Mathematical Modelling and the Development of Integral Thinking

Abstract

Inspired by a mathematical modelling project and by the theoretical discussions that support the concepts of numerical thinking, geometrical thinking, and algebraic thinking, our objective, in this paper, is to propose and to characterize a first version of a theoretical construct called integral thinking. The modelling project was carried out by 6th grade students, from elementary school, and one of its purposes was to calculate the surface area of the mud that covered a region of the County of Brumadinho, in Minas Gerais, Brazil, after the rupture of an iron ore-tailing dam. It is, therefore, an empirical-theoretical essay, because it is based on a school practice of modelling in mathematics education in dialogue with theoretical references. We mobilized discussions about the teaching of integral, in particular the idea of approximation, and specific concepts from mathematics education in basic education to describe, from the experience in the modelling project, the knowledge involved in the calculation of areas of regions of any format and that can be developed by elementary school students.