Domain-specific Studies Of Approximate Number System:Processing Mechanisms Independent Of Working Memory

The approximate number system(ANS),as one of the core cognitive systems,has long been considered as the foundation for the development of early mathematical abilities.However,the relationship between this core cognitive function and other core cognitive functions remains unclear.Specifically,the literature and empirical evidence on the association between ANS and general cognitive abilities have been inconsistent,leading to extensive debates and controversies.Against this background,this paper explores 1)whether ANS and working memory share some psychological resources,and 2)whether they have consistent effects on mathematical abilities(such as mathematical opration ability),starting from their relationship.In this way,we attempt to analyze the independence of ANS as a domain-specific cognitive system.This study investigates the relationship between ANS and working memory from different perspectives through three experiments.Experiment 1 systematically investigates whether ANS shares cognitive resources with working memory.Thirtythree college students participated in the study,and a dual-task paradigm was used to investigate whether visual working memory load affects two key features of ANS,namely,numerosity comparison precision and numerosity adaptation effect.Experiment 2 explores whether ANS and working memory have independent predictive effects on individual mathematical performance in adults.Fifty-eight college students participated in the study,and their numerosity comparison and adaptation,visual and verbal working memory,mathematical fluency,and mathematical operation abilities were measured,to explore the relationships between these variables.Compared with adults with fully developed cognitive abilities,elementary school students are in a critical period of magnitude representation development.Based on Experiment 2,Experiment 3 explores the predictive effects of ANS and working memory on mathematical performance in primary school students who are currently in a crucial stage of mathematical cognition development.Seventy-two second-grade and seventy fifth-grade primary school children participated in the study,and their numerosity comparison and adaptation,visual and verbal working memory,mathematical fluency,and mathematical operation abilities were measured,to explore the relationships between these variables.The results show that(1)The precision and adaptation effect of ANS is not affected by working memory load.Additionally,it appears that ANS does not utilize the same cognitive resources as working memory.(2)The precision and adaptation effect of ANS cannot predict mathematical performance in adults,whereas working memory positively predicts mathematical performance.(3)The precision and adaptation effect of ANS cannot predict mathematical performance in primary school children at different grades,whereas working memory positively predicts mathematical performance,and there is no significant difference in the prediction path between different grades.The results of the three studies are consistent,indicating that at least from the primary school stage,the core numerosity representation function of ANS is relatively independent and can no longer significantly predict mathematical skill learning or performance for working memory.