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Uma Visita Ao Universo Matemático De Lewis Carroll E O (Re)Encontro Com a Sua Lógica Do Nonsense

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Uma Visita Ao Universo Matemático De Lewis Carroll E O (Re)Encontro Com a Sua Lógica Do Nonsense UNIVERSIDADE FEDERAL DO RIO GRANDE DO NORTE CENTRO DE CIÊNCIAS SOCIAIS APLICADAS PROGRAMA DE PÓS-GRADUAÇÃO EM EDUCAÇÃO EDUCAÇÃO MATEMÁTICA UMA VISITA AO UNIVERSO MATEMÁTICO DE LEWIS CARROLL E O (RE)ENCONTRO COM A SUA LÓGICA DO NONSENSE Rafael Montoito Teixeira Orientador: Prof. Dr. Iran Abreu Mendes NATAL 2007 Livros Grátis http://www.livrosgratis.com.br Milhares de livros grátis para download. 2 UNIVERSIDADE FEDERAL DO RIO GRANDE DO NORTE CENTRO DE CIÊNCIAS SOCIAIS APLICADAS PROGRAMA DE PÓS-GRADUAÇÃO EM EDUCAÇÃO RAFAEL MONTOITO TEIXEIRA UMA VISITA AO UNIVERSO MATEMÁTICO DE LEWIS CARROLL E O (RE)ENCONTRO COM A SUA LÓGICA DO NONSENSE NATAL 2007 3 RAFAEL MONTOITO TEIXEIRA UMA VISITA AO UNIVERSO MATEMÁTICO DE LEWIS CARROLL E O (RE)ENCONTRO COM A SUA LÓGICA DO NONSENSE Dissertação apresentada à Pós-Graduação em Educação da Universidade Federal do Rio Grande do Norte como requisito parcial para obtenção do grau de Mestre em Educação (Educação Matemática). Orientador: Prof. Dr. Iran Abreu Mendes NATAL 2007 4 RAFAEL MONTOITO TEIXEIRA UMA VISITA AO UNIVERSO MATEMÁTICO DE LEWIS CARROLL E UM (RE)ENCONTRO COM A SUA LÓGICA DO NONSENSE Dissertação apresentada à Pós-Graduação em Educação da Universidade Federal do Rio Grande do Norte como requisito parcial para obtenção do grau de Mestre em Educação (Educação Matemática). Aprovado em BANCA EXAMINADORA Iran Abreu Mendes Universidade Federal do Rio Grande do Norte – UFRN John Andrew Fossa Universidade Federal do Rio Grande do Norte – UFRN Lígia Arantes Sad Universidade Federal do Espírito Santo – UFES _________________________________________________________________________ Maria da Conceição Xavier de Almeida Universidade Federal do Rio Grande do Norte – UFRN 5 Dedicatória Desde que decidi trocar o Rio Grande do Sul pelo Rio Grande do Norte, a fim de investir nesta nova etapa do meu conhecimento, muitas foram as pessoas que lá, aqui ou em outros lugares, me apoiaram e se mantiveram do meu lado. Relembrando-as agora com carinho, dedico este estudo para: ─ meus pais, Sérgio Luís Nunes Teixeira e Maria da Graça Montoito Teixeira , os quais, além de terem me dado, ao longo da minha vida, tudo que um filho precisa, são sempre os primeiros a me apoiar e a acreditar em mim; ─ minha irmã, Danielle Montoito Teixeira , que me equilibra em vários aspectos, com uma personalidade um pouco diferente da minha, e que também está sempre do meu lado; ─ minha numerosa família, a qual sempre se reunia para me receber, quando eu voltava para a cidade, ou para se despedir, quando eu estava partindo. O carinho que sempre me deram foi alimento para os dias que passei longe; ─ meu querido amigo Leandro Zanetti , que nunca permitiu que eu me sentisse sozinho, e em cujas orações eu sei que me faço presente; ─ minhas amigas, Ana Paula Costa Barcelos , Jafé Eliasibe Vieira Löper e Patrícia Parente , colegas de graduação e pessoas incríveis que sempre torcem por mim (e eu por elas) ─ meu orientador, professor Iran Abreu Mendes , que esteve do meu lado desde o primeiro momento em que pus os pés em Natal, desempenhando um papel misto de orientador, amigo e conselheiro. Por fim, dedico estas páginas aos meus amigos que, assim como Alice serviu de inspiração a Carroll para sua história, inspiraram-me para a construção dos meus personagens: Andréa Batalha , Adilson de Freitas Jr. (conhecido entre seus amigos pelo apelido de Stuart ) e Newton, cuja timidez me impede de referir seu sobrenome. Os três são amigos que conheci primeiro virtual, depois pessoalmente, e que se fizeram muito presentes conversando comigo pelo computador, nas madrugadas em que eu pesquisava. E claro, não posso deixar de dedicar e agradecer a Lewis Carroll , brilhante matemático, que deixou uma vasta obra que foi por mim analisada com muito prazer. 6 Agradecimentos Na certeza de que nenhuma conquista é possível sem a ajuda de outras pessoas, gostaria de agradecer àqueles que, seja de maneira grande ou pequena, contribuíram para que este estudo tivesse a forma e o conteúdo com os quais se apresenta. Digo ‘muito obrigado’, com carinho e respeito, para: ─ Deus , de onde seguramente proveio minha inspiração para o tema e minha determinação para estudá-lo; ─ Prof. Iran Abreu Mendes , cujas orientações, conselhos, discussões e horas dedicadas ao meu estudo não são passíveis de ser medidas e quantificadas. Nenhuma palavra pode expressar o quanto sou grato por ter tido oportunidade de ser seu aluno; ─ Carlos Aldemir Farias e Maria da Conceição Xavier de Almeida , amigos, leitores vorazes e pesquisadores da área da educação, que através de várias conversas contribuíram com idéias, críticas e muitos incentivos; ─ Jaques Silveira