Área de figuras planas: uma análise de produções stricto sensu

Abstract

The main goal of this research is to map and analyze stricto sensu productions in the area of teaching available in the catalogue of thesis and dissertations from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and in the Biblioteca Digital Brasileira de Teses e Dissertações (BDTD) that address the area of plane figures. For that, it considers theorical assumptions of area as a Greatness from Douady e Perrin-Glorain, Bellemain e Lima, Baltar e Ferreira, as much as the registers of semiotic representation with emphasis in the figural apprehension according to Duval. Through the qualitative approach the dissertation is structured as a multipaper, composed by four manuscripts with the respective specific objectives: Analyzing the aspects regarding plane figures area in the elementary school according to the Parâmetros Curriculares Nacionais (PCN) and the Base Nacional Curricular (BNCC), mapping studies subsidized by the theorical-mehodological perspective of meta-analysis in the field of Mathematical education, available at the BDTD, considering institutional, procedural and thematic aspects; mapping and analyzing Brazilian thesis and dissertations, available at the BDTD and in the CAPES catalogue for thesis and dissertations, that have as focus of study the concept of plane figures area, considering institutional and procedural aspects; analyzing stricto sensu Brazilian productions, available at the BDTD and in the CAPES catalogue for thesis and dissertations, regarding of plane figures which have developed didactic sequences with the support of dynamic geometry software in the context of elementary education. To fulfill such goals, each manuscript has singularities, the first is a documental analysis, the second and third are defined as mapping and the fourth is a qualitative meta-analysis. Among the results it is highlighted the importance given by the PCN and BNCC to addressing the concept of area in the primary school. Furthermore, it is noticed that the number of stricto sensu investigations about the area of plane figures has been increasing over last years, considering the period of 1998-2019. The biggest quantity is from institutions belonging to the southwest and northwest regions in Brazil, from academic master degree courses and, followed by professional master degree courses and doctorates. It is noticed that 30 out of 54 studies mapped have developed didactic sequences, yet in the data production, are also identified analysis of: classroom notebooks from students and/or teachers, books and/or teaching materials, micro world, curriculum guidelines, thesis and/or dissertations, teaching orienting activities, interviews, observations and/or class registers and/or recordings and/or photography, formative processes, projects, questionnaires and exams. From the ones that developed didactic sequences, it is observed that 11 investigations used dynamic geometry software in the Elementary education context. In these studies were noticed situations of comparison, measuring, conversion of units and production, being the ones with comparison very expressive. Besides, such situations were the ones that showed more indications of mobilizing the perceptive, discursive and operative apprehensions, as well as the dynamic conversion of description through justifications and/or relations that are observed from the dynamic treatments of reconfiguration (composition, decomposition and deformation).