Operações fundamentais nos anos iniciais do ensino fundamental: um estudo centrado em atividades exploratório-investigativa

Abstract

This research arises from the importance of understanding fundamental operations by early elementary students to ensure their ability to engage with subsequent content. Its general objective is to understand how teachers' Didactic-Mathematical knowledge is applied, as well as how early elementary students develop their comprehension of fundamental operations through the implementation of a didactic sequence centered on exploratory-investigative tasks. The study was guided by the following question: “How are the teaching and learning processes of fundamental operations developed and constructed by teachers and students in the early elementary years through a didactic sequence based on exploratory-investigative tasks?” This dissertation is organized in a multipaper format, comprising an introduction, three papers, and closing remarks. In Paper No. 1, a bibliographic study mapping and analyzing Brazilian research on the teaching and learning processes of fundamental operations in the early elementary years. Searches were conducted in the Brazilian Library of Theses and Dissertations (BDTD) and the Coordination for the Improvement of Higher Education Personnel's Catalog of Theses and Dissertations (CAPES), identifying five theses and seven dissertations. In Paper No. 2, an analysis of semi-structured interviews conducted with early elementary mathematics teachers (specifically 5th-grade teachers) to identify their Didactic-Mathematical thinking. In Paper No. 3, a analyze the comprehension of mathematical operations through the particular representations that emerge from the resolution and discussions of exploratory-investigative tasks developed by 5th-grade elementary students. In Paper No. 1, the studies reviewed emphasize the importance of teaching practices that support students' comprehension of fundamental operations. In Paper No. 2, the semi-structured interviews reveal that teachers possess basic knowledge for teaching fundamental operations, as per Godino’s Didactic Mathematical Knowledge Theory (2009). However, advanced knowledge was found to be lacking due to insufficient mathematical training. In Paper No. 3, drawing on Duval’s Theory of Semiotic Representation Registers (2003), the proposed didactic sequence highlighted increased class engagement, shifts in students' ideas, and knowledge construction. Through solving fundamental operations using material manipulation and multiple representation registers, students demons