The Development,the Internal Relationship,and The Training Of The Number Sense In 3～6 Years Old Preschoolers

In preschoolers,the formation and development of the number sense profoundly impact future formal mathematics learning.Preschoolers’ number sense includes two parts: perceiving and understanding quantity and number,which means forming quantity representation;Perceiving and understanding quantitative relations,including the quantity comparison and the arithmetic ability.In the past studies,preschoolers’ number sense mainly was measured and classified from explicit behaviour.However,this classification method is challenging to clarify the various abilities involved in developing the number sense of preschoolers.It also fails to reveal the development,relationship mechanism,and mutual influence of various abilities in the number sense of preschoolers.Thus,it is also unfavourable to design effective training programs of number sense for preschoolers.Based on cognitive theories of number sense,including the Triple-Code Model and the Four-step Developmental Model,this study made out four abilities involved in the development of preschoolers’ number sense: approximate number system acuity,symbolic number knowledge,mapping ability,and arithmetic ability,and explore the development of various abilities and the inner mechanism in preschoolers’ number sense.In study 1,154 preschoolers aged 3-6 years were recruited to accept four tests: the dot comparison task measured the approximate number system acuity.The symbolic number knowledge test measured symbolic number knowledge.The dots-number Comparison task measured the mapping ability.A simple arithmetic test measured arithmetic ability.The results showed that: 1)in preschoolers of 3 to 5,older children have better performance in the approximate number system acuity and symbolic number knowledge.In preschoolers of 4 to 5,older children have better performance in mapping ability and arithmetic ability.2)After controlling for age,both the approximate number system acuity and the symbolic number knowledge can significantly predict the mapping ability,and the symbolic number knowledge has a more considerable predictive effect in preschoolers aged 3 to 6.3)After controlling for age,mapping ability is a complete mediator between ANS acuity and arithmetic ability,and a partial mediator between symbolic number knowledge and arithmetic ability in preschoolers aged 3 to 6.Meanwhile,to explore whether the mapping ability training is more effective in improving arithmetic ability than the approximate number system acuity training,82 preschoolers,aged 4 to 5,participated in study 2 were allocated into three groups according to age and gender.Every group accepts one kind of training respectively,including approximate number system acuity training(ANS group),mapping ability training(mapping group),and picture book activity(parallel control group).Each kind of training has four lessons for three weeks.This experiment was conducted by adopting a pretest-posttest control group design.The results showed that 1)after controlling the pretest scores,the ANS group had significantly higher post-test scores of approximate number system acuity than the parallel control group,and the mapping group had significantly higher post-test scores of mapping ability than the parallel control group.2)after controlling the pretest scores,only the mapping group had significantly higher post-test scores of arithmetic ability than the parallel control group.The results indicate that the mapping ability training can effectively improve preschoolers’ arithmetic ability,while the approximate number system training has no significant effect on preschoolers’ arithmetic ability.Those results provide enlightenment for the cultivation of preschoolers’ number sense.This study concludes: In preschoolers aged 3 to 6,the developing trend of various abilities in number sense is similar,and older preschoolers have more excellent abilities than youngers.In preschoolers aged 3 to 6,both ANS acuity and symbolic number knowledge are the premise of mapping ability,and they predict arithmetic ability by the mediator of mapping ability.Mapping ability training can effectively improve arithmetic ability in preschoolers aged 4 to 5.These findings provide empirical evidence for the development and internal mechanism of number sense in preschoolers and inspire the education program’s design in preschoolers’ number sense.