Making sense of fractions at primary school - the case of teacher João

Abstract

The most recent Portuguese guidelines for the Primary School Mathematics preconize an in-depth contact with fractions, dealing with quotient, part-whole, measure and operator interpretations for fractions. It is well known that teachers often struggle on teaching such matters. Since fractions are traditionally approached mainly in part-whole and operator interpretations, it seems pertinent to inves-tigate whether the actual teaching practices reflect those innovative guidelines. This study focuses on teaching practices on fractions and aims to understand primary school teachers constrains and difficul-ties when teaching fractions. It addresses three questions: 1) How does the teacher make sense of frac-tions in the classroom? 2) Does the teacher properly promote the connections between fractions and everyday situations? 3) How does the teacher articulate distinct interpretations of fractions in the class-room? Four primary school teachers participated in a collaborative working program about fractions with the researcher (one of the authors of this paper) and their classes were observed. This paper presents the results related to the observed classes of one of the participating teachers – João (fictitious name). A qualitative analysis of the observed lessons suggests some fragilities regarding the teaching of the different interpretations of fractions, namely: on approaching the equivalence and the ordering of frac-tions in quotient interpretation; on marking fractions on the number line; on articulating the interpreta-tions of fractions. Therefore, in-service teacher training should be regularly promoted for primary school teachers in order to ensure greater convergence between curriculum and teaching practices, improving the quality of the latter.