Sequências numéricas como desencadeadoras do conceito de convergência: episódios de resolução de tarefas

Abstract

The present dissertation results from the process of elaborating a proposal of a set of tasks for the initial study of numerical sequences and convergence criteria in episodes of task resolution, as triggers of limit teaching in the context of Differential and Integral Calculus (CDI) 1. The general objective of the research was to propose tasks that would allow students to explore ideas necessary to understand the concept of limit, especially tasks that allow the intuitive exploration of elements necessary to formulate the concept of convergence of a sequence numerical value. It adopts assumptions of the methodology known as Design Research and RME Realistic Mathematics Education. In the analysis of the process, Guided Reinvention as the guiding principle of the work from the application of this proposal in regular classes of an Engineering course of the Federal Technological University of Paraná (UTFPR) of the Londrina campus and Cornelio Procopio. After the application of the research cycles and retrospective analysis, three tasks were included to compose the final product. Because it is a master's degree in the professional field, the intention was to prepare a workbook (educational product) that after its redesign and application; we made available a result of our research proposition.