This paper reports the results of an international comparative study conducted in Switzerland and Japan of an elementary school mathematics lesson. The principal aim of the study was to advance understanding of the cultural specificities of a mathematics lesson in its totality using concrete examples of lesson design and implementation and of how cultural factors within and beyond the classroom/school shape and produce mathematics lessons in a particular country. We analysed two Grade 4 mathematics lessons designed and implemented in Switzerland and Japan by pre-service teachers in the context of a project-based international exchange programme. The lesson, initially designed collaboratively by the pre-service teachers of the two countries, was ultimately realised in different ways in each country. Specifically, we found differences between the Japanese and Swiss lessons in the structure of the lesson and validation of solutions. To elucidate these differences and identify the cultural factors that yield them, we analysed the resources developed and used during lesson design and implementation (lesson plans, official documents, and textbooks). Furthermore, we discuss three aspects of mathematics lessons that account for the main characteristics of each lesson: collective or individualistic teaching and learning, problem-solving lessons, and distance between theory and practice.

Purpose – The purpose of this paper is to present French Didactique des Mathématiques (DM) to the Lesson Study (LS) community. Design/methodology/approach – This theoretical paper presents the origins of DM in the Theory of Didactical Situations (TDS) by Brousseau. It elaborates about didactical engineering, fundamental situation and other fundamental concepts. It briefly presents other Didactique theories: the theory of conceptual fields, the anthropological theory of the didactic, the joint action theory in didactics and the double approach. It considers importance of the (TDS) and influences over teaching of mathematics. This paper finishes by highlighting the ways Didactique and LS could contribute to each other in a profitable dialogue. Findings – The paper contrasts DM with some LS main features. It highlights the parallels despite fundamental differences in the initial goals of the perspectives. It shows that these differences could lead to productive dialogue by producing more practice-oriented forms of didactical engineering for the first and making teachers’ principles for lessons more explicit for the latter. Originality/value – The paper presents a very quick overview of the parallels between DM and LS. Additionally, this paper gives many accessible references in English for the reader to explore Didactique further.

Purpose The purpose of this paper is to elaborate on the commonality between the Theory of Didactical Situations (TDS) and lesson study to propose a model of lesson study using both the predominant graphical representation of lesson study by Lewis and the model of the didactical situation at the heart of TDS by Brousseau. Design/methodology/approach Starting by describing and adapting the predominant graphical representation of lesson study by Lewis and the model of the didactical situation at the heart of TDS by Brousseau, the paper integrates the two representations to highlight the commonalities between the students’ learning situation and the teachers’. Based on this integrated graphical representation, the key phases of lesson study are then conceptualised by the mean of the dialectic between didactical and adidactical situation. Findings The reflection about the use of the TDS graphical representation embedded in the lesson study diagram helps the reflection on the use of TDS itself to analyse lesson study. This theoretical analysis describes the process of teacher learning in lesson study and the link between their learning and the student’s. It also shows that lesson study is a good candidate for the fundamental situation of the knowledge for teaching. Originality/value The graphical conceptualisation of lesson study as a learning situation for teachers offers new insight about how teachers learn in lesson study.

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