Abstract: Mathematical ability is a crucial component of human cognitive function, which is defined as the ability to acquire, process, and store mathematical information. Although many studies have established a close relationship between working memory and mathematical ability, current empirical evidence lacks a comprehensive understanding of the specificity of associations between different types of working memory and various domains of mathematical ability, as well as their developmental trajectories. Further, traditional methodologies in previous research, such as structural equation modeling, frequently fail to adequately uncover complex interactions among the subcomponents of these two cognitive constructs. To address these gaps, this network analysis study is the first to systematically examine the relationship between different types of working memory and domains of mathematical ability in elementary school children, and explore whether the patterns of these connections vary across developmental stages in elementary school children.
The study sample comprised 875 elementary school children. Verbal working memory capacity was assessed using digit span forward and backward tasks, and visuospatial working memory capacity was measured with forward and backward Corsi span tasks. The verbal 1-back task and spatial 1-back task were employed to assess the children’s verbal working memory updating and visuospatial working memory updating, respectively. For mathematical ability, five tests measured mathematical operations, logical reasoning, and spatial imagination abilities. Family socioeconomic status, non-verbal intelligence, attention, gender, and age were included as covariates in all of the analyses. For network analysis, separate network models were estimated for every grade cohort. Developmental differences in network structures were examined using the network comparison test.
The results demonstrated that upper-grade children exhibited significantly higher scores across all of the working memory components and three mathematical domains compared to lower-grade children. Network estimation revealed distinct developmental patterns: (1) In the lower grades, verbal working memory capacity and verbal working memory updating exhibit the strongest positive associations with mathematical operations. (2) Visuospatial working memory capacity shows the largest positive association with mathematical operations among children in the middle and upper grades. (3) Verbal working memory capacity is most strongly associated with logical reasoning in the middle grades, and with spatial imagination in the upper grades. (4) Network comparison tests determined that the strength of the connection between verbal working memory updating and mathematical operations in the middle grades is significantly weaker than in the lower and upper grades. Further, the connection between verbal working memory updating and spatial imagination in the lower grades is significantly weaker than in the upper grades.
These findings support the domain-specific models of working memory, thus demonstrating that working memory-mathematics relationships show systematic variation based on the specific working memory subcomponents assessed and mathematical domain involved. These results advance the theoretical understanding of cognitive structure through novel empirical evidence and also provide a framework for evidence-based interventions to improve mathematical abilities in elementary school children.

Key words: working memory, mathematical ability, elementary school children, network analysis