Area of flat figures in the mathematics textbook for the 4th year of elementary school

Abstract

This study aims to understand the mathematical and didactic approach in the mathematics textbook of the 5th year of Elementary School in relation to knowing the area of ​​flat figures. The theoretical foundation is supported by the Anthropological Theory of Didactics developed by Chevallard, the type of Didactic Organization proposed by Gascón and the area model as a magnitude proposed by Douady and Perrin-Glorian and Lima and Bellemain. The methodology is qualitative and documentary in nature, which consists of analyzing the mathematical and didactic organization of the collection. The results indicate, among the tasks tracked, the predominance of those belonging to type T2 (Determine area of ​​flat figures) with 19 representative tasks for which the techniques are applied: unit surface counting and multiplication of adjacent sides. The technological-theoretical block that prevailed was the additivity of area and multiplication as a rectangular configuration under the domain of natural numbers. Of the six study moments, five were observed, leaving out the moment of praxeological assessment. The emphasis in the constitution of the theoretical technological environment is on the numerical framework. The institutionalization of knowledge in the area is considered as a measure, which can contribute to the development of gaps in student learning, strengthening the promotion of numerical conception. Due to the emphasis of the didactic organization of the books being on the exploratory moment and on technical work, we characterize the conception of textbook as empiricist, that is, learning occurs through an inductive didactic process.