Exponential Functions and their Derivatives in the light of Conceptual Image and Conceptual Definition

Abstract

This article is an excerpt from a dissertation carried out with students studying Differential and Integral Calculus in the first term of the Information Systems course at the State University of Montes Claros and is based on the theoretical constructs of symbolic interactionism and advanced mathematical thinking, specifically the conceptual image and the conceptual definition of exponential functions. It aimed to understand how and in what way mathematical definitions are used in discussions held in interactions between students and professors during the students’ presentation of a seminar. From the analysis of the data, it was possible to observe divergences between the images and the conceptual definitions of exponential functions and their derivatives. We concluded that the students had made progress in understanding the formal definitions from the advanced mathematical thinking perspective.