Formação do campo conceitual do algoritmo da divisão: análise de aprendizagem

Abstract

The motivation for this work arose from the difficulties faced by students in the final years of Elementary School when performing division operations, a constant concern in the pedagogical context. The theoretical framework of this study incorporates relevant works from various authors, selected for their thematic relevance, with the ideas from these studies being grouped and related to the research at hand. The research is grounded in Gérard Vergnaud's Approach and his Theory of Conceptual Fields, which investigates the theme of division and explores the two conceptions proposed by Vergnaud: division by partition and division by quotients. These conceptions are integrated to form a broader understanding and to attribute meaning to the division operation. The central theme focuses on the investigation of the acquisition of concepts and skills during the division learning process, conducted through weekly workshops in two elementary schools, with two groups of four students each. Based on Gérard Vergnaud's Theory of Conceptual Fields, the study seeks to understand the formation of the conceptual field of the division algorithm using concrete and pedagogical materials, observing the interaction between students and reasoning in response to questions, exploring different resolution strategies, and promoting collaboration among peers and teachers. The detailed analysis of the conceptual formation process involves understanding the initial concept of division, practical application in mathematical problems, the construction of division strategies, and the interpretation of results. Finally, the study analyzes the obtained results, aligned with the principles of Bardin's analysis (2002).