Effects of Arithmetic Principle Cognitive Performance on Mathematical Achievement in Elementary School Students: Controlling for Executive Functions

Objective: This study investigated how elementary students' understanding of core arithmetic principles (inversion, commutativity, associativity, distributivity) relates to their math achievement, while accounting for foundational skills and executive functions. Data & Methods: 77 second-graders completed tests measuring executive functions (working memory, cognitive flexibility, inhibition), number sense, arithmetic fluency, integer computation, and a novel task assessing accuracy and speed on different arithmetic principles. Broad math achievement was also tested. Key Findings: Principle Difficulty Varies: The inversion principle was easiest (highest accuracy, fastest speed). Problems requiring no principle were hardest, confirming the task's validity. Principles Predict Achievement: Even after controlling for executive functions, accuracy on the arithmetic principles task was significantly correlated with overall math achievement. Distinct Student Profiles: Analysis revealed three distinct groups: High Ability (25%): Excelled in both procedural fluency and principle understanding. Moderate Ability (69%): Average performance across domains. Low Ability (6%): Struggled severely, especially in math achievement and computation. Interpretation & Use: Mastering formal arithmetic principles is a key cognitive component of math success. The findings suggest classroom instruction should explicitly connect conceptual rules with procedural practice. The student profiles can help educators identify those at risk (Low Ability group) and tailor interventions. The principle task itself is a useful diagnostic tool to distinguish conceptual gaps from mere lack of practice.