A comparative study of didactic moments in a first chapter on algebra in Danish and Japanese middle school textbooks

Abstract

Teachers often base their teaching on textbook material. Textbooks play a role as mediators between official guidelines and teachers’ work. Therefore, it is interesting to study the mathematical organization of material and its connection to curricula. This paper presents a comparative analysis of Japanese and Danish textbook material based on the foundation of the anthropological theory of didactics. Our analysis focuses on how the very first introduction to algebra is organized in Danish and Japanese textbooks for the middle school, and in particular, how the distributive law is treated as a central, specific element of algebraic theory. We more generally look at the roles of algebraic theory that textbooks can facilitate. One result is that the stepwise, modular progression in the Japanese curriculum is indeed reflected in the Japanese textbook material, which treats one mathematical subject area after the other, in a clear progression. The Danish competence-based curriculum with its spiral structure is also reflected in the Danish textbook material, where the content areas are revisited and expanded over the grades.