# Lesson study in prospective mathematics teacher education: didactic and paradidactic technology in the post-lesson reflection

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## Abstract

This paper presents a detailed analysis of the post-lesson reflection, carried out in the context of eight cases of lesson study conducted by teams of Danish, lower secondary prospective teachers and their supervisors. The participants, representing different institutions, were all new to the lesson study format. Nevertheless, it is demonstrated how their interaction shape the development of discourse about mathematical learning. The anthropological theory of the didactic is employed as the theoretical approach to analyse the mathematical and primarily didactical praxeologies developed and discussed during the meetings. The study investigates what happens when lesson study, a well-established Japanese “system” for professional teacher development, is transposed to another educational and cultural context, with the aim of enhancing prospective teacher learning during the practicum of a teacher education programme. The findings highlight significant different positions in the discourse during the post-lesson reflection. Specific practice-related knowledge is developed, to the benefit of prospective teachers, educators and researchers alike. This kind of knowledge is of interest and concern to the whole profession of mathematics teachers and the analysis adds to our insight into the potential of lesson study in prospective education as a meeting place where pertinent actors contribute to the expansion and dissemination of shared professional knowledge.

## Keywords

Lesson study Reflective practice Mathematical praxeology Anthropological theory of the didactic Paradidactic infrastructure Didactic praxeology## Notes

### Acknowledgments

The author would like to acknowledge the Lundbeck Foundation for financial support and Professor Carl Winsløw, the JMTE editor and the anonymous reviewers for many useful comments to earlier versions of the paper.

