Fractals as a context of comprehension of the meanings of the sequence and the limit in a Dynamic Computer Software environment

It has been ascertained through research but also through  experience in class , that students encounter difficulties in the construction and perception  of the concept of the limit. It has been  investigated  how the DGS environment can develop the connection between  procedural and conceptual knowledge  resulting from the interaction of  15 year-old students in activities of a dynamic computer software environment such as Geometer Sketchpad v.4 (N.Jackiw ,1988).We will examine how the DGS environment may assist students through guided activities in fractals, to construct the concepts of  sequence and  limit and  to  discuss the potential of the development of the connection between  procedural and conceptual knowledge.

The proposed approach leads the students to consider the limit as an object but they (do not) loose the sense of the process that lies beneath the object itself (Robutti,  2004). What appears to hold fast  DGS environment and the iteration process (N.Jackiw&N.Sinclair, 2004) function as an intermediate link between the direct experience of the user and the  abstract mathematical meaning. The underlying notion  is that  through this  particular work  the following be achieved: “as schoolteachers, instead of formulating definitions and then expecting students to participate, we can create the motives so that via suitable activities they can discover concepts  and mathematic relations”.