Testing the whole number interference hypothesis: Contributions of inhibitory control and whole number knowledge to fraction understanding.

Abstract

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.

High School Students’ Fraction Comparison Strategy Profiles Relate to Rational Number Difficulties and Cognitive Outcomes

“…However, in this study, performance in incongruent and congruent trials was averaged; thus, this null result may be explained by the lack of relation between inhibitory control and congruent trials typically reported in other papers (e.g., Abreu-Mendoza et al, 2020;Coulanges et al, 2021;Gomez et al, 2015). More recently, Leib et al (2023) found that among third-to-seventh graders, inhibitory skills, assessed with a Color-Word Stroop task and a letter Flanker task, contribute to both, congruent and incongruent fraction comparison problems. Similarly, Van Hoof et al (2021) showed a similar cognitive cost in switching from misleading to consistent than when switching from consistent to misleading problems.…”

“…Overall, the current and past results suggest that fraction learning may be better captured by non-linear, categorical transitions, rather than continuous, cumulative changes. Consistently, cross-sectional data show that at the group level, the degree of use of some comparison strategies decreases with age (e.g., whole-number bias), while more sophisticated yet flawed ones (e.g., reversed bias and gap thinking) increase (González-Forte et al, 2023;Leib et al, 2023). However, only longitudinal designs combined with person-oriented approaches could allow us to describe how students transition from one category to another and whether there are students who may be at a higher risk of stagnation.…”

“…When working with rational numbers, inhibitory control is thought to help students overcome interference from whole-number information. Correlational evidence finds that students with high inhibitory control ability have strong nonsymbolic and symbolic proportional comparison skills (Abreu-Mendoza et al, 2020;Coulanges et al, 2021;De Keersmaeker et al, 2022;Gomez et al, 2015;Leib et al, 2023). Particularly to fraction comparison tasks, Gomez et al (2015) found that middle schoolers' performance in a numerical Stroop task relates to accuracy in the incongruent trials of a fraction comparison task.…”

“…Both, working memory and cognitive flexibility have been related to different aspects of fraction knowledge. In particular, correlational studies have found that students with stronger working memory skills have higher fraction comparison skills, and conceptual and procedural fraction knowledge (Abreu-Mendoza et al, 2018;Bailey et al, 2012;Hansen et al, 2015;Jordan et al, 2013;Leib et al, 2023). However, some studies indicate that this executive function skill might have stronger contributions to procedural than conceptual skills.…”

Attending to what’s important: what heat maps may reveal about attention, inhibitory control, and fraction arithmetic performance

“…This finding is aligned with our hypothesis and also contributes to the prior literature by employing a domain-specific measure of inhibitory control (Numerical Stroop). Greater inhibitory control may be particularly beneficial in the context of fraction arithmetic as this cognitive skill may enable individuals to "overcome" the whole-number bias by helping them inhibit whole number strategies that are largely automatized due to the extensive experience individuals have with whole numbers (Siegler et al, 2011;Fitzsimmons et al, 2020b;Leib et al, 2023). Indeed, when dealing with fractions, generalizing some whole-number strategies can be counterproductive.…”