Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/9086 |
Resumo: | This research was started because of concerns regarding the teaching and learning of Counting Problems in Elementary School. With the intent of contributing to the construction of basic Combinatorial concepts, we elaborated exploratory-investigative tasks and we tried through these tasks, to analyze the answers that were made by students of an 8th grade of Elementary School, in order to answer the following investigative question: what learning occurs with the mobilization of registers of semiotic representation theory to do counting in a scenario of exploratory- investigative tasks in an 8th grade of Elementary School? The theoretical and methodological reference is constituted by the registers of semiotic representation theory propounded by Duval; by the theory of Mathematical Investigations, Ponte et al. Besides that the research also had the collaboration of Pessoa and Borba. We present a brief historical retrospective on the subject, besides a previous analysis of other works in the area and official documents aimed at teaching and learning of Mathematics subject regarding to contents of Counting Problems in Elementary School. The research was developed with a group of 25 students of the 8th grade Elementary School in a public school in São Paulo state, in the year 2016. The data collection was done through field notes (logbook), and from the records written by the students during the development of the sequence of tasks. Through this investigation, we could verify that the study of Counting Problems through exploratory-investigative tasks allows the articulation of different registers of semiotic representation, leading to a better understanding of this topic. |
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Lara, Wanderson Mendes deNoel Filho, Antoniohttp://lattes.cnpq.br/5234064498436000http://lattes.cnpq.br/6898603390655783ebea112a-df8b-4666-a3f2-c2bf0b3cdd772017-09-20T14:05:26Z2017-09-20T14:05:26Z2017-06-29LARA, Wanderson Mendes de. Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica. 2017. Dissertação (Mestrado em Matemática em Rede Nacional) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9086.https://repositorio.ufscar.br/handle/ufscar/9086This research was started because of concerns regarding the teaching and learning of Counting Problems in Elementary School. With the intent of contributing to the construction of basic Combinatorial concepts, we elaborated exploratory-investigative tasks and we tried through these tasks, to analyze the answers that were made by students of an 8th grade of Elementary School, in order to answer the following investigative question: what learning occurs with the mobilization of registers of semiotic representation theory to do counting in a scenario of exploratory- investigative tasks in an 8th grade of Elementary School? The theoretical and methodological reference is constituted by the registers of semiotic representation theory propounded by Duval; by the theory of Mathematical Investigations, Ponte et al. Besides that the research also had the collaboration of Pessoa and Borba. We present a brief historical retrospective on the subject, besides a previous analysis of other works in the area and official documents aimed at teaching and learning of Mathematics subject regarding to contents of Counting Problems in Elementary School. The research was developed with a group of 25 students of the 8th grade Elementary School in a public school in São Paulo state, in the year 2016. The data collection was done through field notes (logbook), and from the records written by the students during the development of the sequence of tasks. Through this investigation, we could verify that the study of Counting Problems through exploratory-investigative tasks allows the articulation of different registers of semiotic representation, leading to a better understanding of this topic.Esta pesquisa originou-se a partir de inquietações relacionadas ao ensino e aprendizagem de Problemas de Contagem no Ensino Fundamental. Com a intenção de contribuir para a construção de conceitos básicos de Combinatória, elaboramos tarefas de natureza exploratório-investigativas e procuramos por meio destas, analisar as respostas produzidas por estudantes de um 8o ano do Ensino Fundamental, com o intuito de responder a seguinte questão de investigação: que aprendizagem ocorre com a mobilização de registros de representação semiótica para a realização de contagens em um cenário de tarefas exploratório-investigativas num 8o ano do Ensino Fundamental? O referencial teórico e metodológico é constituído pela teoria dos registros de representação semiótica proposta por Duval e pela teoria das Investigações Matemáticas, proposta Ponte et al. Além disso o trabalho também contou com a colaboração de Pessoa e Borba. Realizamos um breve retrospecto histórico sobre o tema, além de uma análise previa de outros trabalhos na área, e documentos oficiais voltados para o ensino e aprendizagem da Matemática no que diz respeito a conteúdos relacionados a Problemas de Contagem no Ensino Fundamental. A pesquisa foi desenvolvida em uma turma de 25 alunos do 8o ano Ensino Fundamental de uma escola da rede pública de ensino do estado de São Paulo, no ano de 2016. A coleta de dados se deu por meio de notas de campo (diário de bordo), e dos registros produzidos pelos estudantes ao logo do desenvolvimento da sequência de tarefas. Através desta investigação, pudemos verificar que o estudo de Problemas de Contagem por meio de tarefas exploratório- investigativas possibilita a articulação entre diferentes registros de representação semiótica, o que leva a um melhor entendimento desse tema.