## References

- Andersen, N. Å. (2003).
*Discoursive analytical strategies: Understanding foucault*. Koselleck: The Policy Press.Google Scholar - Bae, B. (2012). Children and teachers as partners in communication: Focus on spacious and narrow interactional patterns.
*International Journal of Early Childhood,**44*(1), 53–69.CrossRefGoogle Scholar - Bergsten, C., Grevholm, B., Favilli, F., Bednarz, N., Proulx, J., Mewborn, D., et al. (2009). Learning to teach mathematics: Expanding the role of practicum as an integrated part of a teacher education programme. In R. Even & D. L. Ball (Eds.),
*The professional education and development of teachers of mathematics*(pp. 57–70). Berlin: Springer.CrossRefGoogle Scholar - Bosch, M., Chevallard, Y., & Gascón, J. (2006)
*Science of magic? The use of models and theories in didactics of mathematics*. In M. Bosch (Ed.),*4th Conference of the European Society for Research in Mathematics Education*. Larnaca, Cyprus.Google Scholar - Bosch, M., & Gascón, J. (2002). Organiser l’étude, 2. Théories et emperies. Actes de la 11e école d’été de didactique des mathématiques (pp. 23–40). La Pensée Sauvage.Google Scholar
- Carlgren, I., Klette, K., Mýrdal, S., Schnack, K., & Simola, H. (2006). Changes in Nordic teaching practices: From individualised teaching to the teaching of individuals.
*Scandinavian Journal of Educational Research,**50*(3), 301–326.CrossRefGoogle Scholar - Chaliès, S., Ria, L., Bertone, S., Trohel, J., & Durand, M. (2004). Interactions between preservice and cooperating teachers and knowledge construction during post-lesson interviews.
*Teaching and Teacher Education,**20*(8), 765–781.CrossRefGoogle Scholar - Chevallard, Y. (2004). La place des mathématiques vivantes dans l’éducation secondaire: Transposition didactique des mathématiques et nouvelle épistémologie scolaire’. In C. Ducourtioux, & P. L. Hennequin (Eds.), La place des mathématiques vivantes dans l’éducation secondaire (pp. 239–263). Paris: APMEP.Google Scholar
- Chevallard, Y. (2009).
*Remarques sur la notion d’infrastructure didactique et sur le rôle des PER*. Lyon: Journées Ampère.Google Scholar - Durand-Guerrier, V., Winsløw, C., & Yoshida, H. (2010).
*A model of mathematics teacher knowledge and a comparative study in Denmark*. France and Japan: Annales de Didactique et de Sciences Cognitives. 15.Google Scholar - Elipane, L. E. (2012).
*Integrating the essential elements of lesson study in pre-service mathematics teacher education*. IND Skriftserie: Copenhagen University.Google Scholar - Fernández, M. L. (2010). Investigating how and what prospective teachers learn through microteaching lesson study.
*Teaching and Teacher Education,**26*(2), 351–362.CrossRefGoogle Scholar - Fernandez, C., & Yoshida, M. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. Routledge.Google Scholar
- Fernandez, M. L., & Zilliox, J. (2011). Investigating approaches to lesson study in prospective mathematics teacher education. In L. C. Hart, A. S. Alston, & A. Murata (Eds.), Lesson study research and practice in mathematics education (pp. 85–102). Springer, Berlin.Google Scholar
- Ghaye, T. (2010). Teaching and learning through reflective practice: A practical guide for positive action. Routledge.Google Scholar
- Glaser, B. G., & Strauss, A. L. (2009). The discovery of grounded theory: Strategies for qualitative research. Transaction Books.Google Scholar
- Gloppen, B. H. (2013). Trepartssamtalen–en arena for å styrke samspillet mellom høgskolens undervisning og praksis? Eksempler fra lærerutdanningen. Uniped,
*36*(1).Google Scholar - Grootenboer, P. (2006). The impact of the school-based practicum on pre-service teachers’ affective development in mathematics.
*Mathematics Teacher Education and Development,**7*, 18–32.Google Scholar - Howe, E. R. (2006). Exemplary teacher induction: An international review.
*Educational Philosophy and Theory,**38*(3), 287–297.CrossRefGoogle Scholar - Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study.
*Educational Researcher,**35*(3), 3–14.CrossRefGoogle Scholar - McMahon, M. T., & Hines, E. (2008). Lesson study with preservice teachers.
*The Mathematics Teacher,**102*(3), 186–191.Google Scholar - Miyakawa, T., & Winsløw, C. (2013). Developing mathematics teacher knowledge: The paradidactic infrastructure of “open lesson” in Japan.
*Journal of Mathematics Teacher Education,**16*(3), 185–209.CrossRefGoogle Scholar - Murata, A., & Pothen, B. E. (2011). Lesson study in preservice elementary mathematics methods courses: connecting emerging practice and understanding. In L. C. Hart, A. S. Alston, & A. Murata (Eds.), Lesson study research and practice in mathematics education (pp. 103–116). Springer.Google Scholar
- Padilla, M., & Riley, J. (2003). Guiding the new teacher: Induction of first-year teachers in Japan. In E. Britton (Ed.),
*Comprehensive teacher induction*(pp. 261–295). Dordrecht: Klüwer Academic Publishers.CrossRefGoogle Scholar - Peterson, B. E. (2005). Student teaching in Japan: The lesson.
*Journal of Mathematics Teacher Education,**8*(1), 61–74.CrossRefGoogle Scholar - Rasmussen, J. (2007).
*Trepartssamtalen—et forsøgs og udviklingsarbejde*. Denmark: Forlaget PUC.Google Scholar - Shimizu, Y. (1999). Aspects of mathematics teacher education in Japan: Focusing on teachers’ roles.
*Journal of Mathematics Teacher Education,**2*(1), 107–116.CrossRefGoogle Scholar - Stigler, J. W., & Hiebert, J. (1999).
*The teaching gap: Best ideas from the world’s teachers for improving education in the classroom*. New York: Summit.Google Scholar - Undervisningsministeriet (2011). Bekendtgørelse om uddannelsen til professionsbachelor som lærer i folkeskolen. In D. m. o. Education (Ed.), BEK nr. 562.Google Scholar
- Watson, A., & Williams, M. (2004). Post-lesson debriefing: Delayed or immediate? An investigation of student teacher talk.
*Journal of Education for Teaching,**30*(2), 85–96.CrossRefGoogle Scholar - 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*(7th ed., pp. 291–304). Netherlands: Springer.CrossRefGoogle Scholar - York-Barr, J., Sommers, W. A., Ghere, G. S., & Montie, J. K. (2005). Reflective practice to improve schools: An action guide for educators (2nd ed.). Corwin Press.Google Scholar
- Yu, P. W. (2011). Lesson study as a framework for preservice teachers’ early field-based experiences. In Lesson study research and practice in mathematics education, 117–126.Google Scholar