar 

  • Hirata, K., & Warschauer, M. (2014). Japan: The paradox of harmony. Yale University Press.

  • Inoue, N. (2011). Zen and the art of neriage: Facilitating consensus building in mathematics inquiry lessons through lesson study. Journal of Mathematics Teacher Education, 14, 5–23. https://doi.org/10.1007/s10857-010-9150-z

    Article  Google Scholar 

  • Ito, S. (1987). Sansuka ni oite, ima naze, mondai-kaiketsu ka [Why problem-solving in arithmetic, now?]. In S. Ito & Saitama-ken Kasahara Shogakko (Eds.), Sansuka, atarashii mondai-kaiketsu no shido (Kiso hen) [Teaching of new problem-solving in arithmetic (Basics)] (pp. 5–25). Toyokan.

  • Ito, S. (2000). Teaching methods of mathematics education: Focusing on a historical research of problem-solving. Journal of Japan Society of Mathematical Education, 82(7-8: Special issues), 182–186.

    Google Scholar 

  • Jackson, P. W. (1990). Life in classrooms. Teachers College Press.

  • Jaworski, B., & Potari, D. (2009). Bridging the macro- and micro-divide: Using an activity theory model to capture sociocultural complexity in mathematics teaching and its development. Educational Studies in Mathematics, 72, 219–236. https://doi.org/10.1007/s10649-009-9190-4

  • Jurdak, M. E. (2006). Contrasting perspectives and performance of high school students on problem solving in real world situated, and school contexts. Educational Studies in Mathematics, 63, 283–301. https://doi.org/10.1007/s10649-005-9008-y

    Article  Google Scholar 

  • Kaptelinin, V. (2005). The object of activity: Making sense of the sense-maker. Mind, Culture, and Activity, 12(1), 4–18. https://doi.org/10.1207/s15327884mca1201_2

    Article  Google Scholar 

  • Karabenick, S. A. (Ed.). (1998). Strategic help seeking: Implications for learning and teaching. Routledge. https://doi.org/10.4324/9781410602701

  • Karabenick, S. A., & Newman, R. S. (Eds.). (2006). Help seeking in academic settings: Goals, groups, and contexts. Routledge. https://doi.org/10.4324/9780203726563

  • Katagiri, S., Koto, S., & Hiraoka, T. (Eds.). (1985). Mondai-kaiketsu no noryoku wo nobasu shido [Teaching for developing problem-solving abilities]. Meiji Tosho.

  • Keitel, C., & Kilpatrick, J. (1999). The rationality and irrationality of international comparative studies. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 241–256). Falmer Press. https://doi.org/10.4324/9780203012086

  • Koike, Y. (2015). Sansu sugaku no jugyo ni okeru neriage no juyosei to sono arikata ni kansuru ichi kosatsu [A study on neriage in arithmetic and mathematics lessons: Its importance and current problems]. Japan Society for Science Education Research Report, 29(9), 59–64.

    Google Scholar 

  • Koto, S. (1985). Mondai-kaiketsu kenkyu no igi to sono doko [The value and recent trends of problem-solving research]. In S. Katagiri, S. Koto, & T. Hiraoka (Eds.), Mondai-kaiketsu no noryoku wo nobasu shido [Teaching for developing problem-solving abilities] (pp. 8–23). Meiji Tosho.

  • LeTendre, G. K. (1999). The problem of Japan: Qualitative studies and international educational comparisons. Educational Researcher, 28(2), 38–48. https://doi.org/10.3102/0013189X028002038

    Article  Google Scholar 

  • LeTendre, G. K., Baker, D. P., Akiba, M., Goesling, B., & Wiseman, A. (2001). Teachers' work: Institutional isomorphism and cultural variation in the U.S., Germany, and Japan. Educational Researcher, 30(6), 3–15. https://doi.org/10.3102/0013189X030006003

    Article  Google Scholar 

  • Mehan, H. (1979). Learning lessons: Social organization in the classroom. Harvard University Press.

  • Nabeshima, S., & Toda, K. (Eds.). (1957). Chugakko sugaku kyozai kenkyu koza 6: Modai-kaiketsu [Teaching material study course for junior-high school mathematics No. 6: Problem-solving]. Kaneko Shobo.

