With GeoGebra introduced into mathematics instruction the teaching/learning process is not improved in terms of speed and quality only. Mathematical concepts, rules and procedures must be adjusted to the new environment. On the other hand, characteristics of the computer and the educational software in use must be thoroughly examined and a successful teacher has to use their advantages and avoid their flaws in order to maximize the efficiency of the instruction process. This paper deals with development of ideas when the concept of ellipse is being built with GeoGebra. We shift from dynamic applets that show the ellipse characteristics to applets that are built by students and teacher together. The old applets were perceived by students as dynamic representations of the ellipse and its characteristics. They offered a very low level of freedom for students to explore the material on their own. This meant the students were expected only to receive and learn information about the ellipse. On the contrary, the new applets were designed in a way that the genesis of the ellipse and its relations to other objects were clearly visible. Besides, the process of building new applets enables students to discover independently the ellipse characteristics. Thus, the students become active participants in the process of the knowledge building. In other words, we use GeoGebra to move from static exploration to dynamic exploration. This process could easily be accomplished in Dynamic and Interactive Mathematics Learning Environments (DIMLE). All the information and procedures meant to be learnt by students were presented within the “I – you – we” concept that was very easy to implement in such an environment.