Three- to seven-year-old chilren were trained through reinforcement to select either the more or less numerous of two rows of squares. One group was shown rows in which number covaried with row length, one group saw rows in which number covaried with row density, and a third group saw rows in which number did not covary with other dimensions. The children's operational stage was assessed by a number conservation test. All children successfully judged relative numerosity when number covaried with length or with density, but only concrete operational children were successful when number did not covary with other dimensions. Preoperational children are thus not able to base judgments of relative numerosity solely on number.