This paper reports on an experiment which attempted to: (1) empirically validate a hypothesized hierarchical sequence of three double classification tasks; (2) investigate transfer to an untrained Piagetian double classification task; and (3) assess the effects of overtraining a relatively easy task on the learning of a more difficult task, as compared with learning a related task of intermediate difficulty. Fifty-five kindergarten children, who were shown by pretesting to possess negligible double classification skills, were trained over a period of two months on matrix tasks involving color and shape dimensions. The subjects were divided into four groups and were either: (a) trained on three matrix tasks in the hypothesized optimal sequence (simplest to most complex); (b) trained on the same three tasks in the reverse sequence; (c) given overtraining on the simplest task followed immediately by training on the most complex task. The results strongly supported the existence of a hierarchical relationship among the three tasks. More subjects learned the most complex task, and they learned it in fewer trials, when taught in the optimal order. No subject learned a higher-level task without also having learned the lower-level one. High, though not complete, positive transfer to a different double classification task was also demonstrated for those subjects who learned the most complex task in the hierarchy. (Author)