Differentiated Contributions of Executive Functions to Domain-Specific Numerical Precursors in Preschool Children

Executive functions (EFs) are well-established predictors of early mathematical development, yet whether distinct components contribute differentially to specific numerical precursors during the preschool years remains unclear. The present study examined the unique contributions of inhibitory control, verbal short-term memory (VSTM), visuospatial working memory (VSWM), and set-shifting to three precursors (procedural cardinality, non-symbolic quantity reproduction, and Approximate Number System [ANS] performance) while controlling for the domain-general contributions of receptive language and rapid automatized naming (RAN) and tested whether age moderated these associations. A total of 316 Italian preschoolers (M = 59.85 months, range 38-76; 158 females) completed nine tasks from the DAP-T tablet-based battery; hierarchical regression and moderation analyses were conducted on multiply imputed datasets (50 imputations), with Holm-Bonferroni correction applied to individual coefficients and complete-case sensitivity analyses performed to assess robustness. Age moderation was examined through six interaction terms with Bonferroni correction. Age was the strongest predictor across outcomes. Above and beyond age and domain-general covariates, procedural cardinality was uniquely predicted by VSTM (β = 0.205); ANS performance by inhibitory control (β = 0.191) and RAN (β = 0.252); non-symbolic quantity reproduction by RAN (β = 0.182) and age alone. RAN emerged as the most consistent cross-domain predictor of numerical performance after age, with effects surviving correction on non-symbolic quantity reproduction and ANS. Set-shifting contributed to no outcome robustly after correction. None of the six age-moderation interactions survived Bonferroni correction; a single nominal effect emerged for Age × VSTM on procedural cardinality (p = .044), which should be regarded as exploratory. EFs thus show a differentiated profile across numerical precursors, with VSTM and inhibitory control as primary executive supports for procedural cardinality and non-symbolic comparison, respectively, whereas non-symbolic quantity reproduction appears to draw more on domain-general processing efficiency than on standard executive control.