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Previous issue date: 2009-02-19 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This work aims to analyze the historical and epistemological development of the Group concept related to the theory on advanced mathematical thinking proposed by Dreyfus (1991). Thus it presents pedagogical resources that enable learning and teaching of algebraic structures as well as propose greater meaning of this concept in mathematical graduation programs. This study also proposes an answer to the following question: in what way a teaching approach that is centered in the Theory of Numbers and Theory of Equations is a model for the teaching of the concept of Group? To answer this question a historical reconstruction of the development of this concept is done on relating Lagrange to Cayley. This is done considering Foucault s (2007) knowledge archeology proposal
theoretically reinforced by Dreyfus (1991). An exploratory research was performed in Mathematic graduation courses in Universidade Federal do Par? (UFPA) and Universidade
Federal do Rio Grande do Norte (UFRN). The research aimed to evaluate the formation of concept images of the students in two algebra courses based on a traditional teaching
model. Another experience was realized in algebra at UFPA and it involved historical components (MENDES, 2001a; 2001b; 2006b), the development of multiple representations (DREYFUS, 1991) as well as the formation of concept images (VINNER, 1991). The efficiency of this approach related to the extent of learning was evaluated, aiming to acknowledge the conceptual image established in student s minds. At the end, a classification based on Dreyfus (1991) was done relating the historical periods of the historical and epistemological development of group concepts in the process of representation, generalization, synthesis, and abstraction, proposed here for the teaching of algebra in Mathematics graduation course / O presente estudo analisa o desenvolvimento hist?rico-epistemol?gico do conceito de Grupo a luz da teoria do pensamento matem?tico avan?ado, proposto por Dreyfus (1991) e apresenta subs?dios did?ticos que contribuam para o ensino-aprendizagem das estruturas alg?bricas, visando dar maior significado ao referido conceito abordado na gradua??o em Matem?tica. Nesse sentido, o estudo responde a seguinte pergunta: de que maneira uma abordagem de ensino, inicialmente, centrada na Teoria dos N?meros e na Teoria das
Equa??es se constituiria em um modelo de efetiva??o do ensino do conceito de Grupo? Para responder a quest?o fizemos uma reconstru??o hist?rica do desenvolvimento desse
conceito, de Lagrange a Cayley, em uma reescrita orientada na arqueologia do saber proposta e discutida por Foucault (2007) e com o apoio te?rico em Dreyfus (1991) analisamos o material hist?rico elaborado. Em seguida, fizemos uma pesquisa explorat?ria com turmas da gradua??o em Matem?tica da Universidade Federal do Par? (UFPA) e da
Universidade Federal do Rio Grande do Norte (UFRN), para avaliar a forma??o de imagens conceituais nos alunos participantes de dois cursos de ?lgebra baseado em um
modelo tradicional de ensino. Al?m disso, realizamos outra experi?ncia, na UFPA, com o ensino de ?lgebra envolvendo, conjuntamente, a inclus?o da componente hist?rica (MENDES, 2001a; 2001b; 2006b), o desenvolvimento de m?ltiplas representa??es (DREYFUS, 1991) e a forma??o das imagens conceituais (VINNER, 1991). Avaliamos a efic?cia da abordagem em termos da profundidade no alcance do aprendizado, ou seja, a imagem conceitual estabelecida na mente dos alunos. Ao final, apresentamos uma classifica??o, baseada em Dreyfus (1991), que relaciona per?odos hist?ricos do desenvolvimento hist?rico-epistemol?gico do conceito de grupo aos processos de representa??o, generaliza??o, s?ntese e abstra??o, e uma proposta para um curso de ?lgebra na gradua??o em Matem?tica
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/14197 |
| Date | 19 February 2009 |
| Creators | Quaresma, Jo?o Cl?udio Brandemberg |
| Contributors | CPF:12432962249, http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4704236U8, Nogueira, Romildo Albuquerque, CPF:03394425491, S?, Pedro Franco de, CPF:14551284220, http://lattes.cnpq.br/4323922632919962, Fossa, John Andrew, CPF:13056476453, http://lattes.cnpq.br/2466525106349625, Morey, Bernadete Barbosa, CPF:59616571834, http://lattes.cnpq.br/7554818862651491, Mendes, Iran Abreu |
| Publisher | Universidade Federal do Rio Grande do Norte, Programa de P?s-Gradua??o em Educa??o, UFRN, BR, Educa??o |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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