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

TLDR: 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.

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.