This article discusses the challenge mathematics educators face in deciding what and how mathematics is to be taught, and offers some suggestions for teachers of young children based on Piaget's developmental theory of mathematics. Piaget's cognitive stages are briefly described and the concrete stage, which spans the age range included in early childhood education, is singled out for detailed examination. Within this stage, three areas of knowledge are dealt with: (1) physical, (2) spatial-temporal, and (3) logico-mathematical. Physical knowledge is described as deriving from the observations of physical phenomena in the environment. The primary recommendation for fostering this type of knowledge in the classroom is to provide plenty of opportunity for object manipulation. Spatial-temporal knowledge is described as thinking structures reflecting concepts of space and time and topological activities are suggested to foster its development in the classroom. Logico-mathematical knowledge is described as dealing with the study of relationships between and among objects. Activities involving classification, seriation, number concepts, and arithmetic operations are recommended at the classroom level. Finally, four benefits of a developmental view of mathematics are noted. (JMB)