近似数量系统与数学能力的关系：一项元分析

"Numerous researches have been dedicated to explore the association between the approximate number system (ANS) and mathematical competence in the past two decades. However, various contradictory results have been reported. It remains unclear whether and to what extent the relationship differs systematically between ANS and mathematical competence and whether category variables such as index, task format and task type of ANS, math content and academic stages, continuous variables such as female rates, age and sample size are additional moderators. We investigated these questions by means of a meta-analysis of cross-sectional studies. The literature yielded 40 articles, 44 independent samples reporting 153 effect sizes found with 8132 participants. A random-effects model was selected to conduct the meta-analysis in Comprehensive Meta-analysis 3.3 software. The heterogeneity test showed that there was significant heterogeneity among 153 effect sizes, indicating that the random-effect model was adequate for subsequent meta-analysis. Based on the results of the funnel plot, Eggers test of regression to the intercept and Classic Fail-safe N, no significant publication was found in the included studies.The main effect analysis indicated a significant positive correlation between ANS and mathematical competence(r = 0.299) which was larger than other similar researches and reached high effect size according to new standard. The moderation analysis revealed that the link between ANS and mathematical competence was moderated by category variables including index of ANS, math content and academic stages, and continuous variables including female rates and age. Specially, with regard to the index of ANS, compared with w and RT, accuracy had the strongest correlation with math competency; with regard to age, compared with older students and adult, the relation between ANS and math competence was strongest among kindergarteners; with regard to math content, compared with other contents of mathematical competence, early math concept and overall mathematical competence showed strongest relationship with ANS. However, other moderators such as task format and task type of ANS, and sample size did not moderate the relationship between these two constructs. In addition, 85 or more participants are needed to detect the effect with 80% power at an alpha level of 0.05, which means further research need a sample of more than 85 participates to detect the association between ANS and math competence . The study set the foundation for further experimental research to induce causal link between ANS and mathematical competence, and for further longitudinal research to reveal the dynamic relationship between ANS and mathematical competence among the spectrum of human life. Moreover, it also called for educational support for the disadvantaged from the perspective of ANS intervention and view of mathematical education which care more about fundamental mathematical competence.