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.