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Mestrado Profissional em Matemática em Rede Nacional - PROFMATUFSCarEnsino fundamentalProblemas de contagemRegistros de representação semióticaTarefas exploratório-investigativasElementary schoolCounting problemsRegisters of semiotic representation theoryExploratory-investigative tasksCIENCIAS EXATAS E DA TERRA::MATEMATICAProblemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semióticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline60052e0c3fa-c6fc-4c5c-8d2a-228042ca2e66info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALDissWML.pdfDissWML.pdfapplication/pdf4207155https://repositorio.ufscar.br/bitstream/ufscar/9086/1/DissWML.pdf5811f047e7b65dbd43f52f60e16255baMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/9086/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTDissWML.pdf.txtDissWML.pdf.txtExtracted texttext/plain179653https://repositorio.ufscar.br/bitstream/ufscar/9086/3/DissWML.pdf.txt5a572677dcb1feb5bd44e2db3fdbd387MD53THUMBNAILDissWML.pdf.jpgDissWML.pdf.jpgIM Thumbnailimage/jpeg6577https://repositorio.ufscar.br/bitstream/ufscar/9086/4/DissWML.pdf.jpg261b4b52fd3753627e8aabfb91a9523bMD54ufscar/90862023-09-18 18:31:43.8oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:43Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
title |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
spellingShingle |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica Lara, Wanderson Mendes de Ensino fundamental Problemas de contagem Registros de representação semiótica Tarefas exploratório-investigativas Elementary school Counting problems Registers of semiotic representation theory Exploratory-investigative tasks CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
title_full |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
title_fullStr |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
title_full_unstemmed |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
title_sort |
Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica |
author |
Lara, Wanderson Mendes de |
author_facet |
Lara, Wanderson Mendes de |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/6898603390655783 |
dc.contributor.author.fl_str_mv |
Lara, Wanderson Mendes de |
dc.contributor.advisor1.fl_str_mv |
Noel Filho, Antonio |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/5234064498436000 |
dc.contributor.authorID.fl_str_mv |
ebea112a-df8b-4666-a3f2-c2bf0b3cdd77 |
contributor_str_mv |
Noel Filho, Antonio |
dc.subject.por.fl_str_mv |
Ensino fundamental Problemas de contagem Registros de representação semiótica Tarefas exploratório-investigativas |
topic |
Ensino fundamental Problemas de contagem Registros de representação semiótica Tarefas exploratório-investigativas Elementary school Counting problems Registers of semiotic representation theory Exploratory-investigative tasks CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Elementary school Counting problems Registers of semiotic representation theory Exploratory-investigative tasks |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This research was started because of concerns regarding the teaching and learning of Counting Problems in Elementary School. With the intent of contributing to the construction of basic Combinatorial concepts, we elaborated exploratory-investigative tasks and we tried through these tasks, to analyze the answers that were made by students of an 8th grade of Elementary School, in order to answer the following investigative question: what learning occurs with the mobilization of registers of semiotic representation theory to do counting in a scenario of exploratory- investigative tasks in an 8th grade of Elementary School? The theoretical and methodological reference is constituted by the registers of semiotic representation theory propounded by Duval; by the theory of Mathematical Investigations, Ponte et al. Besides that the research also had the collaboration of Pessoa and Borba. We present a brief historical retrospective on the subject, besides a previous analysis of other works in the area and official documents aimed at teaching and learning of Mathematics subject regarding to contents of Counting Problems in Elementary School. The research was developed with a group of 25 students of the 8th grade Elementary School in a public school in São Paulo state, in the year 2016. The data collection was done through field notes (logbook), and from the records written by the students during the development of the sequence of tasks. Through this investigation, we could verify that the study of Counting Problems through exploratory-investigative tasks allows the articulation of different registers of semiotic representation, leading to a better understanding of this topic. |
publishDate |
2017 |
dc.date.accessioned.fl_str_mv |
2017-09-20T14:05:26Z |
dc.date.available.fl_str_mv |
2017-09-20T14:05:26Z |
dc.date.issued.fl_str_mv |
2017-06-29 |
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.citation.fl_str_mv |
LARA, Wanderson Mendes de. Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica. 2017. Dissertação (Mestrado em Matemática em Rede Nacional) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9086. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/9086 |
identifier_str_mv |
LARA, Wanderson Mendes de. Problemas de contagem no ensino fundamental : uma experiência com tarefas exploratório-investigativas e registros de representação semiótica. 2017. Dissertação (Mestrado em Matemática em Rede Nacional) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9086. |
url |
https://repositorio.ufscar.br/handle/ufscar/9086 |
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por |
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openAccess |
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Universidade Federal de São Carlos Câmpus São Carlos |
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Programa de Mestrado Profissional em Matemática em Rede Nacional - PROFMAT |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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