The Association Between Basic Numerical Processing And Approximate Arithmetic In Preschool Children

Basic numerical processing ability,which includes numerical semantic processing and numerical spatial processing,is the foundation of arithmetic ability.Through previous studies,we know that these two kinds of basic numerical processing abilities depend on a different mechanism.Approximate arithmetic is one part of arithmetic ability,which plays a crucial role in individual development,mathematics learning and life practices.Previous studies indicated that approximate arithmetic is positively associated with numerical semantic processing.Besides,approximate arithmetic is positively associated with numerical spatial processing.However,whether two kinds numerical processing abilities make an equal contribution to approximate arithmetic or not is still poorly understood.In addition,it is related to the difficulty of arithmetic on the question of on which basic numerical processing arithmetic more depends.Therefore,we designed two sub-studies in order to reveal the potential association between basic numerical processing and approximate arithmetic of different difficulties.Sub-study 1 was a correlation study,in which we examined whether and to which extent these basic numerical processing abilities are related to performance on approximate arithmetic of different difficulties in six-year-olds preschool children.Results suggested that preschool children have got some basic numerical processing and approximate arithmetic capabilities.Associations with approximate arithmetic were observed for both basic numerical processing measures.As the arithmetic's difficulty increased,numerical spatial processing explained more variance in the arithmetic,whereas the contribution of the numerical semantic processing gradually decreased.Sub-study 2 was a causal study,in which we trained two kinds of basic numerical processing abilities between the participants.Results of sub-study 2 suggested that both training effectively improved the performance on approximate arithmetic.Numerical semantic processing training improved the performance on three difficulty levels of approximate arithmetic;the more difficult the arithmetic was,the better the improvement of the training,while numerical spatial processing training improved performance on the hardest arithmetic.The current data indicate the important effect of numerical semantic processing and numerical spatial processing in the development of approximate arithmetic ability.The relative contribution of basic numerical processing depends on the difficulty of approximate arithmetic.The present result fills in a gap in the study of the relationship between preschool children's approximate arithmetic ability and two kinds of basic numerical processing abilities,indicating that adults need to pay more attention to children's basic numerical processing ability in early mathematics education.