The Development Of Number Sense In Children Aged 3-6 And Its Influencing Mechanism

Number sense is an intuitive understanding of what numbers mean and of numerical relationships.Number sense not only makes a difference on identifying mathematical difficulties,but also is an effective intervention indicator to prevent mathematical difficulties.Most studies examine number sense by measuring early calculation ability.The five-component model is widely used because of its clear hierarchy and simple operation.Furthermore,evidence demonstrated that the validity of the streamlined number sense screening tool(SNSST)based on this model was the best predictor of later mathematics achievement.However,this tool focused only on counting,number knowledge,and number operations,rather than on number acuity and numerical estimation.Additionally,due to the regularity of Chinese numbers naming and parents' direct instruction and encouragement on children's mathematic learning,Chinese preschool and kindergarten children scored higher in a test of mathematics abilities than their peers of European Americans.Therefore,the SNSST cannot evaluate the number sense of Chinese children aged 3 to 6 effectively.With respect to the research on developmental characteristics of number sense,previous cross-sectional studies only revealed the age difference at a certain point,which would be influenced by cultural and historical factors.And the longitudinal studies only depicted the development trend of number sense in children aged 5 to 6,but did not explore that of aged 3 to 4.In addition,it is still unclear that the cognitive mechanism of individual differences in the development of number sense.Studies have confirmed that the development of children's sense of number is influenced by both domain-general cognitive abilities and domain-specific basic numerical processing skills,but the specific influence mechanism and the law of change with age have not been known.The current paper used three studies to solve the above problems.Study 1 constructed the Number Sense Test for preschooler to determine the content and structure of children's number sense.Results showed that all the psychometric properties of the 41-item test were satisfactory.Then,359 preschoolers from grades 1-3 of kindergarten were tested in number sense at 3 points across one years by using cohort-sequential latent growth curve(LGC)models to determine longitudinal growth patterns(Study 2).It revealed that counting grew steadily from 3-to 6-year-old,and the growth rate decreased with age.Number acuity developed steadily before age 5,and grew rapidly after that.The development of number knowledge turned around at the age of 3.5,with a rapid growth before that,and became stable after half a year of flat growth,then appeared a six-month growth peak,finally leveled off near the age of 6.Number estimation grew rapidly throughout the whole preschool period.Number operations grew steadily and rapidly throughout preschool.Study 3 implemented three experiments to explore the influence mechanism of domain-general and domain-specific abilities on the development of number sense.Children aged 3,4,and 5 years completed Number Sense Test for preschooler,domain-general cognitive abilities(including verbal comprehension,spatial perception,and executive function)test,and domain-specific skills(including ANSacc,cardinality knowledge,ordinality skills,calculation fluency,and number line estimation)test.Experiment 1 used Bayesian factor analysis to reveal which combination of these variables best explained individual differences in number sense.The analyses identified three unique important variables to explaining individual differences in the three groups of preschool children's number sense:ANSacc,cardinality knowledge,and executive function in 3-year-old children;ordinality skills,ANSacc,and executive function in 4-year-old children;and calculation fluency,verbal comprehension,and spatial perception skills in 5-year-old children.Experiment 2 aimed to investigate the effect of these key cognitive factors on the initial level and growth rate of number sense and its subdomains by constructing a conditional latent growth model.Results showed that the unique cognitive factors could significantly predict the initial level and growth rate of number sense and its subdomains.Overall,domain-specific skills were much more important to explaining individual differences in number sense among 3-and 4-year-old children,but these two abilities were equally important for that of 5-year-old children.Considering the common effect of ANSacc and executive function on the number sense in 3-and 4-year-old children,as well as the synchronous development of ANSacc and executive function.The purpose of Experiment 3 was to examine the mediation effect of executive function,cardinality knowledge,and ordinality skills on the link between ANSacc and the growth of number sense in children aged 3 and 4.Longitudinal mediation analysis revealed that executive function fully mediated the relationship between ANSacc and number sense growth,and higher ANSacc predicted higher cardinal-knower level in 3.5-year-old children,but higher ordinality skills in 4.5-year-old children,which in turn predicted growth in number sense from 3 to 5 years.Overall,these findings suggest that:Firstly,the number sense of preschoolers has five dimensions:counting,number acuity,number knowledge,number estimation,and number operations.Number Sense Test for Preschooler could measure preschool children's number sense effectively.Preschoolers with lower initial number sense proficiency grew more quickly than preschoolers with higher proficiency.The developmental of basic counting,number acuity,number knowledge,and number estimation lays the foundation for the growth of number operations.Secondly,the relative significance of the effect of domain-general cognitive ability and domain-specific skills on the individual differences of number sense varies with age.The contribution of these abilities on the initial level of number sense was more significant than that on the growth rate.The significance of these abilities shifted from the basic numerical dimensions to the advanced dimensions with age.Thirdly,results revealed the influence of ANSacc on the growth of number sense was dynamic,from the mediation effect of cardinal knowledge to that of the ordinality skills,for children aged 3 to 5 years.Preschool children first understand the meaning and sequence information represented by non-symbolic quantitative information,and this symbolic and non-symbolic mapping skills,in turn,may help them learn more advanced symbolic information and then performed better number sense.In summary,the Number Sense Test for preschooler compiled in this study has a concise structure and clear dimensions,which provides an effective assessment tool for educators and researchers to measure the development of children's number sense and screen children at risk of number sense.These current studies not only examined and expanded the assumptions of mathematical development,resolved the inconsistent conclusion of the effect of non-symbolic numerical representation on children's number sense,but also provided specific operational mathematical teaching guidance for preschool educators,helping them monitor the difficulties that children may encounter in the process of mathematics learning and developing appropriate and effective interventions.