Um olhar para a abordagem do conteúdo de divisão de números naturais em livros didáticos de matemática dos anos iniciais do ensino fundamental

Abstract

The aim of this research was to investigate how the most popular mathematics textbooks chosen by public schools in Cuiabá-MT, discuss the contents of the division of natural numbers in the early years of Elementary School. To achieve that, we analyzed two collections from the 1st to 5th years of Elementary School, in view of the introduction of the contents of division, and the different examples presented on each volume of the collections. Our research has a qualitative approach to interpretative analysis, as we thought it to be the most coherent option for our theme. Such choice is based in the fact that not only the product is appreciated, but also the process. As theoretical and methodological reference, we use Anthropological Theory of Didactics (TAD). By the means of the study of Didactic Organizations we focus on the analysis on the types of tasks, techniques and ostensible objects (problem solving, game, calculator and image), which contemplate the division content. Based on the analysis, we found that only the meanings of the division of equal parts and measures (how many fit) are discussed in the examples of the authors in both collections. A striking feature of both collections is the introduction of the division content from the ostensible problem solving, which is usually followed by ostensible image. Among the findings we highlight that the types of tasks correspond to the division into equal parts and measuring. All of the twelve techniques listed are applied to the collection A and two techniques are absent in the collection B. We consider that the division content is discussed with a certain overstatement in collection A, as far as the systematization of the content in the books of the 2nd and 3rd year is concerned. In the collection B, the division content is gradually discussed, and in the books of the 4th and 5th years the division content is effectively systematized. In both collections the 4th volume is the one that most emphasize the natural numbers division content, both in the applications of the different techniques and in the utilization of ostensible problem solving and image.