Serial Regularities and Proportions

Abstract

The apparatus used in Experiment I did not allow the concrete sedation of sizes. The functional relation was that of a reciprocal compensation of two magnitudes of the same nature, i.e. the length of a segment. But if these magnitudes are materially distinct, and if their progression occurs in the same direction (for example, larger implies further), will the search for a functional relation be facilitated? In addition, when these series of sizes are presented in a regular manner, would perceptions contribute to the correct attainment of the results? If this were so, would the coordination between two seriations be sufficient to result in the isolation of a relationship of proportionality? In order to study this set of questions we present the child with a series of circles to be placed on a series of sticks. We define in advance the role of the size of the circles: it is as if the same circle grew as it was displaced on the stick. The place of a given circle is thus a function of its size. We will leave the child free to choose the criterion of size: the surface area, the diameter or the radius.