Fraction Division Representation-Experience in a Teacher Education Course Focused on the Reference Unit

Abstract

This study focuses on the knowledge revealed and developed by Elementary Mathematics teachers, in a teacher education course related to the representation of fraction division and the flexibility of the reference unit. The teachers solved a task aimed at mobilizing (and accessing) their knowledge related to their approaches to the sense of division, representation, and reference unit regarding fraction division. The results suggest that teachers face challenges when representing and justifying fraction divisions using pictorial models, especially when the divisor is a non-unit fraction. This is based in a gap regarding the flexibility of the reference unit to which the numbers refer in their representations, as well as a challenge concerning the sense of fraction division and the different forms of representation. With this research we intend to contribute to reducing the scarcity of empirical studies in the area and the importance of this specialized teachers’ knowledge to deal with this topic.