Interpretations of national curricula: the case of geometry in Japan and the UK

Description/Abstract

This paper presents an analysis of how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically Scotland, is interpreted by textbook writers. While, of course, textbooks are not the only critical influences on student learning, such texts, as analyses of data from the Trends in International Mathematics and Science Study (TIMSS) confirm, do have a major impact and are thus important subjects for study. Our analysis is framed by the procedures derived from the work associated with TIMSS. The results presented focus on identifying features of geometry, and approaches to geometry learning, privileged in the textbooks, together with a discussion of how these designs might influence students’ performance in geometry. Our analysis indicates that, following the specification of the mathematics curriculum in these countries, Japanese textbooks set out to develop students’ deductive reasoning skills through the explicit teaching of proof in geometry, whereas comparative Scottish textbooks tend, at this level, to concentrate on measuring, drawing, finding angles, and so on, coupled with a modicum of opportunities for conjecturing and inductive reasoning. The available research suggests that each approach has its own strengths and weaknesses. Finding ways of capitalising on the strengths and mitigating the weaknesses could prove helpful in formulating new curricular models and designing new student textbooks. An emerging issue is how the design of textbooks might either build on, or neglect, students’ intuitive skills when they tackle geometrical problems.