Examples can play a critical role in the exploration of conjectures and in the subsequent
development of proofs. Although proof has been an object of extensive study, there is more …

Various studies have been conducted regarding the use of examples in a mathematical
proof. This study aims to describe how the students use the example in the proof analyzed …

The paper provides an overview of the broad field of research on the roles and use of
examples in mathematical learning and thinking, specifically in concept learning and …

A persistent challenge in supporting students' proof activity is fostering the transition from
less formal, empirical arguments to formal deductive arguments. A number of researchers …

This case study investigated the development of group cognition by tracing the change in
mathematical discourse of a team of three middle-school students as they worked on a …

We report on a study investigating high-school students' understanding of the interplay
between examples and proving or disproving of statements drawn from high-school algebra …

Examples can be a powerful tool for students to learn to prove, particularly if used
purposefully and strategically, but there is a pressing need to better understand the nature of …

Tasks that require students to construct examples that meet certain constraints are frequently
used in mathematics education. Although examples do not serve as proofs for general …

The four chapters in this section address issues related to the use of examples in proof and
proving. Several questions arise from reading these chapters. I structure this chapter around …

Examples play a critical role in mathematical practice, particularly in the exploration of
conjectures and in the subsequent development of proofs. Although proof has been an …