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 is 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.

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This discussion group aimed to use a work-in-progress project as an example to fuel discussion of curriculum coherence and the importance of the relationships between curriculum, context, and implementation. These are major considerations influencing curriculum development at national and international levels. Our example was the framework being developed by Cambridge Mathematics for presenting and organising the domain of school mathematics in a form that emphasises connections and interdependencies between learners' mathematical experiences, and the different routes that can successfully facilitate learners' development mathematical understanding.Two themes stood out strongly in both sessions. The first had to do with the importance of finding ways of communicating design, design methods, and research methods that can drive productive collaboration among researchers, administrators, policy makers, and teachers during framework development. Focal points for communication with one group of stakeholders might not provide critical information needed for another to engage. Consideration of the priorities and needs of each group in the collaborative process can help to make the final result more useful for all groups, and consequently more likely to be put to use and refined.Some specific features of a curriculum framework were identified as having the potential to benefit collaboration around emerging curriculum frameworks, and the subsequent quality of those frameworks. Framework design and documentation should be able to: