| J Piaget (1896-1980) is famous in the world for establishing the genetic epistemology, which has enriched the knowledge of the human beings to know themselves exactly.Piaget has made significant contributes in the psychology of children's cognition as follows: First, he produces a complete theory of children's cognition structures which is full of dialectical thoughts; Second, he depicts the cognitive developing line of children from their birth to early youth; Third, he is the first psychologist one who introduce mathematical logic to draw children' development of thinking; Finally, he sets up the theoretical construction of genetic epistemology.Modern cognitive development theorists make a deep research on children's cognition at the degree of in formation-processing. They subtly research the process of cognitive development and impacts the study of development of children's cognition deeply in the way of their new theories and abundant results.L-S-Vygotsky who represented the school of social culture points put that the process of individual's evolution is affected not only by the experiences of social cultural practice and the incentives of activities, but also by the tissues of individual's continuous integration.R Case, an eminent representative of neo-piagetian theories, brings forward the unique "process and structures" theory, which inherits from the most key ideas of Piaget's children's cognitive development that the development has a qualitative process assuming some quality phases. His theory reflects the thoughts of phases profoundly and sticks to in the cognitive development with the domain of general character. Case takes in some unique concepts from the ideas of experience and school of social historical culture, and integrates in the way of information-processing. Accordingly, the Case's theory of children's cognitive development on "process and structure" is based of the general theory.Case and his colleagues begin with research in children's executive control structure and working-memory, and expand to the theories of knowledge fields and standard modularity. They divide the process of children's cognitive development into a series of fundamental fields, in which they research the central conceptual structures about number, society and space. Researching singly each field of children's cognitive development, they establish the new theory of children's cognitive structures.This article investigates the general rule of children's cognitive development at the degrees of number, space and narrative, and analy/es the synchronization and un-synchronization of cognitive development. It validates and develops Case's theory from the factors such as nationalities, regions, nations, ages, gender, and tries to enrich the theory of children's cognitive development. To attain the aim, the author reforms Case's experimental design in Chinese thinking and unifying qualities, and comes up with four experimental designs, such as "the children's daily mathematical knowledge-the skill about dealing with money", "the children's spatial structure -mapping", "the children's senses of parental role" and "the children's understanding capabilities about society". The author tries to discover specific practice about the theory of " process and structures" in three fields of mathematical thoughts, spatial thoughts and narrative thoughts.The subjects are selected from Nanjian County in Yunnan Provence, 99 children aged 4 to 10 of Han nationality are selected from the kindergarten and primary school of Nanjian County, 72 children of Han nationality and 95 children of Yi nationality aged 6 to 12 are selected from Xiaowan Town where is about 60 kilometers from the county city.The conclusion of this research can be listed as follows:1. Case's phase-levels thoughts has been rigorously verified by the children's cognition (daily mathematical practice and spatial construction) and social cognition (understanding of social meaning) in min-developed region, has not been demonstrated in undevelope...
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