In this chapter we focus on the concept of proof, which is important for students'
mathematical education but also hard for teachers to teach and difficult for students to learn …

In the chapter on proof in the previous PME Research Handbook, Mariotti (2006) observed
that there had seemed to be “a general consensus on the fact that the development of a …

Currently, studies focusing on mathematics education pay more attention to the study of the
lecturer's knowledge, aiming to understand this knowledge, its development, and how it is …

Although proving is core to mathematics as a sense-making activity, it currently has a
marginal place in elementary classrooms internationally. Blending research with practical …

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 …

Proof is central to mathematical practice, yet a perennial concern is that students of all ages
struggle in learning to prove. Mathematics education scholars have suggested that …

Recent research in university mathematics education has moved beyond the traditional
focus on the transition from secondary to tertiary education and students' understanding of …

A generic proof is, roughly, a proof carried out on a generic example. We introduce the term
generic proving to denote any mathematical or educational activity surrounding a generic …

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 …

This paper describes outcomes from a project conducted at a small US university where 23
secondary school mathematics teachers participated in the study. Based on sketches …