An Inquiry Perspective on Statistics in Lower Secondary School in Denmark and Japan–An Elaboration and Modelling of the Anthropological Theory of the Didactic Through Two Statistics Classrooms

Camilla Hellsten Østergaard 1 *
More Detail
1 Department of Science Education, University of Copenhagen, Copenhagen, DENMARK
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 4, pp. 529-546.
Published: 26 August 2022
OPEN ACCESS   1165 Views   508 Downloads
Download Full Text (PDF)


We present a detailed analysis of two statistics lessons in lower secondary school, one in Denmark and the other in Japan. The aim of the study is to better understand how inquiry perspectives are implemented in statistics education and what cultural factors shape them. In particular, we draw on the theoretical framework of the Anthropological Theory of the Didactic. The first impressions of the lessons changed during the analysis, and the main differences became explicit in the two question and answer diagrams and the praxeological analysis of the lessons. The two lessons involved cases comprising an “experimental activity with many questions” (Denmark) and “structured problem-solving” (Japan), which differed on a number of points that we shall demonstrate in the analysis. We shall also discuss hypotheses on the possible causes of these differences. We emphasize that our use of question and answer diagrams offers a new way in which to distinguish various kinds of “inquiry-oriented” lessons.


Østergaard, C. H. (2022). An Inquiry Perspective on Statistics in Lower Secondary School in Denmark and Japan–An Elaboration and Modelling of the Anthropological Theory of the Didactic Through Two Statistics Classrooms. European Journal of Science and Mathematics Education, 10(4), 529-546.


  • Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM, 45(6), 797-810.
  • Barfod, K., Ejbye-Ernst, N., Mygind, L., & Bentsen, P. (2016). Increased provision of udeskole in Danish schools: An updated national population survey. Urban Forestry & Urban Greening, 20, 277-281.
  • Bentsen, P., & Jensen, F. S. (2012). The nature of udeskole: Outdoor learning theory and practice in Danish schools. Journal of Adventure Education & Outdoor Learning, 12(3), 199-219.
  • Ben-Zvi, D., Gravemeijer, K., & Ainley, J. (2018). Design of statistics learning environments. In D. Ben-Zvi, K.Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 473-502). Springer.
  • Bosch, M., & Winsløw, C. (2016). Linking problem solving and learning contents: The challenge of self-sustained study and research processes. Recherches en Didactique des Mathématiques [Research in Didactics of Mathematics], 35(2), 357-399.
  • Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. Research in Didactique of Mathematics: Selected Papers, 131-168.
  • Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique [The analysis of teaching practices from the anthropological theory of the didactic]. Recherches en Didactique des Mathématiques [Research in Didactics of Mathematics], 19(2), 221-265.
  • Chevallard, Y. (2015). Teaching mathematics in tomorrow’s society: A case for an oncoming counter paradigm. In Proceedings of the 12th International Congress on Mathematical Education (pp. 173-187). Springer.
  • Clivaz, S., & Miyakawa, T. (2020). The effects of culture on mathematics lessons: An international comparative study of a collaboratively designed lesson. Educational Studies in Mathematics, 105(1), 53-70.
  • Fujii, T., Matano, H., Amano, H, Ichikawa, S., Ohta, S., Ohtake, K., Ohtani, M. Okada, H. Ginnan, Y, Kudo, M., Kodera, T., Sakaori, F., Sasa, H., Shimizu, Y., Seino, T., Soeda, Y., Takahashi, H., Takahashi, H, Takeuchi, A. … Tokyo, S. (2012) Atarashii Suugaku 1 [New Mathematics 1]. Tokyo Shoseki.
  • Holte, H., Thomsen, H., Weng, P., Andersen, M. W., & Lindhardt B. (2009). KonteXt 8, kernebog. Alinea.
  • Ikeno, N. (2013). Tairitsu to sentaku kara kanousei wo miidasu [The discovery of possibilities through confrontation and choice]. Shakaika Kyouiku [Social Education], 12, 54-55.
  • Isoda, M. (2010). Junior high school teaching guide for the Japanese course of study: Mathematics (Grade 7-9). CRICED, University of Tsukuba.
  • Jessen, B. E. (2014). How can study and research paths contribute to the teaching of mathematics in an interdisciplinary settings? Annales de Didactiques et de Sciences Cognitives [Annals of Didactics and Cognitive Sciences], 19, 199-224.
  • Jessen, B., Otaki, K., Miyakawa, T., Hamanaka, H., Mizoguchi, T., Shinno, Y., & Winsløw, C. (2019). The ecology of study and research paths in upper secondary school. In M. Bosch, Y. Chevallard, F. Carcía, & J. Monaghan (Eds.), Working with the anthropological theory of the didactic in mathematics education: A comprehensive casebook (pp. 118).
  • Lehrer, R., & English, L. (2018). Introducing children to modeling variability. In D. BenZvi, K. Makar, & J. Garfield (Eds.), International handbook of research in statistics education (pp. 229-260). Springer.
  • Ministry of Education. (2017). Bekendtgørelse af lov om folkeskolen § 15 [Promulgation of section 15 of the primary and lower secondary school act].
  • Ministry of Education. (2019). Matematik, fælles mål [Mathematics, common goals].ællesMål_Matematik.pdf
  • Miyakawa, T., & Winsløw, C. (2019). Paradidactic infrastructure for sharing and documenting mathematics teacher knowledge: A case study of “practice research” in Japan. Journal of Mathematics Teacher Education, 22(3), 281-303.
  • Okamoto, M. (2018) Bansho, note-shido no kihon to idea [Basic idea of guidance for Bansho]. Natsumesha.
  • Østergaard, C. H., & Winsløw, C. (2021). Sustainable lesson study and paradidactic infrastructure: The case of Denmark. Hiroshima Journal of Mathematics Education, 14, 1-15.
  • Pfannkuch, M., Ben-Zvi, D., & Budgett, S. (2018). Innovations in statistical modeling to connect data, chance and context. ZDM, 50(7), 1113-1123.
  • Rea, T., & Waite, S. (2009). International perspectives on outdoor and experiential learning. International Journal of Primary, Elementary and Early Years Education. International Perspectives on Outdoor and Experiential Learning, 37(1), 1-4.
  • Stigler, J. W., & Hiebert, J. (1998). Teaching is a cultural activity. American Educator, 22(4), 4-11.
  • Tan, S. Fukaya, K., & Nozaki, S. (2018). Development of bansho (board writing) analysis as a research method to improve observation an analysis of instruction in lesson study. International Journal for Lesson and Learning Studies, 7(3), 230-247.
  • Tukey, J. W. (1977). Exploratory data analysis. Addison Wealey.
  • University of Tsukuba, Attached Elementary School Mathematics Department. (2016) Bansho de miru zentangen, zenjikan no jugyo no subete [Looking at the lessons through bansho]. Toyokan Shuppansha.
  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-265.
  • Winsløw, C. (2011). A comparative perspective on teacher collaboration: The cases of lesson study in Japan and of multidisciplinary teaching in Denmark. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to “lived” resources (pp. 291-304). Springer.
  • Winsløw, C., Matheron, Y., & Mercier, A. (2013). Study and research courses as an epistemological model for didactics. Educational Studies in Mathematics, 83(2), 267-284.
  • Winter-Jensen, T. (2004). Comparative education in a world of globalization. World Studies in Education, 5(2), 81-94.
  • Yin, R. K. (2013). Validity and generalization in future case study evaluations. Evaluation, 19(3), 321-332.