A robótica educacional como recurso de mobilização e explicitação de invariantes operatórios na resolução de problemas

Abstract

The research reported in this thesis analyzes the use of Digital Technologies (TD) in a constructionist approach, based on Vergnaud's Conceptual Field Theory, seeking to raise its potential as a tool for explicitation of operative invariants among undergraduate students and teachers who teach mathematics. The Theory of Conceptual Fields belongs to the role of cognitive theories and aims to provide an explanation for the phenomenon of learning. According to the author, Gérard Vergnaud, the theory establishes that every concept is constituted of three sets: situations (S), operative invariants (I) and symbolic representations (R). Of these three sets, the one of operative invariants has great importance, because in it reside the operative schemes of the situations, that are expressed through the symbolic representations. However, in solving a problem associated with a situation, the subject generally does not make explicit such invariants, since he is not aware of them. The purpose was to answer the following question: what are the potentialities of the use of educational robotics in the process of explicitation of the operative invariants mobilized by the research subjects in solving problems in mathematics? The general objective is to identify the evidence that validates the use of educational robotics and associated computational thinking as an instrument to explain the operative invariants mobilized by the research subjects in solving problems involving elementary algebra and geometry. The assertion is sought if the said resource constitutes a valid tool to cause the student to explain the operative invariants mobilized to solve a proposed challenging situation. In order to solve problems, the subjects use strategies consolidated in their set of knowledge, which are not easy to be explained. The proposal is to identify such strategies in the symbolic representations expressed by the student and to establish questions in order to make explicit the theorems-in-action and concepts-inaction, both for communication purposes with their peers, and for structuring and organizing its own path of conceptualization. In order to carry out the research, the methodology used was the qualitative interpretive approach, having as an instrument to obtain data the proposition of didactic sequences structured by Didactic Engineering, applied in the scope of the Robotics and Automation Clubs, which figure as an educational product. After work in the clubs, written productions were requested and interviews were conducted with three club monitors, constituting survey data. The data were submitted to a process of discursive textual analysis of the procedures scripts elaborated by the researched subjects, besides the oral explanation recorded in audio during the interviews. Different problem-solving strategies were identified in relation to the proposed situations, evidencing the use of automatisms and consolidated formalisms, usually unthinking. Thus, it was possible to corroborate the assertion that educational robotics can be a valid instrument to obtain indicators of operative invariants, in the present case related to mathematical concepts.