Um estudo sobre estrutura algébrica grupo: potencialidades e limitações para generalização e formalização

• Autor(a) principal: Oliveira, Ana Paula Teles de
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/20383
• topic: Álgebra; Estrutura algébrica grupo; Álgebra - Estudo e ensino; Algebraic structure group; Algebra - Study and teaching; Design Experiments; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this research our aim is to investigate and evaluate a collection of data that will help understand the concept of the algebraic group, according to the question: What are the strength and limitations of a group of activities mentioned in examples and counterexamples in the algebraic structure group to generalize and formalize the context referred? It is possible to observe that this concept is organized through the following definitions: axiom and theories both containing examples and counterexamples. Our proposal consists on doing the opposite, meaning through examples and counterexamples it will be possible to study the concept involved. To start the research, we elaborated three activities, reorganized in four subgroups, which were elaborated in numeric and geometric exercises and fundamentals mentioned in Brousseau theories. We implemented the method of Design Experiments which helped us improve the activities, and thus evolve them with five individuals and subdivisions with two teams. This methodology has two perspectives: a prospective – that addresses a study of the activates proposed in the ways that will provide possible answers and further reflections - presenting an analysis of the answers and reflections obtained with the goal of meeting the proposed objective (the concepts of structure in the algebraic group). The people that took part in this research are students enrolled on the post-graduate of Mathematical Education. As a result, we point out as potentiality the movement between the phases of didactic situations in necessary concepts of the group algebraic structure identity element and associative property and also in relation to the worked examples as the reflection, composition of geometric transformations as an operation and when the same is closed in a given set and identity transformation as identity element in the set of geometric transformations. As limitations we observe that the phases of didactic situations did not occur in concepts such as binary and closed operation and the group algebraic structure. The activates done are not self-explanatory and thus needs to be clarified by individuals with the basic idea of element inverse, identity element, commutative and associative properties, composition of functions and symmetries in addition to the algebraic language