Um Estudo do Campo Aditivo em Uma Coleção de Livros Didáticos do 4° e 5° anos com Base em Vergnaud

Abstract

This Final Course Project aims to analyze how the additive field, referring to addition and subtraction operations, is presented in a collection of textbooks for the 4th and 5th grades of Elementary School, using Gérard Vergnaud's Theory of Conceptual Fields as a framework. The choice of the topic arose from observing an error made by a student during a classroom activity, which motivated the investigation into how textbooks structure additive situations and contribute to the construction of mathematical knowledge. To carry out this qualitative and documentary research, we analyzed two volumes of the collection "A Conquista da Matemática" (The Conquest of Mathematics), approved by the PNLD 2023-2026, seeking to identify and categorize the proposed situations according to those defined by Vergnaud. Furthermore, the study engages with official documents, such as the National Common Curricular Base (BNCC), and with previous research dealing with the teaching of additive operations. The results show significant differences between the two grades analyzed. In the 4th grade, situations related to categories I (composition) and II (transformation) predominate, with the use of concrete materials, number decomposition, and activities focused on the algorithm. In the 5th grade, there is an advance towards more complex situations, with a greater presence of categories II and III (comparison), as well as problems that require graph interpretation, estimation, and strategy planning. It was also found that not all of Vergnaud's categories appear with the same intensity in the two volumes. It is concluded that the analysis by Vergnaud allows for a deeper look at the role of textbooks in the mathematical education of students, highlighting advances, gaps, and possibilities for improvement in working with the additive field in the early years.