Number lines, but not area models, support children’s accuracy and conceptual models of fraction division

Abstract

The Common Core State Standards in Mathematics recommends that children should use visual models to represent fraction operations, such as fraction division. However, there is little experimental research on which visual models are the most effective for helping children to accurately solve and conceptualize these operations. In the current study, 123 fifth and sixth grade students solved fraction division problems in one of four visual model conditions: number lines, circular area models, rectangular area models, or no visual model at all. Children who solved the problems accompanied by a number line were more accurate and showed evidence of consistently producing sound conceptual models across the majority of problems than did children who completed problems with either area model or no visual model at all. These findings are particularly striking given that children have experienced partitioning area models into equal shares as early as first grade, thus circles and rectangles were likely familiar to children. The number line advantage may stem from the fact that they afford the ability to represent both operand magnitudes in relation to one another and relative to a common endpoint. Future work should investigate the optimal order that instructors should introduce various visual models to promote children’s representational fluency across number lines and area models.