Testing the Whole Number Interference Hypothesis: Contributions of Inhibitory Control and Whole Number Knowledge to Fraction Understanding

The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is whole number knowledge, then it should hinder fraction understanding. These predictions were tested in a racially and socioeconomically diverse sample of U.S. children (N = 765; 337 female) in Grades 3 (ages 8-9), 5 (ages 10-11), and 7 (ages 12-13) who completed a battery of computerized tests. The fraction comparison task included problems with both shared components (e.g., 3/5 > 2/5) and distinct components (e.g., 2/3 > 5/9), and problems that were congruent (e.g., 5/6 > 3/4) and incongruent (e.g., 3/4 > 5/7) with whole number knowledge. Inhibitory control predicted fraction comparison performance over and above working memory across component and congruency types. Whole number knowledge did not hinder performance and instead positively predicted performance for fractions with shared components. These results highlight a role for inhibitory control in rational number understanding and suggest that its contribution may be distinct from inhibiting whole number magnitude knowledge.