Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…

The objective of this paper is to discuss the didactic potential offered by the use of a Dynamic Geometry System (DGS) in introducing students to theoretical thinking and specifically to the practice of proof. Starting from a discussion about what constitutes the general objective in developing students' sense of proof, the notion of Theorem is…

A model of reading comprehension of geometric proofs (RCGP) has recently been proposed by the authors. This article further investigates students' development of such comprehension based on this model, looking at the relationship between students' reading comprehension and their prior knowledge and logical reasoning. The results show that (1)…

Three issues about students' reasoning, proving and understanding proof in number patterns are investigated in this paper. The first is to elaborate the features of junior high students' reasoning on linear and quadratic number patterns. The second is to study the relationships between 9th graders' justification of mathematical statements about…