DEVELOPMENTAL FOUNDATIONS OF RATIO KNOWLEDGE

理解相称性的发展基础 分数是非常需要研究的，这两个原因都是因为 分数概念在小学数学教育中的作用 由于分数之间的差异具有显著性， 数的发展理论中的概念和整数知识。 尽管有一种很有影响力的观点认为分数概念 比整数概念更直观或自然， 为他们的发展提供正式指导，研究的某些结果 婴儿对物体之间物理关系的理解意味着， 比例关系从很小的时候就被感知到了。 本 因此，研究探讨了 比例知觉理解与儿童发展 理解比率的数值特性。 第一 研究的一个组成部分探讨了空间配置的作用， 学前儿童比例关系知觉中的信息;第二， 考察儿童对数字属性的发展知识， 在更广泛的年龄跨度的比率;第三个调查的主观 比例、分数和 分数的相应符号表示;最后， 第四，使用微遗传设计来检查从 对空间构型比的知觉理解， 理解数字比例。

Developmental foundations for an understanding of proportionality and fractions are critically in need of study, both because of the critical role of fraction concepts in elementary mathematics education and because of the significance attributed to differences between fraction concepts and whole-number knowledge in theories of number development. Although an influential view is that fraction concepts are less intuitive or natural than whole-number concepts and more dependent on formal instruction for their development, certain findings from research on infants understanding of physical relations among objects imply that proportional relations are perceived from a very early age. The present research therefore addresses the developmental relation between the perceptual apprehension of proportionality and children's developing understanding of the numerical properties of ratios. The first component of the research examines the role of spatial-configurational information in preschoolers' perception of ratio relations; the second examines childrens' developing knowledge of the numerical properties of ratios over a broader age span; the third investigates the subjective distance relations among ratios, fractional quantities, and corresponding symbolic representations of fractions; and finally, the fourth uses a microgenetic design to examine the transition from the perceptual apprehension of spatial-configurational ratios to an understanding of numerical ratios.