Learning rational numbers: a study on 6th grade students' (mis)conceptions of fractions

Abstract

This study compares students’ understanding of fractions across quotient, part-whole and operator interpretations of fractions. Two questions were addressed: (1) How do students understand the equivalence and ordering of fractions in these interpretations? And (2) how do students master the fraction representation in these interpretations? A survey was conducted using an individual questionnaire with 11 and 12-year-olds Portuguese students (N=158), who were familiar predominantly with part-whole and operator interpretations, but not with the quotient interpretation. A quantitative analysis showed that students performed better on equivalence and ordering tasks presented in quotient interpretation than in part-whole and operator interpretations; they performed better on labelling tasks in part-whole and operator interpretations than in quotient interpretations. Educational implications of these results will be discussed.