O ensino da função afim a partir dos registros de representação semiótica
Ano de defesa: | 2010 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | , , , , |
Tipo de documento: | Dissertação |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade do Grande Rio
|
Programa de Pós-Graduação: |
Programa de Pós-Graduação em Ensino das Ciências
|
Departamento: |
Unigranrio::Ensino das Ciências
|
País: |
Brasil
|
Palavras-chave em Português: | |
Área do conhecimento CNPq: | |
Link de acesso: | http://localhost:8080/tede/handle/tede/15 |
Resumo: | This case study aims to evaluate the difficulties in teaching and learning of the affine function for students of the 1st year of state high schools in Rio de Janeiro – RJ. The work was developed through activities prepared by the teacher and applied to three classes, being effective participants a total of one hundred and thirteen students. Ten activities were done but some of them were split, which resulted in a total of twenty-five items. The main objective was to verify from which changes on conversion among different registers of representation of the affine function (natural language, algebraic expressions, tables, and graphical form) students have more difficulties and facilities. To do so, the teacher included at least two different forms of representation in the activities, following the guidelines of the National Curriculum Parameters (NCP's) to High School. The theoretical framework was based on the "study of registers of semiotic representation for learning math," developed by Raymond Duval, and they were also a basis for the proposal to diversify the methodological procedures used in teaching linear functions. We tried to answer the following question: Has the use of registers of semiotic representations helped the teaching and understanding of their various representations? The theme affine function was chosen rather than the other types of mathematical function studied in the 1st year of high school because this is the first function taught to students, which allows us to observe more clearly the difficulties in teaching and learning this subject. In conducting this study we explored the variety of representations of the affine function, so that students could perform tasks that required conversion between registers with changes from: a) natural language to algebraic, tabular, graphic forms, b) algebraic form to the tabular form and vice versa; c) algebraic form to the graphical form and vice versa, and d) tabular form to the graphic form and vice versa. |
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Friedmann, Clícia Valladares PeixotoLima, Jacqueline de Cassia PinheiroFriedmann, Clícia Valladares PeixotoLima, Jacqueline de Cassia Pinheiro LimaVianna, Claudia Coelho de SegadasSilva Filho, Hamilton Simões daLozano, Rodolfo GarciaDelgado, Carlos José Borges2016-05-31T21:28:18Z2010-09-13Delgado, Carlos José Borges. O ensino da função afim a partir dos registros de representação semiótica. 2010. 152 f. Dissertação( Programa de Pós-Graduação em Ensino das Ciências) - Universidade do Grande Rio, Duque de Caxias .http://localhost:8080/tede/handle/tede/15This case study aims to evaluate the difficulties in teaching and learning of the affine function for students of the 1st year of state high schools in Rio de Janeiro – RJ. The work was developed through activities prepared by the teacher and applied to three classes, being effective participants a total of one hundred and thirteen students. Ten activities were done but some of them were split, which resulted in a total of twenty-five items. The main objective was to verify from which changes on conversion among different registers of representation of the affine function (natural language, algebraic expressions, tables, and graphical form) students have more difficulties and facilities. To do so, the teacher included at least two different forms of representation in the activities, following the guidelines of the National Curriculum Parameters (NCP's) to High School. The theoretical framework was based on the "study of registers of semiotic representation for learning math," developed by Raymond Duval, and they were also a basis for the proposal to diversify the methodological procedures used in teaching linear functions. We tried to answer the following question: Has the use of registers of semiotic representations helped the teaching and understanding of their various representations? The theme affine function was chosen rather than the other types of mathematical function studied in the 1st year of high school because this is the first function taught to students, which allows