  • Nakajima, K. (Ed.). (1985). Sugaku-teki kangaekata to mondai-kaiketsu 1 (Kenkyu Riron hen) [Mathematical thinking and problem-solving 1 (Research theories)]. Kaneko Shobo.

  • Nakane, C. (1973). Japanese society: A practical guide to understanding the Japanese mindset and culture. Tuttle Publishing.

  • Nardi, B. A. (Ed.). (1996). Context and consciousness: Activity theory and human-computer interaction. The MIT Press.

  • National Council of Teachers of Mathematics (1980). An agenda for action: Recommendations for school mathematics of the 1980s. National Council of Teachers of Mathematics.

  • Nelson-Le Gall, S. (1981). Help-seeking: An understudied problem-solving skill in children. Developmental Review, 1, 224–246. https://doi.org/10.1016/0273-2297(81)90019-8

    Article  Google Scholar 

  • Nohda, N. (1994). Mondai-kaiketsu to kadai-gakushu [Problem-solving and problem-learning]. In T. Hiraoka, S. Koto, M. Shoda, Y. Sugiyama, N. Nohda, & S. Shimizu (Eds.), Chugakko sugakka kyoiku jissen koza 11: Mondai-kaiketsu, kadai-gakushu [Junior high school mathematics teaching seminar no. 11: Problem-solving and problem-learning] (pp. 225–245). Nichibun.

  • Núñez, I. (2009). Activity theory and the utilisation of the activity system according to the mathematics educational community. Educate~, Kaleidoscope Special Issue, 7–20. http://www.educatejournal.org/index.php/educate/article/view/217/201

  • O'Donnell, A. M., & Hmelo-Silver, C. E. (2013). Introduction: What is collaborative learning? An overview. In C. E. Hmelo-Silver, C. A. Chinn, C. K. K. Chan, & A. M. O'Donnell (Eds.), International handbook of collaborative learning (pp. 1–15). Routledge. https://doi.org/10.4324/9780203837290

  • Osawa, T. (2003). Jiriki-kaiketsu wa jugyo no shuyaku ka [Is individual work the leading part of lesson?]. In Zenkoku Sansu Jugyo Kenkyukai (Ed.), Ima, sansu ga abunai: Honto no mondai-kaiketsu no jugyo wo mezashite [A crisis of arithmetic teaching: Toward the true problem-solving lesson] (pp. 66–75). Toyokan.

  • Saito, E., Murase, M., Tsukui, A., & Yeo, J. (2015). Lesson study for learning community: A guide to sustainable school reform. Routledge. https://doi.org/10.4324/9781315814209

  • Sarkar Arani, M. R. S., Fukaya, K., & Lassegard, J. P. (2010). "Lesson Study" as professional culture in Japanese schools: An historical perspective on elementary classroom practices. Japan Review, 22, 171–200 https://www.jstor.org/stable/25791346

    Google Scholar 

  • Sato, M. (1996). Karikyuramu no hihyo: Kokyosei no saikochiku e [Critique on curriculum: Redefining public space]. Seori Shobo.

  • Sato, M. (1999). Manabi no kairaku: Daiarogu e [Learning as pleasure: Toward dialogic practice]. Seori Shobo.

  • Sato, M. (2000). Jugyo wo kaeru gakko ga kawaru [Change lessons, schools change]. Shogakkan.

  • Sato, M. (2004). Shujukudo-betsu shido no nani ga mondai ka [What are the problems with ability grouping?]. Iwanami.

  • Sato, M. (2005). Toward dialogic practice through mediated activity: Theoretical foundation for constructing learning community. In K. Yamazumi, Y. Engeström, & H. Daniels (Eds.), New learning challenges: Going beyond the industrial age system of school and work (pp. 103–134). Kansai University Press.

  • Sato, M. (2012). Gakko wo kaikakusuru [Reforming schools]. Iwanami.

  • Sato, M. (2015). Manabiau kyoshitsu-sodachiau gakko: Manabi no kyodotai no kaikaku [Learning together in the classroom, growing together at school: Reform through School as Learning Community]. Shogakkan.

  • Sato, M. (2019). Spread and progress of School as Learning Community in Asia. In A. Tsukui & M. Murase (Eds.), Lesson study and School as Learning Communities: Asian school reform in theory and practice (pp. 3–13). Routledge. https://doi.org/10.4324/9781315690322

  • Schwartz, T. (1989). The structure of national cultures. In P. Funke (Ed.), Understanding the USA: A cross-cultural perspective (pp. 110–149). Gunter Narr Verlag.

