Six Piagetian-type tasks, designed to examine associated topological groupings, were examined to determine if a hierarchical relationship existed among them. The groupings examined were: the partitioning of sets and addition of subsets, reciprocity of proximities, one-to-one multiplication of elements, order of placement, symmetrical interval relations, and one-to-one multiplication of relations. The tasks were individually administered, in random order, to thirty-six students from each grade one, three, and five. The order of attainment of the tasks indicated by this study differs from the order suggested by Piaget and Inhelder. The author presents reasons for this difference, and implications of the study useful to educators are discussed. (MK)