Abstract
My purpose in this paper is to show how modelling and othernon-deductive forms of reasoning, as employed by a highly creative mathematician, can be productiveof important conceptual innovations, and, by the same token, can serve as effective tools for stimulatingconceptual development in the process of learning mathematics. After a – necessarily brief – characterizationof 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 knowledgeand are therefore highly expedient for the construction of anintegrated conceptual framework for understanding mathematics,its relations with science and technology, and its practical uses.
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