The semiotics of Peirce and Saussure, contributions and limits to the theory of semitical representations of Raymond Duval and the analysis of form and content in mathematics

Abstract

The Semiotic Representation Theory of Raymond Duval consists of an important subsidy for the analysis of students’ production in math classes, since it deals with intellectual gestures, which are materialized through the use of representations, such as numerical writing. The present paper rescues historical aspects of Semiotics, presents in the works of Charles Sanders Peirce and Ferdinand de Saussure. These two authors have notes by Raymond Duval and are considered founders of models of analysis of the various representations of human thought. With these findings, this paper question what are the contributions and limitations of the works of Charles Sanders Peirce and Ferdinand de Saussure considered by Raymond Duval in Semiotic Representations Theory? What reflections about the Mathematics are possible from the analysis of the historical aspects that to go around the Semiotics Representations Theory? Based on these questions, the present paper, of a qualitative nature and a bibliographic delineation, aims to investigate aspects of the life and work of these two theorists, pointing out some of the concepts present in their works, as well as contributions and limitations about the perspective of theorist Raymond Duval in relation the Theory of Semiotic Representations. Peirce with the tricotomy of the sign, object and interpretant and Saussure in analyzing the signs within the semiotic system of the language, throw important theoretical keys for the analysis of the semiotic systems used in Mathematics.