مرکز منطقه ای اطلاع رساني علوم و فناوري - Essence of Mathematical Objects and their Representations: Analyses of the Classical Semiotic Triangle’s Implications in Geometry

Abstract :

The main purpose of this study is to introduce a theoretical framework based on classical semiotic triangle Reference-Signifier-Signified. This theorical framework is used to examine the relationship between drawings and mathematical objects. In the study, prospective teachers are placed in a transition from drawings towards dynamic drawings. Their process of interpreting variations in a geometrical object’s signifier in a dynamic geometry environment; changes in their signified are analyzed in terms of relations between reference and signifier. The study is a qualitative research and the experimental part consists of two times. In the first time, realized in paper and pencil environment, geometrical drawing activities concerning the concept tangent line to a circle is directed to prospective teachers. In the second time, prospective teachers is asked to realize the same drawing activities in a dynamic geometry environment. Results of the research reveal that as signifiers, drawings in paper and pencil environment are insufficient; but working on dynamic drawings provides rapprochements in the signified of the tangent line concept towards the related reference.