us to observe more clearly the difficulties in teaching and learning this subject. In conducting this study we explored the variety of representations of the affine function, so that students could perform tasks that required conversion between registers with changes from: a) natural language to algebraic, tabular, graphic forms, b) algebraic form to the tabular form and vice versa; c) algebraic form to the graphical form and vice versa, and d) tabular form to the graphic form and vice versa.Trata-se de um estudo de caso, que tem como objetivo avaliar as dificuldades de ensino e aprendizagem da função afim aos alunos do 1a ano do Ensino Médio da Rede Pública Estadual na cidade do Rio de Janeiro – RJ. O trabalho foi desenvolvido, por meio de atividades, junto a três turmas da qual o autor foi o professor, num total de cento e treze alunos participantes efetivos. Foram realizadas dez atividades, com algumas delas subdivididas, perfazendo um total de vinte e cinco itens. O objetivo principal foi a verificação de quais transformações por conversão entre os diferentes registros de representação da função afim (língua natural, expressões algébricas, tabelas de valores e forma gráfica) os alunos possuem maiores dificuldades e facilidades. Para tanto, tomou-se o cuidado de se colocar nas atividades, pelo menos, duas diferentes formas de representação seguindo as orientações dos Parâmetros Curriculares Nacionais (PCN ́s) do Ensino Médio. O referencial teórico foi pautado no “estudo dos registros de representação semiótica para a aprendizagem matemática”, desenvolvido por Raymond Duval, e serviram também de base na proposta de se diversificar os procedimentos metodológicos utilizados no ensino de função afim. Procurou-se responder ao final a seguinte pergunta: A utilização dos Registros de Representações Semióticas auxiliou no ensino e compreensão de suas várias representações? A escolha do tema “função afim”, em detrimento aos outros tipos de função matemática estudados no 1o ano do Ensino Médio, é por ser esta a primeira trabalhada com os alunos, permitindo-se observar com maior nitidez as dificuldades de ensino e aprendizagem deste assunto. Na execução deste trabalho foi explorada a multiplicidade de representações da função afim, ao se fazer com que os alunos realizassem tarefas que exigissem a conversão entre os registros, com a passagem da: a) língua natural para as formas algébrica, tabular e gráfica; b) forma algébrica para a forma tabular e vice-versa; c) forma algébrica para a forma gráfica e vice-versa e, d) forma tabular para a forma gráfica e vice-versa.Submitted by Patricia Vieira Silva (patricia.silva@unigranrio.com.br) on 2016-05-31T21:28:18Z No. of bitstreams: 1 Carlos José Borges Delgado.pdf: 1874308 bytes, checksum: 52f39570590557efe308652b105a426b (MD5)Made available in DSpace on 2016-05-31T21:28:18Z (GMT). No. of bitstreams: 1 Carlos José Borges Delgado.pdf: 1874308 bytes, checksum: 52f39570590557efe308652b105a426b (MD5) Previous issue date: 2010-09-13application/pdfporUniversidade do Grande RioPrograma de Pós-Graduação em Ensino das CiênciasUNIGRANRIOBrasilUnigranrio::Ensino das CiênciasEducaçãoMatemática – Ensino MédioFunção AfimRepresentação SemióticaConversão MatemáticaEDUCACAO::ENSINO-APRENDIZAGEMO ensino da função afim a partir dos registros de representação semióticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis-6099596823942813475005006002692911169152837214-4452917836576020174info:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UNIGRANRIOinstname:Universidade do Grande Rio (UNIGRANRIO)instacron:UNIGRANRIOLICENSElicense.txtlicense.txttext/plain; charset=utf-81982http://localhost:8080/tede/bitstream/tede/15/1/license.txt4a50535e8405f611398e6e2d408dbd1bMD51ORIGINALCarlos José Borges Delgado.pdfCarlos José Borges Delgado.pdfapplication/pdf1874308http://localhost:8080/tede/bitstream/tede/15/2/Carlos+Jos%C3%A9+Borges+Delgado.pdf52f39570590557efe308652b105a426bMD52tede/152016-05-31 18:28:18.491oai:localhost: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Biblioteca Digital de Teses e Dissertaçõeshttp://tede.unigranrio.edu.br/PUBhttp://tede.unigranrio.edu.br/oai/requestrepositorio@instituicao.br||repositorio@instituicao.bropendoar:2016-05-31T21:28:18Biblioteca Digital de Teses e Dissertações da UNIGRANRIO - Universidade do Grande Rio (UNIGRANRIO)false |
dc.title.por.fl_str_mv |
O ensino da função afim a partir dos registros de representação semiótica |
title |
O ensino da função afim a partir dos registros de representação semiótica |
spellingShingle |
