Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions

Abstract

Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N = 52) saw combinations of cherry juice and water in displays that highlighted either part–whole or part–part relations. Their task was to indicate on a continuous rating scale how much each mixture would taste of cherries. Ratings suggested the use of a proportional integration rule for both kinds of displays, although more robustly and accurately for part–whole displays. The findings indicate that children may be more likely to scale proportional components when being presented with part–whole as compared with part–part displays. Crucially, ratings for part–whole problems correlated with fraction knowledge, even after controlling for age, suggesting that a sense of spatial proportions is associated with an understanding of fractional quantities.