A comparison between mathematicians’ and students’ use of examples for conjecturing and proving

Examples can play a productive role in the development of conjectures and proofs, but there is more to learn about what makes example use productive. The example use of mathematicians, who themselves are experts at developing conjectures and proofs, may provide insight into ways to support students in using examples productively. In this paper, we compare the example use of six mathematicians and 38 middle school, high school, undergraduate students as they reasoned about interviewer-provided conjectures and developed their own conjectures. We note broad similarities between the two groups in terms of the purposes for which they used examples and the strategies with which they selected and used examples. In the context of these similarities, we highlight two key areas in which the populations differed: (1) the coordination (or lack thereof) between purpose and strategy of examples, and (2) the role of the logical structure of conjectures in choosing and using examples.