  • Shimizu, Y. (1999). Aspects of mathematics teacher education in Japan: Focusing on teachers’ roles. Journal of Mathematics Teacher Education, 2, 107–116. https://doi.org/10.1023/A:1009960710624

    Article  Google Scholar 

  • Soma, K. (1997). Sugakka "Mondai-kaiketsu no jugyo" ["Problem-solving lesson" in mathematics]. Meiji Tosho.

  • Soma, K. (Ed.). (2017). Sugakka "mondai-kaiketsu no jugyo" gaidobukku [Mathematics "problem-solving lesson" guidebook]. Meiji Tosho.

  • Soma, K., & Sato, T. (Eds.). (2009). Chugakko sugakka: Shin "mondai-kaiketsu no jugyo" ni ikiru "mondai" shu [Junior-high school mathematics: A new collection of "problems" activated in "problem-solving lessons"]. Meiji Tosho.

  • Stevenson, H. W., & Nerison-Low, R. (2002). To sum it up: Case studies of education in Germany, Japan, and the United States. National Institute on Student Achievement, Curriculum, and Assessment (OERI/ED). https://files.eric.ed.gov/fulltext/ED463240.pdf

  • Stevenson, H. W., & Stigler, J. W. (1992). The learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. Summit Books.

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap. Free Press.

  • Stigler, J. W., Gonzales, P., Kawanaka, T., Knoll, S., & Serrano, A. (1999). The TIMSS videotape classroom study: Methods and findings from an exploratory research project on eighth-grade mathematics instruction in Germany, Japan, and the United States (NCES 99-074). U.S. Government Printing Office https://nces.ed.gov/pubs99/1999074.pdf

  • Tsubota, K. (2003). Gakko de manabu koto no kachi no saiko [Reflection on the values of school learning]. In Zenkoku Sansu Jugyo Kenkyukai (Ed.), Ima, sansu ga abunai: Honto no mondai-kaiketsu no jugyo wo mezashite [A crisis of arithmetic teaching: Toward the true problem-solving lesson] (pp. 8–23). Toyokan.

  • Tsujimoto, M. (1999). "Manabi" no hukken: Moho to shujuku [Restoration of "learning": Imitating and mastering]. Kadokawa.

  • Tsukui, A., & Murase, M. (Eds.). (2019). Lesson study and schools as learning communities: Asian school reform in theory and practice. Routledge. https://doi.org/10.4324/9781315690322

  • Webb, N. M. (1989). Peer interaction and learning in small groups. International Journal of Educational Research, 13(1), 21–39. https://doi.org/10.1016/0883-0355(89)90014-1

    Article  Google Scholar 

  • Yamagata-Lynch, L. C. (2010). Activity systems analysis methods: Understanding complex learning environment. Springer. https://doi.org/10.1007/978-1-4419-6321-5

  • Yamazumi, K. (2006). Activity theory and the transformation of pedagogic practice. Educational Studies in Japan: International Yearbook, 1, 77–90 https://files.eric.ed.gov/fulltext/EJ842894.pdf

    Article  Google Scholar 

  • Zenkoku Sansu Jugyo Kenkyukai (Ed.). (2003). Ima, sansu ga abunai: Honto no mondai-kaiketsu no jugyo wo mezashite [A crisis of arithmetic teaching: Toward the true problem-solving lesson]. Toyokan.

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Acknowledgments

I would like to thank a school teacher for permitting me to include a design of her mathematics lesson in this paper, though her name cannot be disclosed to protect the anonymity of the participants.

Funding

A previous version of this paper was presented at Topic Study Group 51 of 13th International Congress on Mathematical Education, Hamburg, 24–31 July 2016. A part of this work was supported by JSPS KAKENHI grant numbers JP26590237 and JP19K02785.

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  1. Faculty of Education, Yamaguchi University, 1677-1 Yoshida, Yamaguchi-shi, 753-8513, Japan

    Yasuhiro Sekiguchi

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Sekiguchi, Y. Activity systems analysis of classroom teaching and learning of mathematics: a case study of Japanese secondary schools. Educ Stud Math 108, 493–511 (2021). https://doi.org/10.1007/s10649-021-10069-6

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