Covariational reasoning of university students in an approach to the concept of definite integral through Riemann sums

Abstract

This study aims to analyze changes in mental actions associated with the covariational reasoning of one pair of students when working on tasks to approach the concept of definite integral through Riemann sums. Mental actions are gathered from student interactions in GeoGebra, from their written reports, and from a semi-structured interview applied to one pair of students from an engineering school in Mexico. Data are analyzed with the theoretical construct of covariational reasoning. The results show an evolution in the way students coordinate simultaneous changes between the variables involved in tasks, from the no coordination level to the chunky continuous covariation level. It is concluded that questions to propose conjectures on the use of rectangles in approximation processes to the area of a region, including their justification, and the process of inferring behaviors from hypothetical situations, reveal behaviors associated with higher levels of covariational reasoning.