O ensino da função afim a partir dos registros de representação semiótica Delgado, Carlos José Borges Educação Matemática – Ensino Médio Função Afim Representação Semiótica Conversão Matemática EDUCACAO::ENSINO-APRENDIZAGEM |
title_short |
O ensino da função afim a partir dos registros de representação semiótica |
title_full |
O ensino da função afim a partir dos registros de representação semiótica |
title_fullStr |
O ensino da função afim a partir dos registros de representação semiótica |
title_full_unstemmed |
O ensino da função afim a partir dos registros de representação semiótica |
title_sort |
O ensino da função afim a partir dos registros de representação semiótica |
author |
Delgado, Carlos José Borges |
author_facet |
Delgado, Carlos José Borges |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Friedmann, Clícia Valladares Peixoto |
dc.contributor.advisor-co1.fl_str_mv |
Lima, Jacqueline de Cassia Pinheiro |
dc.contributor.referee1.fl_str_mv |
Friedmann, Clícia Valladares Peixoto |
dc.contributor.referee2.fl_str_mv |
Lima, Jacqueline de Cassia Pinheiro Lima |
dc.contributor.referee3.fl_str_mv |
Vianna, Claudia Coelho de Segadas |
dc.contributor.referee4.fl_str_mv |
Silva Filho, Hamilton Simões da |
dc.contributor.referee5.fl_str_mv |
Lozano, Rodolfo Garcia |
dc.contributor.author.fl_str_mv |
Delgado, Carlos José Borges |
contributor_str_mv |
Friedmann, Clícia Valladares Peixoto Lima, Jacqueline de Cassia Pinheiro Friedmann, Clícia Valladares Peixoto Lima, Jacqueline de Cassia Pinheiro Lima Vianna, Claudia Coelho de Segadas Silva Filho, Hamilton Simões da Lozano, Rodolfo Garcia |
dc.subject.por.fl_str_mv |
Educação Matemática – Ensino Médio Função Afim Representação Semiótica Conversão Matemática |
topic |
Educação Matemática – Ensino Médio Função Afim Representação Semiótica Conversão Matemática EDUCACAO::ENSINO-APRENDIZAGEM |
dc.subject.cnpq.fl_str_mv |
EDUCACAO::ENSINO-APRENDIZAGEM |
description |
This case study aims to evaluate the difficulties in teaching and learning of the affine function for students of the 1st year of state high schools in Rio de Janeiro – RJ. The work was developed through activities prepared by the teacher and applied to three classes, being effective participants a total of one hundred and thirteen students. Ten activities were done but some of them were split, which resulted in a total of twenty-five items. The main objective was to verify from which changes on conversion among different registers of representation of the affine function (natural language, algebraic expressions, tables, and graphical form) students have more difficulties and facilities. To do so, the teacher included at least two different forms of representation in the activities, following the guidelines of the National Curriculum Parameters (NCP's) to High School. The theoretical framework was based on the "study of registers of semiotic representation for learning math," developed by Raymond Duval, and they were also a basis for the proposal to diversify the methodological procedures used in teaching linear functions. We tried to answer the following question: Has the use of registers of semiotic representations helped the teaching and understanding of their various representations? The theme affine function was chosen rather than the other types of mathematical function studied in the 1st year of high school because this is the first function taught to students, which allows us to observe more clearly the difficulties in teaching and learning this subject. In conducting this study we explored the variety of representations of the affine function, so that students could perform tasks that required conversion between registers with changes from: a) natural language to algebraic, tabular, graphic forms, b) algebraic form to the tabular form and vice versa; c) algebraic form to the graphical form and vice versa, and d) tabular form to the graphic form and vice versa. |
publishDate |
2010 |
dc.date.issued.fl_str_mv |
2010-09-13 |
dc.date.accessioned.fl_str_mv |
2016-05-31T21:28:18Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
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dc.identifier.citation.fl_str_mv |
Delgado, Carlos José Borges. O ensino da função afim a partir dos registros de representação semiótica. 2010. 152 f. Dissertação( Programa de Pós-Graduação em Ensino das Ciências) - Universidade do Grande Rio, Duque de Caxias . |
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Delgado, Carlos José Borges. O ensino da função afim a partir dos registros de representação semiótica. 2010. 152 f. Dissertação( Programa de Pós-Graduação em Ensino das Ciências) - Universidade do Grande Rio, Duque de Caxias . |
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