The Notes of Semiotic Representation and the Theory of Sets: the analysis of a chapter of a textbook.

Abstract

The various types of semiotic representation are of great relevance to understand the cognitive development of subjects with regard to the appropriation of mathematical knowledge. Thus, the different representations of a mathematical object make it possible to solve and the communication of results obtained in an activity. Therefore, the question arises of how the different types of semiotic representations are presented in the chapter of sets of a textbook. To answer this question, we sought to investigate how the records of semiotic representation (RSR) are articulated throughout the chapter in the course of the sets chapter of a textbook and whether these coordinations provide the conversion or treatment. This research has a qualitative approach through the interpretation of Bogdan and Biklen, based on document analysis, as an information collect process, in the understanding of Tozoni-Reis. In this way, we sought to analyze the chapter of sets of a textbook, work approved by the National Textbook Program (NTP) 2021. The mentioned chapter was analyzed in the light of the Theory of Registers of Semiotic Representation (TRSR), by Raymond Duval. At the end of this analysis, it was found that the chapter of sets articulates several types of RSR and these provide coordination between records, as well as the conversion. Finally, it is concluded that, although the analyzed chapter provides coordination between records, it is necessary that students be encouraged to explore more than one representation register, doing, whenever conveniente, converting one record into another.