Are the acuities of magnitude representations of different types and ranges of numbers related? Testing the core assumption of the integrated theory of numerical development

Executive Function and young children's Cardinality Principle: the mediating role of the Approximate Number System and the moderating role of age

Background

Executive Function and the Approximate Number System are well-established as critical components in developing the Cardinality Principle in young children. However, most existing studies explore the relationship between these variables in isolation without examining whether Approximate Number System mediates the relationship between Executive Function and the Cardinality Principle and the role of age in this. This study aimed to address this gap by investigating the mediating role of the Approximate Number System in the relationship between Executive Function and the Cardinality Principle and the moderating role of age in young children.

Methods

This cross-sectional study was conducted in China from February to June 2024. A total of 203 young children (97 boys and 106 girls, Mean age = 68.93 ± 7.076 months) participated. Participants were assessed using a range of tests: the Day-Night Stroop Task, Digit Recall Task, Dimensional Change Card Sort Task, Panamath Test Software, How Many Task, and Give-N Task to measure Executive Function, Approximate Number System, and Cardinality Principle. Data were analyzed using SPSS 26.0 and PROCESS v4.1 (Model 4) to explore the relationships among Executive Function, the Approximate Number System, and the Cardinality Principle through Pearson correlations, multivariate regression, and mediation analysis with 5000 bootstrap samples.

Results

Correlation analysis revealed that the Cardinality Principle was significantly and positively correlated with Inhibitory Control, Working Memory, Cognitive Flexibility, Executive Function, and the Approximate Number System. Regression analyses indicated that Executive Function positively predicted young children's Cardinality Principle. Specifically, Working Memory and Cognitive Flexibility were positive predictors of the Cardinality Principle, while Inhibitory Control was not. Mediation analysis results demonstrated that the Approximate Number System mediated the relationships between Inhibitory Control and the Cardinality Principle, Working Memory and the Cardinality Principle, and Cognitive Flexibility and the Cardinality Principle, respectively. In addition, the study found that young children's age negatively moderated the relationship between the Approximate Number System and the Cardinality Principle.

Conclusions

The study emphasizes that in developing young children's Cardinality Principle, emphasis should be placed on improving their Executive Function and Approximate Number System while considering the age differences of young children and developing appropriate educational methods for different age groups.

Is Nonsymbolic Arithmetic Truly "Arithmetic"? Examining the Computational Capacity of the Approximate Number System in Young Children

Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like structure, like symbolic arithmetic. Children (n = 74 4- to -8-year-olds in Experiment 1; n = 52 7- to 8-year-olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and asked children which of the two derived solutions should be added to the smaller of the two sets to make them "about the same." We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge.

Bidirectional Mapping Between the Symbolic Number System and the Approximate Number System

Abstract. Previous studies have discussed the symmetry of bidirectional mapping between approximate number system (ANS) and symbolic number system (SNS). However, these studies neglected the essential significance of bidirectional mapping in the development of numerical cognition. That is, with age, the connection strength between the ANS and SNS in ANS-SNS mapping could be higher than that in SNS-ANS mapping. Therefore, this study attempted to explore the symmetry of bidirectional mapping by examining whether the connection between the ANS and SNS is the same. Using two types of dot array materials (extensive and intensive) and sequence priming paradigms, this study found a stable negative priming effect in the ANS-SNS priming task, but no priming effect in the SNS-ANS priming task. In addition, although sensory cues (extensive and intensive) could affect performance in the ANS-SNS mapping task, these cues did not affect performance in the ANS-SNS priming task. In general, this study provides valuable insight into the symmetry of bidirectional mapping.