Exhaustive Example Generation: Mathematicians’ Uses of Examples When Developing Conjectures

This paper explores the role examples play as mathematicians formulate conjectures. Although previous research has examined example-related activity during the act of proving, less is known about how examples arise during the formulation of conjectures. We interviewed thirteen mathematicians as they explored tasks requiring the development of conjectures. During the interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating systematic lists of examples that they examined for patterns, an activity that we call “Exhaustive Example Generation.” The results suggest further research and pedagogical implications for explicitly targeting examples in conjecturing, and the study contributes to a body of literature that points to the benefits of exploring, identifying, and leveraging examples in proof-related activity.