Research On The Relationship Between Approximate Quantity System And Mathematical Ability And Spatial Ability

The approximate number system(ANS)refers to a system in which an individual approximates a set of quantities without relying on computation,including two parts:symbol estimation and non-symbol estimation.Some studies have found that ANS is closely related to individual mathematics ability,and can predict individual mathematics ability,but whether the two parts of ANS(symbol and non-symbol estimation)have the same effect on mathematical performance,and whether their effects vary with different mathematical ability tests or grades remains to be further studied.This study is divided into two parts.Study 1 analyzes the effects of two parts of ANS(symbolic and non-symbolic estimates)on different mathematical skills in three grades.ANS(dot estimation and number line estimation),general cognitive ability(non-verbal matrix,expressive attention and digit span forward)and mathematics ability tests(Mathematical problem solving and numerical calculations for all grades,early mathematics ability test(TEMA)in kindergarten,and mathematical fluency in grades 2 and 4)were conducted on 311 children(100 kindergarten children,107 grade2 children and 104 grade 4 children)from two kindergartens and three primary schools in Shanghai,China.The results of the hierarchical regression analysis show that in kindergarten,non-symbolic estimation predicts all mathematical skills after controlling for age,gender,and general cognitive ability.In grades 2 and 4,symbol estimates significantly predicted mathematical problem solving,but did not predict mathematical fluency.The symbol estimate also predicts the numerical operation of grade 2.In summary,these findings suggest that different aspects of ANS contribute to different mathematical skills in the early stages of mathematical development.ANS has an important predictive effect on individual mathematics ability,and through literature review,it is found that the individual's estimation ability is closely related to spatial ability.In order to clarify whether the influence of spatial capabilitieson symbol estimates and non-symbol estimates is the same.Study 2 analyzes the impact of spatial ability(psychological rotation test)on ANS(dot estimation and digital line estimation)of 60 students(30 grade 2 children and 30 grade 4 children)after controlling cognitive ability(math problem solving,numerical operation and mathematical fluency).The results show that spatial ability has a significant impact on students' symbol estimation ability,and has no significant effect on non-symbol estimation ability.Through Study 1 and Study 2,it is concluded that the non-symbol estimation in ANS has a strong predictive effect on the mathematical ability of kindergarten children,and the symbol estimation has a strong predictive effect on the mathematics ability of children in the second and fourth grades.The psychological rotation in spatial ability has a strong predictive effect on symbol estimation.