Designers of educational modules for conceptual learning often rely on procedural frameworks to chart out interaction mechanics through which users will develop target understandings. To date, however, there has been no systematic comparative evaluation of such frameworks in terms of their consequences for learning. This lack of empirical…

An allegorical thought experiment occurring in a pseudo Huxleyean world in the future is conducted, in which "Euclidean" geometry has been forgotten and can only be retrieved by traversing backward in time, physically and virtually by two protagonists, Alpha and Beta, inspired by the challenge issued by their teacher Aleph 1. In the year…

Today math teachers can best reach their students and show them how math surrounds us by using manipulatives, children's literature, and GeoGebra while teaching mathematics. These are some of the best pedagogical practices for teaching mathematics today. In our high-tech world, students need to be proficient in science, technology, engineering,…

Interactive or Dynamic Geometry System (DGS) is a tool that help to teach and learn geometry using a computer-based interactive environment. Traditionally, the interaction with DGS is based on keyboard and mouse events where the functionalities are accessed using a menu of icons. Nevertheless, recent findings suggest that such a traditional model…

In the context of rapid technological changes and modernization of society, the issue of ensuring adequacy of content in secondary education based on the use of advanced information technologies (ICT) is being updated. The necessity of an appropriate level of primary intellectual activity development in a person in terms of the current trends in…

"Cognitive Tutor"® is a secondary mathematics curriculum developed by Carnegie Learning that focuses on how students think about and learn mathematics. Teachers facilitate student learning as students acquire and apply new information and discuss their work. The curriculum can be implemented using a textbook, adaptive software, or…

This paper reports from a case study with teachers at two schools in Norway participating in developmental projects aiming for inquiry communities in mathematics teaching and learning. In the reported case study, the teachers participated in one of the developmental projects focusing on implementation and use of computer software in mathematics…

Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

Spatial ability is a critical skill in geometric learning. Several studies investigate how to use digital games to improve spatial abilities. However, not every learner favors this kind of support. To this end, there is a need to examine how human factors affect learners' reactions to the use of a digital game to support geometric learning. In…

This study develops virtual manipulative, polyominoes kits for junior high school students to explore polyominoes. The current work conducts a non-equivalent group pretest-post-test quasi-experimental design to compare the performance difference between using physical manipulatives and virtual manipulatives in finding the number of polyominoes.…

One of the most useful ways to enhance collaboration is to create scenarios where learners are able to interact more effectively. Nevertheless, the design of pedagogically sound and well-thought-out collaborative learning scenarios is a complex issue. This is due to the context of group learning where the synergy among learners' interactions…

In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper…

The authors investigated the effects of student spatial ability, as measured by Raven's Progressive Colored Matrices (J. C. Raven, 1938) and type of instructional program on geometry achievement. Sixth-grade students worked through either 6 instructional activities in Geometer's Sketchpad (Key Curriculum Press, 1993), a dynamic geometry program,…

Spring term of 2005, three Web-assisted undergraduate mathematics courses were taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers 1; Math 236 Mathematics for Elementary Teachers II; and Math 391 Modern Geometry. While the content of these courses differ, they share common goals: to foster a deep understanding of…

This article examines three important facets of the incorporation of new technologies into educational practice, focusing on emergent usages of the mathematical tools of computer algebra and dynamic geometry. First, it illustrates the interpretative flexibility of these tools, highlighting important differences in ways of conceptualizing and…