Elementary School Students’ Quantitative Reasoning: Processing Whole Numbers and Proportions

Children have great difficulty reasoning about proportions, theoretically because familiar whole number principles do not apply to proportions. This study examines how children’s proportional and whole number reasoning interrelate. Pre-kindergarten through fifth-grade students completed a battery of computerized tasks, including a proportional judgment task, two whole number comparison tasks, and symbolic and non-symbolic number line estimation tasks. The results indicate that though younger children’s performance on the whole number comparison and number line estimation tasks were significantly positively correlated, performance on each was negatively correlated with the proportional judgment task. Older children’s performance on all tasks was positively correlated. These findings support the hypothesis that counting abilities contribute to proportional reasoning errors that are not overcome until later childhood.