The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

In this paper, we analyse a Grade 8 (age 13-14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly-regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully-planned board-work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board-work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board-work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage are not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.