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A Framework for Mathematicians’ Example-Related Activity When Exploring and Proving Mathematical Conjectures

2012; Utrecht University; Linguagem: Inglês

0771-100X

Elise Lockwood, Amy B. Ellis, Muhammed Fatih DOĞAN, Caroline Williams, Eric Knuth,

History and Theory of Mathematics

Examples play a critical role in mathematical practice, particularly in the exploration of conjectures and in the subsequent development of proofs. Although proof has been an object of extensive study, the role that examples play in the process of exploring and proving conjectures has not received the same attention. In this paper, we present a framework that characterizes ways in which mathematicians utilize examples when investigating conjectures and developing proofs. The data consist of 133 mathematicians’ responses to two open-ended survey questions. The framework offers categories for the types of examples, uses of examples, and example strategies that mathematicians discussed in reference to their work with conjectures. In addition to presenting the framework, we also discuss potential educational implications of the results.