Ensino do conceito de fração: uma atividade mediada por recursos á luz da Gênese Instrumental e dos Campos Conceituais

Abstract

This study presents the results of qualitative research using action research procedures carried out at the Cacilda Braule Pinto State School in the city of Manaus. The intervention consisted of applying a sequence of Instrumental Orchestration that aimed to analyze the process of Instrumental Genesis by 9th grade students in situations involving the concept of fraction, with the support of fraction discs, fraction rulers and squares. Instrumental genesis is understood as the cognitive process of transforming the artifact into an instrument. In this sense, we sought theoretical support: Rabardel's Instrumentation Theory, to interpret the processes of instrumental genesis; Instrumental Orchestration (IO), defined by Trouche as a didactic configuration and its modes of exploration and articulation, which supports the students' instrumental genesis; Vergnaud Conceptual Fields Theory (CFT), providing support for the construction of the fraction conceptual field; and Duval's Semiotic Representation Registers theory, as a reference for grasping the mathematical object. The data analysis in this study used the triangulation technique to articulate the data generated from the diagnostic assessments, observation and videotaping. The information obtained was interpreted using Rabardel S.A.C.I model and Vergnaud's schema components. These were relevant to describing the students' processes of Instrumentalization and Instrumentation during the instrumented activities. The results show the appropriation of the three artifacts and the development of instruments capable of dealing with different situations in the conceptual field of fractions. However, the situations involving fractions as numbers, as well as those involving squares, should be reviewed, as the students did not perform well. In this way, the students' Instrumental Genesis proved to be gradual, especially with regard to squares, requiring a medium to long term period for the development of complex skills.