Comparing the Lower Secondary Textbooks of Japan and England: a Praxeological Analysis of Symmetry and Transformations in Geometry

This study is aimed at comparing the content in mathematics textbooks from Japan and England, focusing on symmetry and transformations at the lower secondary level. We adopted the concept of praxeology, a main construct of the Anthropological Theory of the Didactic (ATD). Using the ATD framework, our approach regarded textbooks as an empirical source which can reveal knowledge to be taught in the didactic transposition process. The praxeological analysis results indicated that symmetry and transformations in the Japanese textbooks were strongly influenced by the teaching of geometric proofs, while transformations in the textbooks from England had many connections to other contexts or contents across domains. These findings suggested the ways in which the knowledge of symmetry and transformations is differently situated in the two countries’ textbooks in terms of different praxeological organisations. We further discussed our findings for elaborating the theoretical and methodological aspects of this study, which can potentially contribute to future research on textbooks in mathematics education.