Evidence for the Phase transition from rule I to rule II on the balance scale task.

A central and recurrent theme in developmental psychology is the question whether development proceeds continuously or discontinuously. This question is difficult to answer because the 2 types of development may be hard to distinguish. To investigate whether change is discontinuous, one requires a formal model for discontinuous development. Such a model should provide operational, empirical criteria to investigate the nature of development. The cusp model, which is derived from catastrophe theory, is a formal model of discontinuity that provides such criteria. In the present research, it is tested whether the transition from Rule I to Rule II on the balance scale task proceeds discontinuously. The present research centers around 5 catastrophe flags: bimodality, inaccessible region, sudden jump, divergence, and hysteresis. Two experiments are reported. In Exp 1, a paper-and-pencil version of the balance scale task was administered to 314 children (aged 6-10 yrs). In Exp 2, an adapted version of the test was administered to 302 children (aged 6-10 yrs). Bimodality, inaccessible region, hysteresis, and sudden jump were clearly observed. The presence of 4 of the 5 flags strongly supports the hypothesis that the transition from Rule I to Rule II is discontinuous.