Engenharia didática como metodologia de pesquisa e ensino com o uso de jogos envolvendo números fracionários

Abstract

This article aims to analyze Didactical Engineering as a research and teaching methodology in the context of Rational Numbers through the development of a playful resource. This study was conducted in four consecutive phases, namely: preliminary analysis, which includes an epistemological study of Rational Numbers in fractional form; conception and a priori analysis of the engineering of the game "Assembling a Work of Art"; experimentation, initially conducted in public schools with 45 students from 2nd to 4th grades and 20 students from 6th and 7th grades of Elementary School in the Federal District; as the fourth phase, a posteriori analysis and evaluation, in which we confronted the collected data with the a priori analyses that were conducted (ARTIGUE, 1995). We found the absence of propositions of situations involving the counting of fractional numbers composing values greater than one whole as an epistemological obstacle in the study of Rational Numbers. Additionally, Didactical Engineering in the context of research showed potential for the development of a cyclical investigation process, allowing for feedback loops to think and rethink the game based on the context of the experimentation being experienced and the analyses being carried out. Regarding the teaching context, this methodology provided the construction of didactic-pedagogical guidelines that can be accessed by teachers who teach Mathematics and that can guide them in their didactic practices using the game "Assembling a Work of Art."