A Framework for Analyzing Informal Representation in Mathematics Class

Abstract

　　 The purpose of this article is to construct a framework for analyzing various types of representations used in mathematics classes, which is based on Nakahara’s study on the representational system (Nakahara, 1995). In our framework, “manipulative representations” in Nakahara’s representational system is reconceputualized as “manipulative/embodied representations” to include “verbal natural language” and “gesture”. And, the framework is constructed by combining Nakahara’s five extended modes of representations (symbolic, linguistic, illustrative, manipulative/embodied, realistic) with three types of representations (formal, preformal, informal) in iceberg model (Webb et al., 2008) in two-dimensional array.

　　 With our framework, various types of informal representations used in mathematics classes are extensively exemplified, and an excellent classroom practice that informal representations seem to be effectively used (Masaki, 2009) is also analyzed.

　　 As a result, using the framework, some informal representations corresponding to each cell of the framework are identified, and the potentiality to describe mathematics classes using informal representation is illustrated.