Relationships between school achievement and two theoretically different measures of intelligence, Piagetian and psychometric, are explored in 143 bright, average, and retarded elementary school students. Factor analyses of the California Test of Mental Maturity, the Metropolitan Achievement Test, the Stanford-Binet, and fifteen Piaget-type tasks indicated that these tests overlap to some degree, but that Piagetian tasks appear to measure a different intelligence and a different achievement than psychometric tests. Implications for education are discussed. (SBT)