The Relationship Between Children’ Non-symbolic Numerical Representation And Mathematics Achievement

Human mathematical competence emerges from two representational systems, one is symbolic numerical representation unique to humans who have undergone explicit teaching; the other is non-symbolic numerical representation, an evolutionarily ancient ’approximate number system’(ANS) that is shared by humans and non-human animals.The ANS is a cognitive faculty that represents the cardinality of sets of objects in an approximate fashion, and that system allows individuals to compare, add, and subtract magnitudes.The last two decades have witnessed a rapid growth of interest in the non-symbolic approximate number system. However, evidence for a relation between ANS and formal mathematics knowledge and skills is mixed in children-the correlation between them has dynamic changes in different ages, and the exact mechanisms and mediating skills that help build symbolic mathematics onto the ANS in the course of childhood remain elusive.Accordingly, in Study 1, to examine whether relations between innate approximate number system and acquired mathematics achievement would change with children development, we adopted cross-sectional method and collected data from primary students including grade 1,3,5 with dots comparison paradigm. Further, based on Study 1, the possible mediation mechanisms of symbolic numerical representation and ordering ability were examined respectively in study 2 and 3.The findings of this study can be summarized as follows:(1) In grade 1 non-symbolic numerical representation and mathematics achievement was not significantly related, but in grade 3 and 5 they were both significantly related.(2) Innate non-symbolic numerical representation and acquired symbolic numerical representation was not significantly related. Along with pupils’ constant growth from grade 1 to grade 5, symbolic numerosity was improved, bringing in decreasing estimation error and optimized linear fit.(3) Ordering ability acted as a mediator between non-symbolic numerosity and mathematics achievement, in addition, the mediating effect was only established in grade 5.