m-ICTE2009 http://www.formatex.org/micte2009 © FORMATEX 2009 879 Virtual laboratories within the context of Dynamic Geometry Systems M. Kordaki *1 and G. Alexiou 1 1 Department of Computer Engineering and Informatics, Patras University, 26500, Rion, Patras, Greece This paper presents the concept of Virtual Laboratories (VL) within the context of Dynamic Geometry Systems (DGS). Despite the fact that a plethora of interactive constructions within DGS has been presented in the literature, the idea of forming virtual laboratories within DGS has not yet been reported. For the design of the proposed laboratories, a modelling methodology was developed. This methodology was based on the design of three models, namely: the learning model based on social and constructivist views regarding knowledge construction, the model of the knowledge domain based on the related specific literature and the student model describing his/her behavior while performing essential tasks for the learning of basic aspects of the previously mentioned knowledge domain. Various capabilities of DGS were also combined so as to assist the construction of the proposed laboratories, e.g. a) presentation of information in Multiple Representation Systems (MRS), b) direct manipulation of the geometrical constructions formed using the tools provided, and c) formation of appropriate buttons for illustrating/hiding the specific constructions viewed as appropriate/inappropriate for the learning of specific aspects of the concepts in focus. As a result of the modelling process, an architecture and a typical interface of the said labs were formed. The previously mentioned methodology and architecture were used for the design and implementation of specific VL for the learning of basic issues of Euclidean Geometry. To clarify the methodology and architecture proposed, a specific example regarding the design and implementation of a specific virtual laboratory for the learning of the mathematical concept of angle is also presented. Keywords virtual laboratories; Dynamic Geometry Systems; modelling; angles, constructivism 1. Introduction Diverse potential benefits can be provided by the adoption of e-learning in both formal and informal education. Among the major advantages of online education is its accessibility and convenience, in that learners can be logged on at any time and in any place [1-2]. Thanks to improved software and high-speed connections, but most of all to a new philosophy of learning that stresses interaction, engagement and customization rather than passive receptivity, e-learning has entered a new era. In fact, it is now a requirement for students to interact and communicate not only with their professor, but also, and mainly, with their virtual classmates. A successful e- learning experience is one that creates a sense of a learning community that can be as strong as – perhaps even stronger than – the face-to-face experience [3]. Needless to say, virtual learning communities seem friendly places. Appropriately designed online courses are also flexible, allowing learners to take control of their learning by choosing the flow of specific events that comprise their learning experience, for example, interaction with their peers, reading the provided materials, reading what others are saying in their drafts, practicing the provided exams, etc. Information also streams in on demand – which is to say that each learner has the chance to choose the content, and when, and from where, they pull it. With the advent of modern computer technologies, web-based laboratories are used as an alternative or a supplement to physical labs [4]. Web-based laboratories have been also been termed virtual laboratories, or simply virtual labs, or cyber-labs. In fact, a computer simulation which enables essential functions of laboratory experiments to be carried out on a computer is called a VL [5]. An experiment is replaced by a computer model, and therefore takes place in the form of a simulation. Recently, VLs have been developed in a number of engineering and scientific disciplines such as Computer Science, Electrical and Mechanical Engineering, Natural Sciences, Chemistry, Statistics, Probability etc [6] using various technologies. The educational benefits of Web-based labs are based on their potential use in the “anytime, anyplace, online learning” world of learners as well as on the diversity of the representational capabilities of web-based technologies, such as dynamic, multiple and interlinked representations, at the same time enhancing learners’ opportunities for experimentation and knowledge construction. At this point, it is worth noting that experimentation by using hands-on experience is acknowledged as essential not only for the learning of experimental sciences but also for the learning of mathematics [7,8]. * Corresponding author: e-mail: kordaki@cti.gr, Phone: +30 2610-993102, FAX: +30-2610-990006