Articulación de argumentos del teorema fundamental del cálculo de Newton y de Leibniz para su enseñanza en la formación de ingenieros con el uso de recursos tecnológicos

Abstract

Among the mathematical objects that make up mathematical analysis, the Fundamental Theorem of Calculus (FTC) stands out. However, the teaching and learning process of the FTC has difficulties. For example, some teachers present limitations when teaching it, because they have a low conceptual knowledge, sometimes even procedural, of the definite integral; they do not know how to improve their teaching environments; nor do they know how to create didactical sequences in order to improve the understanding of the theorem; or because they do not consider the complexity of the mathematical objects that compose it. For students the obstacles with the FTC range from having problems understanding previous mathematical notions (continuity, differentiability, ratio of change, etc.) to understanding that∫_a^x▒f(t)dt is a function that depends on x. This doctoral thesis shows that the history of mathematics is still a source of resources, which set with suitable educational software and framed in an appropriate didactical approach, allow the design of tasks for university students.