Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge

Abstract

While preschool-aged children display some skills with quantitative relations, later learning of related fraction concepts is difficult for many students. We present two studies that investigate young children's tendency of Spontaneous Focusing On quantitative Relations (SFOR), which may help explain individual differences in the development of fraction knowledge. In the first study, a cross-sectional sample of 84 kindergarteners to third graders completed tasks measuring their spontaneous recognition and use of quantitative relations and then completed the tasks again with explicit guidance to focus on quantitative relations. Findings suggest that SFOR is a measure of the spontaneous focusing of attention on quantitative relations and the use of these relations in reasoning. In the second (longitudinal) study, 25 first graders completed measures of SFOR tendency and a measure of fraction knowledge three years later. SFOR tendency was found to predict fraction knowledge, suggesting that it plays a role in the development of fraction knowledge.

Notes

Duffy, Huttenlocher, and Levine (2005) presented children with a recognition of relations task in which children must match wooden dowels that are the “exact same size.” Crucially, these tasks were made explicitly mathematical by guiding the children toward absolute amount between dowel and tube by these instructions. They were shown the correct answer on two practice trials prior to the experimental phase as well.