Towards a problematized approach to the Fundamental Theorems of Calculus in the initial mathematics teachers’ education

Abstract

This work aims to propose approaches that try to problematize the Fundamental Theorems of Calculus (FTC), in Calculus, in the initial mathematics teachers’ education. Our attempt is made on three fronts: (i) to address the conceptual question about the integral and its relation with the area; (ii) stress the reason why differentiation and integration operations can be considered as inverse of each other; (iii) deal with intuitive ways of approaching FTC prior to formalization. We hope that the discussions made here point to problematized approaches not only for FTC, but also for Calculus and other disciplines with mathematical content, such as Real Analysis, Abstract Algebra, Linear Algebra, among others.