Presenting multiple representations at the chalkboard: bansho analysis of a Japanese mathematics classroom

ABSTRACT Pupils’ ability to represent mathematical concepts in multiple ways is a central aspect of mathematical competence and communication. Thus, classroom instructions should be able to support learners in using multiple representations (MRs) to increase the quality and quantity of connections to a network of ideas. Given the importance of bansho (board writing and organisation) in Japanese mathematics classrooms, this study aimed to investigate how MRs are presented as bansho in a mathematics classroom. Guided by a coding scheme of MRs on bansho content, the analysis revealed the ways the MRs are facilitating (or hindering) pupils’ understanding. In considering the effect of the sequence and translation of MRs identified in this study, it is important to focus on these aspects of lesson design in the future. The relevant findings are also crucial to illustrate to the educators and researchers how to explore the processes involved in the use of MRs and the critical factor that contribute to the success/failure of such processes through a detailed examination of the bansho.