STUDENTS' INTERPRETATIONS AND REPRESENTATIONS OF NUMBER

Abstract

The findings of major research studies in this country and the United States leave little doubt as to the difficulties which many students experience in dealing with number—difficulties which persist well into the secondary school (Hart et al., 1981; Foxman et al, 1985; Carpenter et al, 1981). A review of the literature also reveals an accumulating body of knowledge concerned with the relationship between the processes children use and the concepts they acquire (Hiebert and Lefevre, 1986; Hiebert and Wearne, 1986, 1992; Nesher, 1986). In particular, research has used terms such as ‘reification’ or ‘encapsulation’ to describe the ‘process-object’ relationship (Sfard, 1991; Gray and Tall, 1994). The work described here, which was conducted entirely off-computer, was part of a larger project, one aim of which was to investigate how the ‘process-object’ relationship would be mediated through working in the computational medium of Boxer.