As teorias dos signos de Saussure e Peirce na educação matemática: um estado da arte nos ICMEs (1969-2021)

Abstract

In this paper, we address the following research questions: How are the sign theories of Saussure and Peirce manifested in the International Congress on Mathematical Education (ICMEs)? What are the trends and teaching methodologies that guide research at ICMEs, and how can they be associated with sign theories applied to mathematics education? Based on these inquiries, we seek to understand how mathematics education adopts the sign theories of Saussure and Peirce in the ICMEs, bringing contributions and implications to practices involving the production of mathematical meanings. We use an exploratory qualitative approach for the analysis of proceedings, selected lectures, and invited lectures, available on public domain websites, to gain insight into the studied objects, along with a literature review on the subject. Regarding our research procedures, since we will analyze the proceedings, selected lectures, and invited lectures from ICME 1 (1969) to ICME 14 (2021), we position our research as a bibliographic study of the state of the art or state of knowledge. As for the methodological procedures, our research is divided into several stages. First, we catalog studies from the ICMEs (1969-2021) that involve sign theories in the teaching of mathematics during this period. Next, we systematize the proceedings, selected lectures, and invited lectures that relate and articulate sign theories in mathematics education. Subsequently, we highlight the keywords, main research topics, trends, and teaching methodologies that guide research at the ICMEs to analyze these contexts as possibilities for practices involving the production of mathematical meanings. Based on the studies of Peirce and Saussure, we analyze the contributions of signs (linguistic and semiotic) presented in the works discussed in this investigation, in the processes of meaning production in mathematics teaching. Finally, we discuss how Peircean signs can be viewed in relation to Saussurean signs. The results indicate that visualizing objects through language, or visualizing language through objects, is a key issue that can provide insights into the connection between Saussure's and Peirce's sign systems. This connection belongs to the internal logic of both conventions and can be established through the foundation of these signs. Regarding how mathematics education adopts the sign theories of Saussure and Peirce, we observe that this contextualization occurs through teaching and learning, methodology, mathematical language, problem-solving, among other aspects. As for the ICMEs, we found that semiotics and linguistics are mentioned in the proceedings, selected lectures, and invited lectures, but are not directly used by researchers. Starting from ICME 13, a thematic discussion group on semiotics in mathematics education emerged, due to the importance of discussing topics related to semiotic processes. This study leads us to the conclusion that establishing relationships concerning sign processes, especially from the studies of Saussure and Peirce, is crucial to practices involving the production of mathematical meanings. Based on the thesis, it can be stated that the sign theories of Saussure and Peirce provide a solid theoretical foundation for understanding and enhancing the production of mathematical meanings in Mathematics Education. The research highlighted how semiotics and linguistics can be applied to enrich pedagogical practices, facilitating the understanding of mathematical concepts and students' interaction with mathematical signs. Furthermore, the analysis of trends and methodologies in the ICMEs revealed new possibilities for teaching mathematics, emphasizing the importance of a semiotic approach to promote more meaningful learning.