Meanings of fractions as demonstrated by future primary teachers in the initial phase of teacher education

Fractions are a fundamental content of primary-level education and must therefore be included in the training courses for primary school teachers. Experts argue that deep understanding is required to improve primary school teachers’ knowledge of this mathematical concept (Ball, 1990; Cramer, Post & del Mas, 2002; Newton, 2008). Our study focuses on the part-whole relationship as a crucial foundation in working with fractions. This paper characterizes some of the meanings of this relationship for a group of future primary school teachers. FRACTIONS AND THE MEANING OF THE PART-WHOLE RELATIOPNSHIP Fractions may be interpreted in various ways (e.g., as ratios, operators, quotients, and measurements), and diverse models have been developed to organize these interpretations. We use proposals by Kieren (1976) and Behr, Lesh, Post and Silver (1983) to establish that these interpretations are organized according to the kind of relationship to which the fraction belongs: part-whole relationship, part-part relationship, and functional relationship, as shown in Figure 1.