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 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…

Having an ability to appreciate, understand, and generate proofs is crucial in being able to evaluate students' mathematical arguments and reasoning. As such, the development of this ability in perspective teachers is imperative. This study examines the work of a group of preservice elementary school teachers in their efforts to generate one-line…

This paper reports on a series of four studies carried out over a period of four years. These related studies were clinical and qualitative as they investigated middle and high school students' development of geometric thought, particularly as it related to three- dimensional visualization. The studies were carried out in the constructivist…

The article describes a research conducted on students at the University in Pula, by which was attempted to establish whether there is a relationship between exam success and a type of online teaching material from which a student learns. Students were subjected to psychological testing that measured factors of intelligence: verbal, non-verbal and…

Can textbook exercises be transformed into problem solving activities that encourage students to develop mathematical thinking? This study documents what high school students showed when they were explicitly asked to use technological tools to examine and solve a routine problem from different angles or perspectives. In this process, students…

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 on one aspect of a longitudinal study which seeks insight into the ways in which spreadsheet experience and teachers' pedagogic strategies shape pupils' construction of meaning for algebra. Using data from stimulated recall interviews we analyse the evolution of meaning for variable through the mediation of the variable cell and the…

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…

Mathematical word problems are notoriously difficult to solve for students at all grade levels. Performance deficiencies have been attributed to students lacking abstract logico-mathematical knowledge or to insufficiently developed language comprehension skills. At least four general sources of difficulty can be distinguished in mathematical word…

The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…