Invariance of Ratio: The Case of Children's Anticipatory Scheme for Constancy of Taste
In this article we study the concept of invariance of ratio through an investigation of children's understanding of constancy of taste—that is, the notion that random samples of a given mixture taste the same—using a device that does not resort to conventional symbolism. The paper begins with a definition of constancy of taste and other quantitative analogues. Then it presents a theoretical analysis of how constancy of taste may emerge from the child's additive world and grow into a conception where taste becomes an intensive quantity. The analysis suggests that one's conception of taste constancy is linked in a fundamental way to one's conception of invariance of ratio. Following this analysis, the paper reports a study that demonstrates the absence of taste constancy among sixth-grade children. More specifically, the study shows that sixth-grade children base their judgment of the relative strength of the taste of two samples from the same mixture on at least one of three (extraneous) variables: the relative volumes of the samples to be tasted, whether the mixture is thought of as consisting of a single ingredient or more than one ingredient, and the relative amount of the ingredients stated in the problem.