Uses of example objects in proving

This paper builds upon discussions of the importance of semantic or intuitive work in proving by identifying three ways in which experienced mathematicians use example objects in constructing and evaluating proofs. It observes that students often do not use objects in these ways, and discusses the pedagogical question of how we might teach students to be more effective in proving by designing instruction to focus their attention on relevant objects. Data are drawn from interviews with five mathematicians experienced in teaching an introductory proofs course