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 two 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. Eight criteria, so-called catastrophe flags, can be derived from the model. Some of these flags are predicted in other models of discontinuity, but others, notably hysteresis, are unique to catastrophe theory. 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 five catastrophe flags: bimodality, inaccessible region, sudden jump, divergence, and hysteresis. Two experiments are reported. In Experiment 1, a paper-and-pencil version of the balance scale task was administered to 314 children who were 6 to 10 years old. In Experiment 2, an adapted version of the test was administered to 302 children who were 6 to 10 years old. Bimodality, inaccessible region, hysteresis, and sudden jump were clearly observed. Divergence was not observed. The presence of four of the five flags strongly supports the hypothesis that the transition from Rule I to Rule II is discontinuous.