Structuring mathematics lessons to develop geometrical reasoning: comparing lower secondary school practices in China, Japan and the UK

Achievement in mathematics continues to be a crucial factor in the success of school systems around the world. As a result, this area of the curriculum 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 central role of teachers, and how they structure their lessons, has emerged as a key factor in pupil learning. A number of projects have examined the structure of mathematics lessons, either to typify individual lessons in specified countries, or as an attempt to describe the variety of lesson structures used by particular teachers in particular countries over a sequence of lessons. To date there has been little comparative work specifically on how teachers structure mathematics lessons to develop geometrical reasoning despite the issue of how to improve geometry teaching being of considerable international concern. This paper reports early data from a larger comparative study that includes the analysis of classroom teaching materials. This paper compares suggestions about how teachers might structure geometry lessons in lower secondary school in three countries, China, Japan, and the UK (specifically England), chosen because they represent some interesting similarities and contrasts. The analysis focuses on the background to the suggestions available to teachers, in particular where approaches are similar and where they diverge. What the implications might be for student achievement in geometry in the three countries is identified as an area for future research