In this paper, we explore theoretical approaches to Japanese teachers’ lesson designs involving the adaptation of mathematics textbooks for instructional change. In Japan, although most teachers use textbooks as the main resource for lesson planning, called kyouzai kenkyuu, the ways in which they use textbooks can differ. In a kyouzai kenkyuu practice, Japanese teachers sometimes attempt to design innovative tasks and/or learning trajectories beyond or parallel to the textbooks and curriculum guidelines. Such practice is often invisible to international researchers, since it is culturally situated in the local context. To make it more visible, in this study we address and advance theoretical approaches using two frameworks which are well-established for research in mathematics education, namely, Anthropological Theory of the Didactic (ATD) and Documentational Approach to Didactics (DAD). Two cases of lesson design regarding fractions using the same textbook chapter for 3rd graders in primary schools in Japan, are used as examples to illustrate crucial elements of each framework and ways of combining and coordinating both frameworks. As a result, we conceptualise teachers’ kyouzai kenkyuu practice using two approaches: from a praxeological analysis based on ATD, the difference in teachers’ mathematical and didactic knowledge was emphasised, while within DAD, the difference in the instrumentalisation process was emphasised. This analysis implies that the two theoretical approaches can be compatible, and used to gain deeper insight into the relationship between lesson design using the textbook and teacher knowledge.

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The world witnessed a growing interest in inquiry-based learning in the past decade. Study and research path (SRP) is a model of such learning based on the anthropological theory of the didactic (ATD). This paper discusses the following research questions through [Formula: see text] maps of the SRPs of university freshmen using the notion of praxeology: (RQ1) how do students/pre-service teachers create SRPs in an online environment in terms of group work? (RQ2) How are the institutional conditions and constraints of each group characterized? In conclusions, the differences in media searches of the student groups lead to differences in final answers to the inquiry. Additionally, the media-milieu dialectic is closely related to the question–answer dialectic.

This research is the first work of the project of cross-cultural study on lesson study between Japan and Thailand. Lesson study is currently an international topic, and we use “lesson study” as a common word. However, are the meanings of each terminology in diverse languages as same completely? Our initial concern is in this point. For this, we observe lesson on video and make comment-reports on it in each. In analyzing these comments, it is required a meta theory for descriptions. In this research, we describe the researchers ways of seeing a lesson using the Anthropological Theory of the Didactic [ATD or TAD in French and Spanish]. In conclusion, we discuss similarities and discrepancies between researchers’ comments of both countries in terms of a) praxis and logos blocks, b) mathematical and didactic organization, and c) the perspective of scale of levels of didactic co-determinacy [LDC].Keywords: Lesson study; Cross-cultural study; Japan and ThailandRésuméCette recherche est le premier travail du projet d’étude interculturelle sur l’étude de la leçon entre le Japon et la Thaïlande. L’étude de la leçon est actuellement un sujet international, et nous utilisons la « lesson study » comme un mot commun. Cependant, les significations de chaque terminologie dans diverses langues sont-elles identiques? Notre préoccupation initiale concerne ce point. Pour cela, nous observons une leçon sur la vidéo et faisons des commentaires sur chacune d’elles. En analysant ces commentaires, il faut une méta-théorie pour les descriptions. Dans cette recherche, nous décrivons les chercheurs pour voir une leçon en utilisant TAD. En conclusion, nous discutons des similitudes et des divergences entre les commentaires des chercheurs des deux pays en termes de blocs de praxis et logos, b) l’organisation mathématique et didactique, et c) la perspective des niveaux de la codétermination didactique.Mots-clés: Étude de cours, Étude interculturelle, Japon et Thaïlande