Examples play a critical role in the exploration and proving of conjectures. Although proof has been studied extensively, the precise ways in which examples might facilitate successful proofs are not well documented or understood. Working within a larger set of studies that argue for the value of examples in proof-related activity, in this paper we present a case study of one mathematician’s work on a conjecture in which his strategic, intentional use of examples led to a proof of that conjecture. By examining his work in detail, we highlight specific mechanisms by which the mathematician’s examples led to successful proof production. These mechanisms shed light on precise ways in which examples can directly lead to proof and inform our understanding of the conceptual landscape of the interplay between examples and proof.
Lockwood, E., Ellis, A., Dogan, M.F., Williams, C.C., & Knuth, E. (2013, November). Strategically chosen examples leading to proof insight: A case study of a mathematician’s proving process. In M.V. Martinez & A.C. Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 245-252). Chicago, IL: University of Illinois at Chicago.