Proportional and Whole Number Reasoning

Document Type


Publication Date



Elementary school-aged children have great difficulty reasoning about proportions, some suggest because proportions do not abide by the same principles as more familiar whole number quantities. This study examines individual differences in proportional reasoning and whole number operation skills. Pre-kindergarten through fifth-grade students completed a battery of computerized tasks, including a proportional equivalence judgment task, “which is more?” and “which is #?” whole number comparison tasks, and symbolic and non-symbolic 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 judgment task. By contrast, older children’s performance on all tasks was positively correlated. These findings support a prediction that better counting abilities early in development might contribute to errors in proportional reasoning, although the two are positively related later in development.


Cognitive Development Society Biennial Meeting (CDS)


Columbus, OH