International Conference on e-Learning and the Knowledge Society - e-Learning’10 - 203 - Geometry of Motion Pavel Boytchev, Evgenia Sendova, Eugenia Kovatcheva Abstract: This paper describes the development of teaching materials for university students. The materials comprise software models of 3D virtual devices, short animations and a 3D film about ellipses. The animations are designed to raise the curiosity of the students and provide them with food for reflection, whereas the programs could be considered as materialized model-like hypotheses about constructions generating specific curves. The pedagogical aims, some suggestions for classroom activities, and a preliminary feedback are also presented. Key words: Virtual Models, Education, Mathematics, Multidisciplinary. INTRODUCTION The introduction of Geometry of Motion course for students enrolled in the Software Engineering program at the Faculty of Mathematics and Informatics (Sofia University) posed a set of interesting challenges. As a part of the curriculum for the second semester of the freshman year, the course had to be designed for students who are novices in Analytical Geometry and Computer Science. Furthermore, being a new course, Geometry of Motion lacks any specific educational and teaching materials. Except for items "borrowed" from other courses, everything else had to be created from scratch. On the other hand, the course was co-taught by faculty members from different departments. The lectures were delivered by a mathematician, while the lab classes and the development of relevant educational materials were the responsibility of a computer scientist (the first author of the paper). Let us note that the educational materials described in the paper were not created solely for the purpose of the course. They are a result of a sequence of activities involving research within two distinct projects – ELICA [2] and InnoMathEd [10]. The ELICA project has already been used in Computer Graphics courses at Sofia University [3] while InnoMathEd emphasizes on the inquiry based learning thus giving students the chance to deepen their mathematical understanding and to acquire key competences essential for lifelong learning [1]. TEACHING MATERIALS One of the unique educational materials for the course is a short film called “Ellipses...” [4] snapshots of which are seen in Fig.1. The film is a part of a larger multimedia collection comprising of 60 software models of virtual 3D devices illustrating mathematical concepts: drawing mathematical curves/surfaces, and implementing geometrical transformations (Fig.2). The collection was created to support freshmen who are novices in Geometry and Computer science by providing easy to rationalize geometrical constructions, which are typically presented as static 2D schemes. Some of the models represent distinct perspectives of the same mathematical concept (ellipse in the quoted film) revealing both variant and invariant properties of the concept. For every model, a corresponding animation shows a predefined 30-second long motion of the model. All the animations are also available publicly [5, 6]. The models could be used as glass-boxes, viz. they are available in two mutually completing formats – as runnable programs (within the Elica environment), and as standalone animations. The animations are designed to raise the curiosity of the students and provide them with food for reflection, whereas the programs could be considered as materialized model- like hypotheses [11] about constructions generating specific curves.