This paper introduces two central questions (1) what are available methodologies for
making claims about mathematical practice and (2) when and how do claims about …

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 …

The last decade has seen a rapid growth in our understanding of the cognitive systems that
underlie mathematical learning and performance, and an increased recognition of the …

Background Changing mathematics curricula and their emphases, lower numbers of student
enrolments in undergraduate mathematics programmes (Barton and Sheryn 2009; and …

In this paper, we present an analytic framework for investigating expert mathematical
learning as the process of building a network of mathematical resources by establishing …

We report on our analysis of data from a dataset of 26 videotapes of university students
working in groups of 2 and 3 on different proving problems. Our aim is to understand the role …

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 …

Prior research showed that many secondary students fail to construct arguments that meet
the standard of proof in mathematics. However, this research tended to use survey methods …

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 …

To improve instruction, conduct communicable studies on student intuition, and provide an
entry point for researchers interested in this area, the meaning of intuition in mathematics …