Covariational Reasoning in an Approach to the Concept of Definite Integral Using GeoGebra Within an Economic Context

Abstract

Definite integral is usually associated with area problems and it is approached through a process of approximation with Riemann sums; this process can be particularly complex for a considerable number of students enrolled in non-science careers, hence it is important to develop intuitive notions in these students, and one option is to do so through the use of digital technologies. This study aims to analyze the covariational reasoning of university students who go through the stages of partition, product, sum and limit, in an approach to the concept of definite integral through the use of GeoGebra in economic context tasks. The theoretical approach of covariational reasoning and a qualitative methodology were considered. Behaviors associated with mental actions of a covariational reasoning up to the level of coordination of values in the stages of partition and sum, and smooth continuous covariation, associated with the use of the notion of limit at infinity, were identified. The use of digital technologies and the fact that the problem considered an economic context related to spending, raised the interest of the students to learn a new mathematical concept.