We believe that current research in creativity (especially in artificial intelligence and to a great extent psychology) focuses too much on the product and on exceptional (big-C) creativity. In this paper we want to argue that creative thinking and creative behavior result from the continuation of typical human cognitive development and that by looking into the early stages of this development, we can learn more about creativity. Furthermore, we wish to see analogy as a core mechanism in human cognitive development rather than a special skill among many. Some developmental psychology results that support this claim are reviewed. Analogy and metaphor are also seen as central for the creative process. Whereas mainstream research in artificial creativity and computational models of reasoning by analogy stresses the importance of matching the structure between the source and the target domains, we suggest that perceptual similarities play a much more important role, at least when it comes to creative problem solving. We provide some empirical data to support these claims and discuss their consequences.