Kilpatrick describes the curriculum program of the School Mathematics Study Group and its philosophy. Mathematical structure, rather than psychological theory, has played the instrumental role in shaping the program. An interesting issue is joined, essentially the same issue provoked by the Karplus paper, i.e., the issue of spontaneous aevelopment in children's thinking versus acceleration of this development through formal instruction and altering the child's experience. The compatibility of certain features of the SMSG curriculum with the results of Piaget's studies are enumerated. The paper concludes with a discussion of the National Longitudinal Study of Mathematical Abilities.