A Study On The Relationship Between Approximate Number Representation Ability And Mathematical Ability Of Primary School Children

Approximate number system(ANS) refers to a system with which an individual can represent a set of numbers approximately without calculation and numerical symbols. ANS along with the precise number system explain our basic number sense and form advanced mathematical abilities of human. ANS that is shared by adults, infants and non-human animals approximately represents the number of objects or events in a nonverbal way. ANS acuity is always indexed by Weber fraction and accuracy acquired by the non-symbolic magnitude comparison task. In this task,subjects are asked to judge which of the two quickly flashed arrays of dots is more numerous.ANS improves quickly in infancy and early childhood, and remains slow growth until peak at~30y. Because of the development characteristic of ANS, most of the current researches come from preschool children or adults and few included primary school students. Previous studies have proved the significant positive correlation between acuity of ANS and mathematical ability, but the developmental association between these two kinds of abilities has not been established. It plays a great important role for early mathematics education and the intervention of mathematics learning disability to explore the development of ANS in primary school children and establish the developmental association between ANS acuity and mathematical ability.This study includes three parts. In the first part, the non-symbolic magnitude comparison task is used to explore the development of ANS and 611 primary school children participate in this experiment. The subject of the second part is the same with part one. Based on the first part,Chinese Students Basic Math Ability Test Scale is used to measure the mathematical ability. The second part amid to examine the relationship between ANS acuity and mathematical ability. The purpose of the third part is to examine the relation between ANS acuity and mathematical ability through a six-month longitudinal study and to explore the possible causality through cross-lagged analysis. The results indicated that:(1) The main effect of grade was significant. With the age increasing, the ANS acuity continued to increase and showed a trend of slow growth.(2) The main effect of area types was significant. Visual information affected the judgment of subjects in non-symbolic magnitude comparison task. It shows that the inhibitory control ability was working in the task.(3) The main effect of grade in the fields of math operation, spatial-visual functions and total score was significant. With the age increasing, these abilities increased. The differences were significant between male and female students in math operation, and boys were more excellent than the girls.(4) The ANS acuity was associated with mathematical ability, even when age and IQ were controlled for. The mathematical ability could predict ANS acuity of primary school students. With the increase of grade, the correlation degree promoted.(5) In the six-month longitudinal study, The ANS acuity and mathematical ability both improved steadily.(6) Cross-lagged regression analysis indicated that The ANS acuity predicted mathematical ability, but mathematical ability did not predict ANS acuity. The results of this study support the proposal that there is a close relationship between emotional intelligence and gratitude, the ANS acuity is the cause of the mathematical ability.