ABSTRACT
This chapter presents a jigsaw of mental pictures of the researchers, teachers, their colleagues and their foreign colleagues regarding the effectiveness of maths teaching. The researchers' unstructured observations tell the typical structure and key features of mathematics lessons in each country. The chapter presents and discusses interviewing data to show teachers' perceptions of effective mathematics lessons, their own judgement of the quality of their observed lessons, their awareness of teaching in the other country and their attitudes and openness towards change in practice. The various views on the lessons are spread around two focused lessons – one from England and the other from China – in the wake of group discussions among teachers locally and internationally. The chapter focuses on three strands of teachers' beliefs such as: a description of an effective maths lesson, the strategies for organising and managing maths lessons and the strategies for differentiation in maths lessons.
