Covariation and temporal contiguity as principles of causal inference in young children

Four- to seven-year-old children observed a simple physical effect which could be attributed to either a consistent but noncontiguous covariate or a contiguous but inconsistent covariate. When there was a physical rationale for the temporal delay between covariate and effect, children attributed the effect to the consistent but noncontiguous covariate. In the absence of such a rationale, they attributed the effect to the contiguous but inconsistent covariate. It was concluded that neither consistent covariation nor strict temporal contiguity were essential aspects of causal inference for these children.     

The logical and empirical bases of conservation judgements

It is argued that conservation judgements are based on a particular combination of logical necessity and empirical belief. The empirical belief is that a given transformation will not alter a particular quantity (Elkind's conservation of identity). The logical aspect is a transitive deductive argument containing an initial equivalence of two quantities and the conservation of identity belief as premises which lead to the conclusion of maintained equivalence (Elkind's conservation of equivalence). In two experiments, it is shown that conservation of identity beliefs can be manipulated in subjects who have long since developed the capacity for transitive deductive inference. Untrained 10 year olds were unaware of how sublimation acts to alter certain quantities over particular transformations of shape. And untrained adults incorrectly believed that both the area and perimeter of a closed figure would be conserved over transformations which elongated the figure. Both groups of subjects could be trained in the correct conservation of identity beliefs and this affected their conservation of equivalence judgements in predicted ways. It is suggested that the locical aspect of conservation is developmentally stable and that the empirical aspect varies widely across problems and individuals because of its dependence on relevant experience.     

Development of the concepts of energy conservation and entropy

Development of the concepts of energy conservation and entropy was studied in children between 5 and 15 years of age. Energy conservation, as illustrated by the operation of double and colliding pendulums, was not well understood until about 15 years of age. Understanding of entropy was dependent on the particular apparatus used. When illustrated by the gradual mixing of rolling marbles of different colors, entropy was understood by 9- to 15-year-olds. But when illustrated by the eventual equalization of water levels in two interconnected containers, entropy was not well understood until about 15 years of age. Errors on a problem used to illustrate the conservation concept could often be characterized by the misapplication of the entropy concept and vice versa.