Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment

The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant way, the learning environments. The common experience is that dynamic geometry software systems (DGSs) significantly help students to acquire knowledge about geometric objects and, more generally, to acquire mathematical rigour. Using geometry automated theorem provers (GATPs) capable of construction validation and production of human readable proofs, will consolidate the knowledge acquired with the use of the DGSs. It will also help studentes to comprehend the connection between a concrete representation of a particular geometric construction and its formal description. An adaptative and collaborative blended-learning Web-environment where the DGS and GATP features could be fully explored would be, in our opinion, a very rich and challenging learning environment for teachers and students. In this text we will describe the Web Geometry Laboratory, a Web environment incorporating a DGS and a repository of geometric problems, that can be used in a synchronous and asynchronous fashion and with some adaptative and collaborative features. As future work we want to enhance the adaptative and collaborative aspects of the environment and also to incorporate a GATP, constructing a learning environment for geometry, a dynamic system where the student has at his/her disposal the necessary tools for the study of theories and models of geometry. A system in which students can be challenged by new problems. A system that allows students the opportunity to collaboratively develop and improve their study in the area of geometry anywhere, at anytime and at their own pace.