From mathematics education, a great variety of studies have focused on analyzing the presence of digital technology from different points of view. Those who work with proof and argumentation have resisted presenting results with a technological component, due to the idea of formality associated with those terms, which has increased the existing…

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study…

Findings synthesized across five empirical laboratory- and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single- and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for computer technologies to support…

Students' development of an understanding of covariation was the focus of a research project that investigated the way in which 12 Year 5/6 students engaged with the learning environment afforded by the graphing software, "TinkerPlots." Using data generated from individual interviews, the results demonstrate that upper primary students…

A key element in the examination of how students process mathematics through digital technologies is considering the ways that digital pedagogical media might influence the learning process. How might students' understanding emerge through engagement in a digital-learning environment? Interactive software that has cross-curricula implications and…

This paper explores the role of the teacher in the orchestration of common knowledge and in the interplay between intuitive/empirical and formal aspects within the context of students learning mathematical proof using a dynamic geometry software. The case of a secondary school teacher is discussed through the analysis of her learning initiative…

This study investigated the actual learning processes of two preservice teachers as they explored geometry problems with dynamic geometry software and the effects of using the software on developing their mathematical reasoning and proof abilities. A constructivist teaching experiment was designed and implemented for the investigation. Through…

We explore how 13 year-olds construct meanings around the notion of curvature in their classroom while working with software that combines symbolic notation to construct geometrical figures with dynamic manipulation of variable. The ideas of curve as intrinsic dynamic construction, and curve as object with properties related to its positioning on…

Results of a study involving pre-constructed, web-based, dynamic geometry sketches in activities at the secondary school level revealed that the provision of accurate images is an issue. Many students do not automatically understand that an on-screen image is accurate. Others inadvertently create a special case by dragging, then generalise from…

This paper analyses a case study of a pair of students working together, who were asked to produce conjectures and to validate them within the dynamic geometry environment Cabri. Our aim is to scrutinize the students' reasoning, how the gap from perception to theory is filled, how Cabri influences the reasoning. We have singled out a sequence of…

We report the findings of an empirical analysis of the performance of a group of middle and high school students before and after an after-school algebra enrichment program using the SimCalc software incorporating classroom networks. The results highlight statistically significant gains in their learning and briefly outline contributing factors of…

This paper provides an historical perspective on the possible roles of cognitive technologies in thinking as "reorganizers" of the mind. It suggests that by understanding the transformational roles of advanced technologies for mathematical thinking, positive contributions can be made to research and practice on the use of computers in…

Mathematics educators often despair at math's austere, "abstract" reputation. This paper describes recent work in developing an application named "HyperGami," which is designed to integrate both the abstract and"real-world" aspects of mathematics by allowing children to design and construct polyhedral models and…