A two-phase study was designed to investigate the relationship between cognitive skills hypothesized (by Piaget) to underlie number competence, and performance on tasks requiring logical reasoning with number-related concepts. During the first phase, a battery of tasks was administered to 60 kindergarten and 60 third-grade students. These tasks were designed to assess acquisition of concepts identified as formally related to various aspects of number concepts. Tasks within a concept area were weighted according to their relative importance and degree of difficulty. Data were analyzed using contingency tables. In the second phase of the study, data were reanalyzed using a set of behavioral indices developed by Brainerd in earlier work. The results of the study support Piagetian theories of cognitive development. (SD)