Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFMT |
Texto Completo: | http://ri.ufmt.br/handle/1/877 |
Resumo: | This research aims to investigate how textbooks propose the study of arithmetic and geometric progressions in the first year of High School. The textbooks that aggregate to this research belong to the first year of High School, which have been selected because they are part of the catalogue of the Textbook Nacional Program for High School, and also because they are used in State schools of Cuiabá. A qualitative research has been used as the methodology of choice, with emphasis on document analysis. The studies of documents of textbooks are based primarily on the Anthropological Theory of Didactics (TAD), more specifically on the praxeologies, proposed by Chevallard (1999) and on the Square Games Theory of Douady (1992). In order to conduct the studies, praxeologies found in textbooks were identified, as well as the tasks, techniques, theoretical-technological discussions and numerical tables, both geometric and algebraic, with attention to the historical aspects concerning progressions, the conceptual part, the tasks addressed by the authors, and the ones proposed to the students. From this, such praxeologies were verified to see if they match the Official Documents proposals and the intentions of authors shown in the manuals. Among the recommendations of the Official Documents, the study highlights the articulation of arithmetic and geometric progressions with the content functions, as well as tasks proposals that prompt the general standards for the development of algebraic thinking. The results of this investigation, associated with the relevant theory, made the diagnosis of textbooks possible, pointing that praxeological organizations of two of the books analyzed did not explain the close relationship between progressions and functions. This articulation is contemplated in both of the books investigated in the conceptual part, although such relationship has not been mentioned in the intentions shown in the manuals. It has also been noticed of the books selected for this study do not frequently propose tasks to stimulate the generalization of patterns, even if this intention is explicit by the authors of four books selected for the study. There is still the predominance of tasks of the type calculate, determine, constituting imitation tasks, which can lead to routinization of the technique. Among other aspects, a limited number of tasks has been identified, which can facilitate the articulation of different frames (numerical, algebraic and geometric) as proposed by Douady (1992). In most cases priority to the algebraic framework. Amongst the books selected for the studies, it has been noticed that none of them is “complete”, with authors that propose a study that contributes effectively to the development of algebraic thinking in the study of progressions. They do not contemplate the recommendations of the Official Documents, and even if they did, it would not be complete. Thus, it is for the teachers to select the book that they consider most appropriate, according to their opinion and according to the reality of their students. |
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Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemáticaLivro didáticoProgressões aritméticas e geométricasOrganização praxeológicaJogos de quadrosCNPQ::CIENCIAS HUMANAS::EDUCACAOTextbooksArithmetic and geometric progressionsPraxeological organizationSquare gameThis research aims to investigate how textbooks propose the study of arithmetic and geometric progressions in the first year of High School. The textbooks that aggregate to this research belong to the first year of High School, which have been selected because they are part of the catalogue of the Textbook Nacional Program for High School, and also because they are used in State schools of Cuiabá. A qualitative research has been used as the methodology of choice, with emphasis on document analysis. The studies of documents of textbooks are based primarily on the Anthropological Theory of Didactics (TAD), more specifically on the praxeologies, proposed by Chevallard (1999) and on the Square Games Theory of Douady (1992). In order to conduct the studies, praxeologies found in textbooks were identified, as well as the tasks, techniques, theoretical-technological discussions and numerical tables, both geometric and algebraic, with attention to the historical aspects concerning progressions, the conceptual part, the tasks addressed by the authors, and the ones proposed to the students. From this, such praxeologies were verified to see if they match the Official Documents proposals and the intentions of authors shown in the manuals. Among the recommendations of the Official Documents, the study highlights the articulation of arithmetic and geometric progressions with the content functions, as well as tasks proposals that prompt the general standards for the development of algebraic thinking. The results of this investigation, associated with the relevant theory, made the diagnosis of textbooks possible, pointing that praxeological organizations of two of the books analyzed did not explain the close relationship between progressions and functions. This articulation is contemplated in both of the books investigated in the conceptual part, although such relationship has not been mentioned in the intentions shown in the manuals. It has also been noticed of the books selected for this study do not frequently propose tasks to stimulate the generalization of patterns, even if this intention is explicit by the authors of four books selected for the study. There is still the predominance of tasks of the type calculate, determine, constituting imitation tasks, which can lead to routinization of the technique. Among other