Klein's model of mathematical creativity

My purpose in this paper is to show how modelling and other non-deductive forms of reasoning, as employed by a highly creative mathematician, can be productive of important conceptual innovations, and, by the same token, can serve as effective tools for stimulating conceptual development in the process of learning mathematics. After a - necessarily brief - characterization of Klein's model-based practice and its philosophical underpinning, the educational implications of the 'model view' of mathematics are discussed. Models typically establish connections between different parts of our knowledge and are therefore highly expedient for the construction of an integrated conceptual framework for understanding mathematics, its relations with science and technology, and its practical uses. © 2002 Kluwer Academic Publishers.