Variation in Children's Understanding of Fractions: Preliminary Findings

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving fraction tasks. Several iterations of coding yielded an emergent coding scheme that helps capture the nuances of children's reasoning with multiple types of fractions representations. Initial results from the interview analyses suggest variation in children's reasoning across four categories: (a) model types, (b) children's use of representations and representational fluency, (c) connectedness of children's informal to formal reasoning type, and (d) meanings of fractions. We discuss the challenges of negotiating first-order versus second-order models of children's meaning of fractions, and the relationship between children's representational fluency and conceptions of fractions.