# 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.

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