The Persistent Difficulty of Early Fraction Ideas in Early Secondary School Mathematics

Abstract

This study explored the nature of difficulties of seventh and eighth grade students who struggled building their conceptual understanding of early fraction ideas, in particular ordering fractions. The participants engaged in a sequence of lessons that involved the use of fraction circles. The intervention of four weekly class sessions was adapted from the Rational Number Project (RNP) curriculum that has been created for and refined through teaching experiments in the RNP research since 1979. Pre and post group interviews were conducted with each student group for a sufficient identification of the nature of the students’ difficulties. This study identified the whole number dominance strategies used by the students for ordering fractions before and even after the intervention. The students also revealed minimal use of informal ordering strategies that involve more conceptual than procedural understanding of the concept of initial fraction ideas. Considering the short intervention, there was subtle (but meaningful) evidence for a positive influence of the fraction circle model developed within the RNP on students’ developing understanding of early fraction ideas. This study suggests the need of a remedial intervention for early secondary students showing the persistent difficulty with early fraction ideas. Students need to be given enough time with not only concrete models but also appropriate usage of language to support a complete understanding of how to use the models.

Keywords: Rational Number Project (RNP), fraction circle model, initial fraction ideas, ordering fractions