Developing Geometrical Reasoning in the Classroom: Learning from Highly Experienced Teachers from China and Japan

Mathematics education has been the subject of considerable international comparative research, mostly focussed on pupil achievement but also examining teaching methods, curricula, and so on. In all this, and perhaps unsurprisingly, the role of teachers has emerged as a key influence on pupil learning. Given that the development of pupils’ capability in geometrical reasoning continues to be an issue of considerable international concern, this paper reports an analysis of lower secondary school lesson suggestions prepared by highly experienced “expert teachers” from China and Japan, countries selected because they represent some interesting similarities and contrasts. The paper also gives background to these lesson suggestions in terms of the educational context in which they are presented. Introduction The (recently renamed) Trends in International Mathematics and Science Study (TIMSS) is continuing to investigate pupil achievement, the mathematics curricula, teaching methods, and so on, across almost 50 countries around the world (see, for example, Mullis et al, 2000). Overall, the results to date of TIMSS suggest that there are significant similarities between the mathematics curricula across countries, especially in terms of topics specified, if not in overall curricular design (Schmidt et al, 1997; Valverde et al, 2002). Yet these broad correspondences of grade level and content become differences if examined more closely; both in the range of content addressed at a particular grade level and in particular developmental sequences where common content is addressed over several grade levels. In terms of geometry teaching, while analysis of TIMSS data continues, a detailed comparative study of geometry specifications (Hoyles, Foxman and Küchemann, 2002), though covering fewer countries than TIMSS, found considerable variation in current approaches to the design of the school geometry curriculum. Thus, for example, the study found, a ‘realistic’ or practical approach apparent in Holland, while a theoretical approach is most evident in France and Japan. The study concludes by noting “there is evidence of a state of flux in the geometry curriculum, with most countries looking to change” (op cit p. 121).