Fifty first- and second-grade children's understanding of logico-mathematical relations were assessed using selected Piagetian tasks to test four hypotheses. The children's abilities to conserve numbers were compared to the means of mathematics concept scores and total mathematics scores of the 1972 Stanford Achievement Test, Form A. The relationships between these Piagetian tasks and individual mathematics concept items on the SAT were assessed; and the relationship between children's stages of cognitive development and their mathematics class achievement ranking as measured by daily classwork were determined. The results were mixed with some Piagetian tasks showing a direct relationship with test scores and others showing none. (MP)