A Dynamic Model of Cognitive Growth in a Population: Spatial Tasks and Conservation

A dynamic model of cognitive growth is developed that is applicable to cross-sectional studies of growth in a population, and that predicts the distribution of scores as a function of age. This model modifies the theory of P. van Geert (1991, Psychological Review, 98, 3-53) for the cognitive growth of an individual under limited resources, by taking into account the effect of schooling or training. The modified theory provides an explanation for the puzzling effect reported by C. J. Brainerd (1977, Psychological Bulletin, 84, 919-939), that the gain in scores obtained in concept training experiments is independent of the initial state of the learner. In developing the modified theory, it was found that the assumption of delayed feedback is unnecessary. To apply the model to populations, it was assumed that the ability parameters that appear in the growth function are distributed normally in the population. A distribution function G(s; t) was derived that predicts the distributions of scores s at age t in terms of a small number of parameters. Although the abilities are assumed to be distributed normally, the score distributions are often bimodal. The model was applied to the studies of H. Thomas and A. Lohaus (1993, Monographs of the Society for Research in Child Development, 58, 1-169) on the growth of the concepts of verticality and horizontality, and to the study of P. M. Bentler (1970, Perceptual and Motor Skills, 31, 855-859) on the growth of the concept of conservation. In these applications the score distributions are clearly bimodal, but there is no evidence of abrupt transitions or catastrophes. This shows that the presence of a "catastrophe flag" (bimodal distributions) does not necessarily imply the presence of a catastrophe. Copyright 1999 Academic Press.