The development of proportional reasoning and the ratio concept Part II—problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring

Abstract

The Orange Juice Experiment, consisting of 23 items of varying degrees of complexity bearing on the concept of ratio, was given to subjects between 6 and 16 years. Stages had been differentiated through statistical analysis and described in Part I of this paper. These stages had been interpreted in terms of the Genevan scale of development. In Part II, given here, the strategies applied at each stage are first analysed, and a second order analysis made to determine the possible processes for passing from one stage to another. A process of “adaptive restructuring” finally evolved, bearing on two periods of development—construction of the ratio concept, and construction of the Common Denominator algorithm.