American Educational Research Association Online Repository
Elementary school-aged children have great difficulty reasoning proportionally and struggle with fractions and decimals, theoretically because proportions do not abide by the same principles as more familiar whole number quantities. The present study examines individual differences in proportional reasoning and whole number representations and tests a prediction for a nonlinearity in the development of relations between the two. Pre-kindergarten through fifth-grade students completed a battery of computerized tasks, including a proportional reasoning task, “which is more?” and “which is #?” whole number comparison tasks, and symbolic and nonsymbolic numerical line-estimation tasks. The results indicate that though younger children’s performance on each of the whole number comparison and number line estimation tasks were significantly positively correlated, performance on each was negatively correlated with performance on the proportional reasoning task. By contrast, older children’s performance on the proportional, whole number comparison, and number line estimation tasks were all positively correlated. These findings support the proposal that better counting abilities early in development interfere with early proportional reasoning capacities, though the two are positively related later in development.
Boyer, Ty W., Natalie Branch.
"Elementary School Students' Quantitative Reasoning: Processing Whole Numbers and Proportions."
American Educational Research Association Online Repository Washington, D.C..