This study examines the classroom practice and craft knowledge underpinning one teacher's integration of the use of GeoGebra software into mathematics teaching. The chosen teacher worked in an English secondary school and was professionally well regarded as an accomplished user of digital technology in mathematics teaching. Designed in accordance…

We argue that dialogic theory, inspired by the Russian scholar Mikhail Bakhtin, has a distinct contribution to the analysis of the genesis of understanding in the mathematics classroom. We begin by contrasting dialogic theory to other leading theoretical approaches to understanding conceptual development in mathematics influenced by Jean Piaget…

In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his "big ideas" as he lived through the most amazing innovations in technology that have changed our lives…

Wireless networks are fast becoming ubiquitous in all aspects of society and the world economy. We describe a method for studying the impacts of combining such technology with dynamic, representationally-rich mathematics software, particularly on participation, expression and projection of identity from a local to a public, shared workspace. We…

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…

Presents an analytic framework to describe and analyze students' answers to proof problems. Employs the framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and improve their proof skills. (Author/MM)

Explores the role of proof in mathematics education and provides justification for its importance in the curriculum. Discusses three applications of dynamic geometry software--heuristics, exploration, and visualization--as tools in the teaching of proof and as potential challenges to the importance of proof. (Author/MM)

Reports on a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school as part of a larger research project. Aims to clarify the role of a particular software, Cabri Geometry, in the teaching/learning process. Focuses on the social construction of knowledge. (Author/MM)

Describes two activities that led students to contradictions between conjectures and findings. Analyzes the conjectures, working methods, and explanations given by students when faced with the contradictions that arose. (Author/MM)

Attempts to develop a global discussion about the roles of dynamic geometry systems (DGS) by addressing four points: (1) the variety of possible contexts for proof in a DGS; (2) the dual nature of proof (cognitive and social) as reflected in the "milieu" constructed around the use of a DGS; (3) from observing to proving; and (4) overcoming the…