Ação pedagógica da etnomodelagem na matemática: a semiótica de Peirce desvelando potencialidades cognitivas, sociais e políticas

Abstract

Mathematical modeling has been establishing itself as an important tool in response to the objectives that contemporary times demand of Mathematics education. In this context, Ethnomodeling emerges as a way to promote a dialogue between Ethnomathematical and academic knowledge through modeling. From there, thinking about the peculiarities that Ethnomodeling has regarding its influence on students' cognitive actions becomes relevant, since it contributes to promoting its application in the classroom with cognitive, social and political developments, increasingly demarcating its region of inquiry. Thus, this work proposes to analyze, from the perspective of Peirce's Semiotics, the pedagogical action of Ethnomodeling in Mathematics, considering cognitive, social and political processes, starting from the question: what are the impacts of the pedagogical action of Ethnomodeling in Mathematics in the cognitive, social and political spheres, considering Peirce's Semiotics? To this end, we developed a pedagogical framework consisting of five phases that seeks to systematize the application of Ethnomodeling in the classroom. We subsequently implemented this framework in four classes (two from the 8th grade and two from the 9th grade of Brazilian Middle School, with students around 13 and 14 years old) of a public school in the countryside of Pernambuco. We aimed to analyze the cognitive actions of analysis, comprehension, situational structuring, interpretation, synthesis, validation and argumentation based on three analytical units extracted from American Semiotics, namely the modes of perception, the triadic structure of the sign and the types of signs. In addition to Peirce, an icon of American Semiotics, we sought to build our theoretical framework based on Modeling, Ethnomathematics and Ethnomodeling, as well as address epistemological questions based on the works of Duval (2011) and Hoffmann (2006). The data collected through participant observation, student production, questionnaires and interviews were analyzed using Moraes and Galiazzi's (2016) Discursive Textual Analysis and validated through the agreement or disagreement of the research subjects and by comparing it with current literature. The results showed that Ethnomodeling applied through the proposed framework impacted cognitive actions by associating cultural artifacts with the constructed mathematical knowledge, bringing forth phenomenological aspects of firstness, secondness, and thirdness, interpretant signs, immediate and dynamic objects involved in attitudes of sensitivity and cultural analysis, a sense of belonging, metacognition, and cultural reflection with social and political developments