A gênese instrumental na interação com a malha quadriculada e o Tangram: uma proposta para o ensino de área e perímetro de figuras planas no campo conceitual das grandezas geométricas

Abstract

This study aims to analyze the process of instrumental genesis of the artifacts grid and Tangram from situations involving the concepts of area and perimeter of flat figures within the conceptual field of geometric quantities. The research has as its theoretical basis the Theory of Conceptual Fields proposed by Vergnaud (1982), which studies conceptualization through task situations linked to the individual's cognitive structure; the instrumental approach proposed by Rabardel (1995), which investigates subjects in activities mediated by instruments; and the Theory of Instrumental Orchestration by Trouche (2005), which provides support for investigations into the interaction between teachers and technology in their teaching practice, with the aim of provoking students' instrumental genesis. This study has a qualitative, exploratory and descriptive approach with an action research design. Data collection took place at the Cacilda Braule Pinto public school, located in the eastern part of the city of Manaus in the state of Amazonas.The research subjects were twenty-three students from the 9th grade of elementary school, with the aim of answering the research question and achieving the proposed objectives. In the light of the analysis, the study revealed some conceptual difficulties faced by the students when solving situations within the conceptual field of geometric quantities and that the inclusion of technologies within the teaching-learning process can promote better levels of learning, provided that they are integrated into the process. The data presented enabled discussions about instrumental orchestration as a theoretical model in the teaching-learning process as a facilitator in the process of instrumental genesis of objects that are presented as artifacts in teaching. In addition, the results obtained provided an articulation between theory and practice in the field of Mathematics Education, in the context of basic education.