Article
Comprehensive example generation: mathematicians’ uses of examples when developing conjectures
Research in Mathematics Education
(2022)
Abstract
In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our 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 “Comprehensive Example Generation”. We elaborate this construct, and we discuss ways in which it afforded productive conjecturing activity. 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.
Keywords
- Examples,
- mathematicians,
- conjecturing,
- proof
Disciplines
Publication Date
December 28, 2022
Citation Information
Alison G Lynch, Elise Lockwood and Amy B. Ellis. "Comprehensive example generation: mathematicians’ uses of examples when developing conjectures" Research in Mathematics Education (2022) Available at: http://works.bepress.com/alison-lynch/9/