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Abstract: This study is on the development of 5-11-yr olds' cognition of two spatialrelationships-equality of areas and verticality. Through children's judgementabout the equality of areas, the developmental process of their mastery of theprinciple "equals minus equals will be equals" was investigated. The resultindicated that various variables in the experiment have different effects onchildren's cognition and that children's cognitive process in the judgement ofequality of areas may be mainly devided into two types, that is the judgementon the basis of direct perception and that on the basis of reasoning, and thereseems to exist a transitional state in the development from the former to thelatter. In the result of children's dealing with verticality, besides the case ofperpendicularity to the slope and that of perpendicularity to the level there isalso a medial phase between, a gradually developing process from the formerto the latter. Both these two results show a common tendency of cognitivedevelopment with the increase of age, consisting of two outstanding stagewisecharacteristics:a rapidly developing period at 6-7 years of age when children'sachievements differ significantly and a relatively stable period at 7-9 yearsof age when children's achievements show little or no increment. In the latterperiod children's cognition is liable to the influence of experimental conditions,their achievements are more changeable than those by other age groups. Thismight be the characteristics of this medial, transitional phase of development.

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