Geometric Conjectures in a Dynamic Geometry Software Environment

Abstract

The use of technology is now widespread at the school as well as college levels. Instructors, however, continuously debate the usefulness of hardware/software in enhancing the learners' knowledge and their understanding of mathematical concepts. This research explores whether technology can contribute to a better student understanding of geometrical concepts and theories. In particular, we explore whether a learning environment that uses Dynamic Geometry Software (DGS) can help students determine the truthfulness of certain geometrical conjectures or whether such an environment can mislead students. Results show that the continuous variations of a geometric figure may sometimes be misleading and that a strategy guiding the investigation process and exploiting the potential of the new technologies are in many cases necessary to properly investigate a given geometrical problem. Results also show that the role of the teacher is, in many cases, critical for the development of the solution strategy.