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.
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