aspects, a limited number of tasks has been identified, which can facilitate the articulation of different frames (numerical, algebraic and geometric) as proposed by Douady (1992). In most cases priority to the algebraic framework. Amongst the books selected for the studies, it has been noticed that none of them is “complete”, with authors that propose a study that contributes effectively to the development of algebraic thinking in the study of progressions. They do not contemplate the recommendations of the Official Documents, and even if they did, it would not be complete. Thus, it is for the teachers to select the book that they consider most appropriate, according to their opinion and according to the reality of their students.Esta pesquisa tem como objetivo geral investigar como os livros didáticos propõem o estudo das progressões aritméticas e geométricas no primeiro ano do Ensino Médio. Os livros que agregam a esta pesquisa pertencem ao primeiro ano do Ensino Médio, os quais foram selecionados por comporem o catálogo do Programa Nacional do Livro Didático para o Ensino Médio e, além disso, por serem utilizados pelas escolas estaduais do município de Cuiabá. Como opção metodológica, adotou-se uma pesquisa qualitativa, com ênfase em análise documental. Os estudos dos documentos livros didáticos se fundamentam essencialmente na Teoria Antropológica do Didático (TAD), mais especificamente nas praxeologias, propostas por Chevallard (1999) e na Teoria dos Jogos de Quadros de Douady (1992). Para realizar os estudos identificou-se nas praxeologias expostas nos livros didáticos, as tarefas, as técnicas, o discurso tecnológico-teórico e os quadros numérico, geométrico e algébrico, cujos olhares se ativeram quanto aos aspectos históricos referentes às progressões, à parte conceitual, as tarefas resolvidas pelos autores e as propostas aos alunos. A partir disso, verificou-se se tais praxeologias condizem com as propostas dos documentos oficiais e com as intencionalidades dos autores expostas nos manuais. Dentre as recomendações dos documentos oficiais, destacam-se a articulação das progressões aritméticas e geométricas com o conteúdo funções, e a proposição de tarefas que instigam a generalização de padrões para o desenvolvimento do pensamento algébrico. Os resultados dessa investigação, associados à teoria pertinente, possibilitou o diagnóstico de livros didáticos, os quais evidenciaram que as organizações praxeológicas de dois dos livros analisados não explicitam a estreita relação entre progressões e funções. Essa articulação é contemplada em dois dos livros investigados na parte conceitual, embora tal relação não seja mencionada nas intencionalidades expostas nos manuais. Percebeu-se também que os livros selecionados para esta investigação não propõem com frequência tarefas que estimulam a generalização de padrões, ainda que esteja explícita como intencionalidade dos autores dos quatro livros selecionados para a investigação. Ainda há o predomínio de tarefas dos gêneros calcular, determinar, que se constituem em tarefas de imitação, podendo conduzir à rotinização da técnica. Entre outros aspectos, identificou-se um número reduzido de tarefas que possibilitem a articulação dos diferentes quadros (numérico, algébrico e geométrico) propostos por Douady (1992). Na maioria das vezes priorizam o quadro algébrico. Entre os livros selecionados para os estudos, constatou-se que nenhum deles é “completo”, de forma a contribuir efetivamente para o desenvolvimento do pensamento algébrico nos estudos das progressões. Mesmo se contemplasse todas as recomendações dos documentos oficiais, não seria completo, então, cabe ao professor selecionar o livro que considerar mais adequado, segundo a sua opinião e de acordo com a realidade de seus estudantes.Universidade Federal de Mato GrossoBrasilInstituto de Educação (IE)UFMT CUC - CuiabáPrograma de Pós-Graduação em EducaçãoWielewski, Gladys Denisehttp://lattes.cnpq.br/4154014326253864Wielewski, Gladys Denise502.478.161-91http://lattes.cnpq.br/4154014326253864Palaro, Luzia Aparecida425.029.429-34http://lattes.cnpq.br/8628905889561788502.478.161-91Silva, Aparecida Augusta da572.295.111-00http://lattes.cnpq.br/6315522947587402Almeida, Eliane Aparecida Martins de2019-02-27T16:01:58Z2012-05-232019-02-27T16:01:58Z2012-03-23info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisALMEIDA, Eliane Aparecida Martins de. Progressões aritméticas e geométricas: praxeologias em livros didáticos de matemática. 2012. 129 f. Dissertação (Mestrado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2012.http://ri.ufmt.br/handle/1/877porinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMTinstname:Universidade Federal de Mato Grosso (UFMT)instacron:UFMT2019-02-28T07:08:50Zoai:localhost:1/877Repositório InstitucionalPUBhttp://ri.ufmt.br/oai/requestjordanbiblio@gmail.comopendoar:2019-02-28T07:08:50Repositório Institucional da UFMT - Universidade Federal de Mato Grosso (UFMT)false |
dc.title.none.fl_str_mv |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
title |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
spellingShingle |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática Almeida, Eliane Aparecida Martins de Livro didático Progressões aritméticas e geométricas Organização praxeológica Jogos de quadros CNPQ::CIENCIAS HUMANAS::EDUCACAO Textbooks Arithmetic and geometric progressions Praxeological organization Square game |
title_short |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
title_full |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
title_fullStr |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
title_full_unstemmed |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
title_sort |
Progressões aritméticas e geométricas : praxeologias em livros didáticos de matemática |
author |
Almeida, Eliane Aparecida Martins de |
