The principal focus of this brief report is on findings and observations from relatively recent research on the learning of mathematics. The distinction between learning and the concepts of curriculum and instruction is first reviewed. Then Piaget's theory of intellectual development is discussed, with the conclusion that it does not provide a basis for determining readiness for mathematics instruction. The contribution of information processing theory is then noted. Four additional observations from contemporary research concern the following: the focus on individuals (versus groups), behavioral objectives, invention or construction of knowledge by young children, and metacognition. A list of references is included. (MNS)