Lopes , Gabriela Lucheze de Oliveira Lopes, Odenise Bezerra e Maroní Lopes , meus colegas de trabalho e amigos pessoais, que me acolheram na cidade, tomaram conta de mim várias vezes, resolveram meus pequenos e grandes problemas e escutaram minhas reclamações, sempre me incentivando a seguir em frente; ─ Talis Lincoln e Demétrios Coutinho , ex-alunos, agora amigos, que foram os primeiros a ser ‘presenteados’ com um livro de Alice, a fim de que eu tivesse com quem discutir algumas das minhas idéias e análises apresentadas na última parte; ─ alguns amigos que, nos últimos dois anos, escutaram meus ‘devaneios’ sobre matemática e as obras literárias de Lewis Carroll, algumas vezes sem entender muita coisa do que eu estava falando, mas demonstrando interesse no assunto. Por fim, ainda que eu tenha conseguido traduzir sozinho a maior parte dos textos e livros que foram analisados, de vez em quando encontrava algumas palavras e expressões que eu desconhecia. Para o francês, agradeço a contribuição da querida amiga Cecille Accioly e, para o italiano, do meu querido amigo Marco Tomei , o qual, muito cortês e paciencioso, garimpou todas as livrarias da sua pequena Lucca para encontrar edições em italiano de algumas obras de Carroll que eu precisava ler. 7 Qualquer um que tenha intenção de educar jovens (refiro-me aos que estão entre 12 e 20 anos) precisa dar-se conta da importância de fornecer-lhes recreações mentais saudáveis (Lewis Carroll) 8 Resumo Exímio professor de matemática, Lewis Carroll, pseudônimo de Charles Lutwidge Dodgson (1832–1898), fez da mistura da matemática com a literatura um ambiente lúdico para a aprendizagem dessa disciplina. Autor dos conhecidos Alice no país das Maravilhas e Alice através do espelho, acabou criando um universo real e complexo no qual se utiliza do que chamamos lógica do nonsense como elemento para motivar o desenvolvimento do pensamento matemática do leitor, levando-o, assim, a aprender, estabelecendo uma ligação entre o concreto (matemática) e o imaginário (seu universo). Com o objetivo de investigar e discutir as potencialidades didáticas de suas obras e de elencar alguns elementos que possam contribuir para uma educação matemática descentralizada da tradicional metodologia de seguir os modelos e decorar fórmulas, visitamos suas obras tendo por base os estudos sobre arqueologia do saber (FOUCAULT, 2007), o pensamento racional e o pensamento simbólico (VERGANI, 2003) e sobre a importância das histórias e narrativas para o desenvolvimento da cognição humana (FARIAS, 2006). Por meio de um estudo descritivo-analítico, utilizamos a construção literária, apresentamos parte de nosso estudo na forma de um romance matemático, visando conferir à matemática escolar um encanto particular, sem privar-lhe de suas propriedades básicas enquanto disciplina e conteúdo. Nosso estudo mostrou o quanto as obras de Carroll possuem uma forte vertente didática que pode se desdobrar nas mais variadas atividades de estudo e ensino para as aulas de matemática. Palavras-chave: Lewis Carroll. Lógica do nonsense. Romances matemáticos. Educação. Educação Matemática. Raciocínio lógico-matemático. 9 Abstract Notable mathematics’ teacher, Lewis Carroll, pseudonym of Charles Lutwidge Dodgson (1832-1898), made the mixture of mathematics with literature a ludic environment for learning that discipline. Author of Alice’s Adventures In Wonderland and its sequel Alice Through The Looking Glass, he eventually created a real and complex universe which uses what we call the logic of the nonsense as an element to motivate the development of mathematical thinking of the reader, taking it as well, learn by establishing a link between the concrete (mathematics) and the imaginary (their universe). In order to investigate and discuss the educational potential of their works and state some elements that can contribute to a decentralized math education from the traditional method of following the models and decorate formulas, we visited his works based on the studies of archeology of knowledge (FOUCAULT, 2007), the rational thought and symbolic thinking (VERGANI, 2003) and about the importance of stories and narratives to the development of human cognition (FARIAS, 2006). Through a descriptive, analytical study, we used the literary construction and presented part of our study in form of a mathematical novel, to give the mathematical school a particular charm, without depriving it of its basics properties as discipline and content. Our study showed how the works of Carroll have a strong didactic element that can deploy in various activities of study and teaching for mathematics classes. Keywords: Lewis Carroll. Logic of nonsense. Mathematics Romances. Education. Mathematics Education. Reasoning logical-mathematical. 10 Sumário Conversando sobre a motivação em aprender 09 Um diálogo sobre como despertar a motivação através do uso de romances matemáticos,
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