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Abstract: This paper summarizes some results of investigation on the developmentof children's cognition of velocity, time, classification, space and so on,The results clarify the view of combining continuity theory with stagetheory. Four points are emphasized in this paper: (1) It is true, as Piaget has claimed, that the developmental process canbe divided into different stages in terms of quality, but the features cha-racterizing higher stages stem from the lower ones. Such features as fragi-lity and immaturity become evident after simplifying or reducing thedemands of the task or eliminating the interference of irrelevant variablesin performance. (2) Often there is a transitional period between a higher and a lowerstage, characterized by conflict between old cognitive factors and newones. Children benefit much from training during this period. (3) The pace of children's progress is not even within a cognitive do-main; the developmental curves remain flat or rise steeply at differenttimes. This offers clues for training at crucial ages. (4) The cognitive developmental processes in various domains are not-synchronous. It is a challenge to developmental psychologists to define cog-nitive developmental stages in correspondence with a wide variety of cog-nitive domains.

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