author_facet |
Almeida, Eliane Aparecida Martins de |
author_role |
author |
dc.contributor.none.fl_str_mv |
Wielewski, Gladys Denise http://lattes.cnpq.br/4154014326253864 Wielewski, Gladys Denise 502.478.161-91 http://lattes.cnpq.br/4154014326253864 Palaro, Luzia Aparecida 425.029.429-34 http://lattes.cnpq.br/8628905889561788 502.478.161-91 Silva, Aparecida Augusta da 572.295.111-00 http://lattes.cnpq.br/6315522947587402 |
dc.contributor.author.fl_str_mv |
Almeida, Eliane Aparecida Martins de |
dc.subject.por.fl_str_mv |
Livro didático Progressões aritméticas e geométricas Organização praxeológica Jogos de quadros CNPQ::CIENCIAS HUMANAS::EDUCACAO Textbooks Arithmetic and geometric progressions Praxeological organization Square game |
topic |
Livro didático Progressões aritméticas e geométricas Organização praxeológica Jogos de quadros CNPQ::CIENCIAS HUMANAS::EDUCACAO Textbooks Arithmetic and geometric progressions Praxeological organization Square game |
description |
This research aims to investigate how textbooks propose the study of arithmetic and geometric progressions in the first year of High School. The textbooks that aggregate to this research belong to the first year of High School, which have been selected because they are part of the catalogue of the Textbook Nacional Program for High School, and also because they are used in State schools of Cuiabá. A qualitative research has been used as the methodology of choice, with emphasis on document analysis. The studies of documents of textbooks are based primarily on the Anthropological Theory of Didactics (TAD), more specifically on the praxeologies, proposed by Chevallard (1999) and on the Square Games Theory of Douady (1992). In order to conduct the studies, praxeologies found in textbooks were identified, as well as the tasks, techniques, theoretical-technological discussions and numerical tables, both geometric and algebraic, with attention to the historical aspects concerning progressions, the conceptual part, the tasks addressed by the authors, and the ones proposed to the students. From this, such praxeologies were verified to see if they match the Official Documents proposals and the intentions of authors shown in the manuals. Among the recommendations of the Official Documents, the study highlights the articulation of arithmetic and geometric progressions with the content functions, as well as tasks proposals that prompt the general standards for the development of algebraic thinking. The results of this investigation, associated with the relevant theory, made the diagnosis of textbooks possible, pointing that praxeological organizations of two of the books analyzed did not explain the close relationship between progressions and functions. This articulation is contemplated in both of the books investigated in the conceptual part, although such relationship has not been mentioned in the intentions shown in the manuals. It has also been noticed of the books selected for this study do not frequently propose tasks to stimulate the generalization of patterns, even if this intention is explicit by the authors of four books selected for the study. There is still the predominance of tasks of the type calculate, determine, constituting imitation tasks, which can lead to routinization of the technique. Among other aspects, a limited number of tasks has been identified, which can facilitate the articulation of different frames (numerical, algebraic and geometric) as proposed by Douady (1992). In most cases priority to the algebraic framework. Amongst the books selected for the studies, it has been noticed that none of them is “complete”, with authors that propose a study that contributes effectively to the development of algebraic thinking in the study of progressions. They do not contemplate the recommendations of the Official Documents, and even if they did, it would not be complete. Thus, it is for the teachers to select the book that they consider most appropriate, according to their opinion and according to the reality of their students. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-05-23 2012-03-23 2019-02-27T16:01:58Z 2019-02-27T16:01:58Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
ALMEIDA, Eliane Aparecida Martins de. Progressões aritméticas e geométricas: praxeologias em livros didáticos de matemática. 2012. 129 f. Dissertação (Mestrado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2012. http://ri.ufmt.br/handle/1/877 |
identifier_str_mv |
ALMEIDA, Eliane Aparecida Martins de. Progressões aritméticas e geométricas: praxeologias em livros didáticos de matemática. 2012. 129 f. Dissertação (Mestrado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2012. |
url |
http://ri.ufmt.br/handle/1/877 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Mato Grosso Brasil Instituto de Educação (IE) UFMT CUC - Cuiabá Programa de Pós-Graduação em Educação |
publisher.none.fl_str_mv |
Universidade Federal de Mato Grosso Brasil Instituto de Educação (IE) UFMT CUC - Cuiabá Programa de Pós-Graduação em Educação |
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reponame:Repositório Institucional da UFMT instname:Universidade Federal de Mato Grosso (UFMT) instacron:UFMT |
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Universidade Federal de Mato Grosso (UFMT) |
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UFMT |
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UFMT |
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Repositório Institucional da UFMT |
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Repositório Institucional da UFMT |
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Repositório Institucional da UFMT - Universidade Federal de Mato Grosso (UFMT) |
repository.mail.fl_str_mv |
jordanbiblio@gmail.com |
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