Recent developments in Cognitive Psychology and in the new discipline of Cognitive Science (an integration of Cognitive Psychology, Computer Science, Linguistics, Philosophy of Mind, and Cognitive Neuroscience) have made it appropriate to consider new ways in which Cognitive Development and Educational Psychology can benefit each other. Cognitive Development can contribute to Educational Psychology by specifying cognitive processes entailed in educationally relevant tasks, by analysing processing loads, and by indicating more efficient ways of using available capacity. Cognitive Psychology and Cognitive Science have now produced some penetrating theories of the cognitive processes that underlie a wide variety of intellectual activities. Although there is still much work remaining to be done, these developments can be used to analyse the strategies children and adults use in solving problems in areas such as mathematics and science. This can result in benefits in both learning and remediation. Educational Psychology can benefit Cognitive Development by offering alternativeconcepts, by providing realistic problems for analysis, and by providing a testing ground for its theories. I will illustrate these ideas in the area of mathematics.