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. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Relational thinking: An overlooked component of executive functioning.

Relational thinking, the ability to represent abstract, generalizable relations, is a core component of reasoning and human cognition. Relational thinking contributes to fluid reasoning and academic achievement, particularly in the domain of math. However, due to the complex nature of many fluid reasoning tasks, it has been difficult to determine the degree to which relational thinking has a separable role from the cognitive processes collectively known as executive functions (EFs). Here, we used a simplified reasoning task to better understand how relational thinking contributes to math achievement in a large, diverse sample of elementary and middle school students (N = 942). Students also performed a set of ten adaptive EF assessments, as well as tests of math fluency and fraction magnitude comparison. We found that relational thinking was significantly correlated with each of the three EF composite scores previously derived from this dataset, albeit no more strongly than they were with each other. Further, relational thinking predicted unique variance in students' math fluency and fraction magnitude comparison scores over and above the three EF composites. Thus, we propose that relational thinking be considered an EF in its own right as one of the core, mid-level cognitive abilities that supports cognition and goal-directed behavior. RESEARCH HIGHLIGHTS: Relational thinking, the process of identifying and integrating relations, develops over childhood and is central to reasoning. We collected data from nearly 1000 elementary and middle schoolers on a test of relational thinking, ten standard executive function tasks, and two math tests. Relational thinking predicts unique variance in math achievement not accounted for by canonical EFs throughout middle childhood. We propose that relational thinking should be conceptualized as a core executive function that supports cognitive development and learning.

Individual differences in fraction arithmetic learning.

Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite, Pyke, and Siegler, 2017), to investigate individual differences in children's fraction arithmetic. FARRA predicted four qualitatively distinct patterns of performance, as well as differences in math achievement among the four patterns. These predictions were confirmed in analyses of two datasets using two methods to classify children's performance-a theory-based method and a data-driven method, Latent Profile Analysis. The findings highlight three dimensions of individual differences that may affect learning in fraction arithmetic, and perhaps other domains as well: effective learning after committing errors, behavioral consistency versus variability, and presence or absence of initial bias. Methodological and educational implications of the findings are discussed.