DEVELOPMENTAL FOUNDATIONS OF RATIO KNOWLEDGE

理解相称性的发展基础和 分数非常需要研究，这两个原因都是因为关键 分数概念在小学数学教育中的作用 因为分数之间的差异具有重要意义 数字发展理论中的概念和整数知识。 尽管有一种有影响力的观点认为分数概念较少 比整数概念更直观或自然，更依赖于 对他们发展的正式指导，来自研究的某些发现 婴幼儿对物体间物理关系的理解意味着 比例关系从很小的时候就被察觉到了。现在 因此，研究解决了儿童与青少年之间的发展关系 比例的知觉理解与儿童的发展 了解比率的数值性质。第一 研究的组成部分考察了空间构型的作用 学龄前儿童对比率关系知觉的信息；第二 考察儿童对数字特性的发展知识。 在更大的年龄跨度上的比率；第三个调查主观的 比率、分数和分数之间的距离关系 分数的相应符号表示；最后， Fourth使用微基因设计来研究从 对空间构型比的知觉理解 对数字比率的理解。

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.