Theoretical approaches to teachers’ lesson designs involving the adaptation of mathematics textbooks: two cases from kyouzai kenkyuu in Japan

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.