A programação de computadores e a função afim: um estudo sobre a representação e a compreensão de invariantes operatórios

Abstract

This research is part of the thematic about the process of mathematical conceptualization mediated by computer programming. Thinking about the conceptual elaboration movement of Mathematics and about the use of technologies in the educational process is fundamental, considering the growing use of technological apparatuses in today's society and the possibilities it presents for education. From the theoretical reference of Gérard Vergnaud's Conceptual Field Theory, more precisely in concepts of situations, operative invariants and representations, and elements of Seymour Papert's Constructivist Theory, notably the model of the learning spiral proposed by José Armando Valente, the research sought to answer the following question: How are the processes of representation and understanding of the operative invariants of the Linear Functional Field of Experiments manifest in two students of the Technical Course in Informatics of the IFRS – Campus Erechim, based on a didactic strategy mediated by computer programming? For that, a qualitative research was carried out with theoretical study on the conceptual bases and empirical study with the students. In this direction, the Conceptual Field of Linear Functions was constituted, in the sense of delimiting the conceptual field of interest in the research, in which the main operative invariants associated to the situations were categorized: IO1 - variable, IO2 - rate of variation, IO3 - fixed rate and IO4 - one-to-one correspondence, which served as analysis categories. Also, a didactic strategy was created based on the use of computer programming and the contribution of the Theory of Learning Styles, in order to serve as a research tool and also as a contribution of the thesis to the didactic elaboration in the school. The empirical research data were produced by performing the situations on Linear Functions with the Scratch programming environment by two selected students, associated with the method of interactive observation. With this, it was possible to identify the operative and predicative forms of the operative invariants and to interpret the representations and understandings to then describe the associated theorems. As results, the research pointed to the extension of the concept of variable (IO1), providing more complex generalization processes and the possibility of concretization and dynamization of the concept of constant rate of variation (IO2). In addition, it allowed to show that the process of manifestation of the representation and understanding of the operative invariants of the Linear Functions Conceptual Field happened through actions of concretization, dynamization, comprehension and reformulation provided, respectively, by the stages of description, execution, reflection and debugging the spiral of conceptualization, based on a didactic strategy mediated by computer programming.