Natural language is known to play a crucial and specific role for children’s learning in school mathematics. Not only does it carry special vocabulary, but subtle differences between natural languages may lead to surprising challenges, for instance, for learners who are not taught mathematics in their mother tongue. In this paper, the anthropological theory of didactic (ATD) is used as a main framework, and we analyse some praxeological anomalies from the teaching of fractions at Japanese schools abroad, while learners attend, at the same time, a regular school in some other language (in this case, the local language, Swedish). Our findings indicate that these praxeological anomalies arise not only from linguistic disparities related to specialised vocabulary and syntax for elementary mathematics but also from institutional and curricular differences. This study gives new insights on these language challenges related to mathematics as taught at expatriate schools, particularly in the case of Japanese.

This workshop introduces a new approach for studying the ecology of teachers’ preparation and reflection on their didactic activities for teaching. A key idea of the approach is paradidactic reality, that is, a reality alongside “didactic” reality. In the same manner as with students’ and teachers’ actions in didactic situations, teachers’ behaviours for managing didactic situations are also affected by different kinds of conditions and constraints. This point of view leads us to a specialised scale of determinacy levels about paradidactic phenomena.

This case study investigates to what extent a specific theory and a practice of mathematics teaching − the Japanese structured problem solving, as formulated by K. Souma can be transferred and applied in a new context (Sweden). The analysis is based on tools from the anthropological theory of the didactic. It turns out that the Swedish teacher can manage the didactic techniques, which are supported by a didactic theory shared within the community of Swedish teachers. However, there are common didactic techniques within the Japanese structured problem solving approach for which this is not the case, and which were indeed difficult to manage for the Swedish teacher. Among these were techniques related to bansho (blackboard organisation); letting the students formulate a kadai (derived task) of the lesson; and kikan-shido (monitoring students’ work to plan a subsequent whole-class discussion). Further, the paper provides an ecological analysis on the underlying conditions and constraints that brought about this phenomenon − a discrepancy concerning the didactic praxeologies of teachers. In Japan, teachers focus on the students’ personal development in the processes of the reflective and collective way of learning, while the Swedish teacher focuses more on individual student’s achievement of the knowledge.

This paper investigates how Japanese mathematics teachers produce and share didactic knowledge together. It is a case study of a post-lesson reflection meeting so-called open lesson. The crucial idea of this study is the dialectic between the specific and generic level of foci of the participants’ reflections about the observed teaching practice; namely, about applied teacher’s specific didactic technique for achieving a specific mathematical goal, and more general pedagogical issues such as realisation of the objectives of mathematics education. This dialectic is mediated by the meso-level notion of mathematical activity, described in the guidelines for Japanese national curriculum. The application of the scale of levels of didactic co-determination, provided by the anthropological theory of the didactic into the analysis shows in what way the dialectic interplay between the teachers’ comments with focus of the specific and generic levels influences the development and establishment of the Japanese teachers’ shared professional scholarship.  

The phenomenon of didactic divide reported in Sweden expresses the disconnection between disciplinary and pedagogical knowledge in both individual teachers' professional knowledge and teacher-education programmes. Within the framework of the anthropological theory of the didactic, we firstly redefine the notion of didactic divide, and secondly, study the ecology of the phenomenon by using our new analytical model rooted in the scale of levels of didactic co-determinacy. As a result, we indicate some constraints on the didactic divide: inter-professional esoteric pact, shortage of didacticians, universality illusion on scholarly knowledge, and transparency illusion on the social reality. 

The aim of this paper is to investigate and compare lessons given in primary school teacher education in Japan, Finland and Sweden. We analyse one lesson from each country and compare them using a common framework. Chevallard’s anthropological theory of the didactic (ATD) is used to frame this analysis and in particular to model teacher educators' didactic organization of the lessons. The focus is on how the didactic organizations of the teacher educators relate to the mathematical and didactic organizations of primary school. Based on official documents and viewpoints of the teacher educators, we also discuss how the contents and descriptions of the national curricula, and the different traditions of the teaching practices in each country, influence the didactic organizations found in the lessons. 

The aim of this paper is to investigate which kind of conditions and constraints affect Japanese and Swedish teacher educators’ pedagogical content knowledge (PCK). We analyse the praxeologies of the lessons in which the educators teach area determination. Our study shows that the Japanese teacher educators’ PCK are more explicitly shared by the community of the teacher educators compared to the Swedish counterpart. Also, the detailed Japanese curriculum and the structured problem solving approach promote to illustrate how to construct rich mathematical and didactical organisations for prospective teachers.

The thesis describes and studies the Japanese mathematics teachers’ professional knowledge and its dissemination. This theme is investigated in several concrete situations: the knowledge of teaching practice of school mathematics taught in the teacher education, the relation between the educational goals described in the national curriculum and concrete teaching methods discussed among the Japanese lower secondary teachers in service. The thesis investigates also critical phenomena, which arise in an attempt to transfer the Japanese teaching practice in a different teaching context.

In this study, we have observed three different teacher educators’ lessons, concerning area determination of polygons in primary school teacher training courses in Japan, Finland and Sweden. The aim of this paper is to investigate the main elements of the lessons and to compare the differences between the countries. We focus on how the teacher educators relate the didactic construction of the lessons for prospective teachers to the school mathematical and didactical organisations by applying Chevallard’s anthropological theory of the didactic (ATD). The analysis shows how the curricula and the different traditions of teaching practice in each country influence the mathematical and didactical construction of the lessons.

In this paper, we examine the implementation of a Japanese teacher educators' lesson, where he applies and, at the same time, inform the students about "structured problem solving". We describe a specific lesson titled "Quantity and Measurement" for elementary school teacher students and we show how the educator make the students aware of the didactic transposition of the material and how he makes the students experience and learn about applying "structured problem solving" in practice. We also show how the Japanese curriculum influences the scale of the mathematical praxeology to be learned and how the students are given opportunities to develop their insight into the PCK during their education in mathematics.