Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics
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Data de Publicação: | 2020 |
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Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Revista de Educação Matemática (Online) |
Texto Completo: | https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/293 |
Resumo: | The present study aims to investigate the contributions of the Problem Solving, Exploration and Posing to the teaching and learning process of Combinatorics in the initial years of Elementary School, based on studies related to the teaching-learning methodology of Problem Solving and Combinatory Education. It`s a qualitative research, dedicated to describing and analyzing in detail the data collected through observations, field notes, written records made by the students and audio recordings. As subjects of the research, we adopted 16 students from a 5th grade classroom from an Elementary School in the municipal public network of Paraíba State, Brazil. The pedagogical actions carried out in a classroom context were supported by the classroom methodological perspective of Problem Solving, Exploration and Posing defended by Andrade (1998, 2017), as well as in studies that discuss the teaching and learning process of Combinatorics. In the opportunity, the four types of combinatorial problems (combination, arrangement, permutation and Cartesian product) that need to be approached in the initial years of Elementary School, based on combinatorial problems drawn from Pessoa's research (2009) and proposed by the students were worked out. It was concluded that the methodological proposal of the Problem Solving, Exploration and Posing contributes to the promotion of the combinatorial learning of the students, enabling the development of a reflective educational process. It was verified that the problematizations provoked during the Problem Solving, Exploration and Posing process potentiated the work of reflection on the invariants of the combinatorial problems, which favored the development of the combinatorial, generalizing and logical reasoning of the students, besides enabling the researchers to explore different dimensions of the proposed problems. |
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Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatoricsResolución, Exploración y Proposición de Problemas en los primeros años de la educación fundamental: contribuciones a la enseñanza y aprendizaje de la combinaciónResolução, Exploração e Proposição de Problemas nos anos iniciais do ensino fundamental: contribuições para o ensino e aprendizagem da combinatóriaProblem ExplorationCombinatorial AnalysisElementary SchoolExploración de ProblemasAnálisis CombinatoriaEnseñanza PrimariaExploração de ProblemasAnálise CombinatóriaEnsino Fundamental.The present study aims to investigate the contributions of the Problem Solving, Exploration and Posing to the teaching and learning process of Combinatorics in the initial years of Elementary School, based on studies related to the teaching-learning methodology of Problem Solving and Combinatory Education. It`s a qualitative research, dedicated to describing and analyzing in detail the data collected through observations, field notes, written records made by the students and audio recordings. As subjects of the research, we adopted 16 students from a 5th grade classroom from an Elementary School in the municipal public network of Paraíba State, Brazil. The pedagogical actions carried out in a classroom context were supported by the classroom methodological perspective of Problem Solving, Exploration and Posing defended by Andrade (1998, 2017), as well as in studies that discuss the teaching and learning process of Combinatorics. In the opportunity, the four types of combinatorial problems (combination, arrangement, permutation and Cartesian product) that need to be approached in the initial years of Elementary School, based on combinatorial problems drawn from Pessoa's research (2009) and proposed by the students were worked out. It was concluded that the methodological proposal of the Problem Solving, Exploration and Posing contributes to the promotion of the combinatorial learning of the students, enabling the development of a reflective educational process. It was verified that the problematizations provoked during the Problem Solving, Exploration and Posing process potentiated the work of reflection on the invariants of the combinatorial problems, which favored the development of the combinatorial, generalizing and logical reasoning of the students, besides enabling the researchers to explore different dimensions of the proposed problems.El presente estudio tiene como objetivo investigar sobre las contribuciones de la Resolución, Exploración y Proposición de Problemas al proceso de enseñanza aprendizaje de la Combinatoria en los años iniciales de la Enseñanza Primaria, tomando como base estudios relacionados a la metodología de la Resolución, Exploración y Proposición de Problemas y la Educación Combinatoria. Este estudio de la investigación de campo posee carácter cualitativo, en razón de que hubo un empeño en describir y analizar detalladamente los datos colectados por medio de observaciones, notas de campo, registros escritos realizados por los alumnos y grabaciones de audio. Como participantes de este estudio, escogimos 16 alumnos del 5° año de la Enseñanza Primaria de un colegio de la red pública municipal del departamento de Paraíba, Brasil. Las acciones pedagógicas realizadas en el contexto de la clase se apoyaron en la perspectiva metodológica de Resolución, Exploración y Proposición de Problemas defendida por Andrade (1998; 2017), bien como en estudios que discuten el proceso de enseñanza y aprendizaje de la Combinatoria. En dicho momento, se trabajaron los cuatro tipos de problemas combinatorios (combinación, arreglos, permutación y producto cartesiano) que necesitan ser abordados en los años iniciales en la Enseñanza Primaria, a partir de problemas combinatorios retirados de la investigación de Pessoa (2009) y propuesto por los alumnos. Se concluyó que la propuesta metodológica de la Resolución, Exploración y Proposición de Problemas contribuye para promover el aprendizaje combinatorio de los alumnos, posibilitando el desarrollo de un proceso educativo reflexivo. Se constató que las problematizaciones provocadas durante el proceso de Resolución, Exploración y Proposición de Problemas potencializaron el trabajo de reflexión sobre los invariantes de los problemas combinatorios, lo que favoreció el desarrollo del raciocinio combinatorio, generalizado y lógico de los alumnos, además de haber posibilitado a la exploración diferentes dimensiones de los problemas propuestos.O presente estudo tem como objetivo investigar as contribuições da Resolução, Exploração e Proposição de Problemas ao processo de ensino e aprendizagem da Combinatória nos anos iniciais do Ensino Fundamental, tomando como base estudos relacionados à metodologia da Resolução, Exploração e Proposição de Problemas e à Educação Combinatória. O estudo da pesquisa de campo possui cunho qualitativo, em razão de que se empenhou em descrever e analisar detalhadamente os dados coletados por meio de observações, notas de campo, registros escritos feitos pelos alunos e gravações de áudio. Como sujeitos da pesquisa, adotaram-se 16 alunos de uma turma de 5º ano do Ensino Fundamental de uma escola da rede pública municipal do Estado da Paraíba. As ações pedagógicas realizadas em contexto de sala de aula apoiaram-se na perspectiva metodológica da Resolução, Exploração e Proposição de Problemas defendida por Andrade (1998; 2017), bem como em estudos que discutem o processo de ensino e aprendizagem da Combinatória. Na oportunidade, trabalharam-se os quatro tipos de problemas combinatórios (combinação, arranjo, permutação e produto cartesiano) que precisam ser abordados nos anos iniciais do Ensino Fundamental, a partir de problemas combinatórios retirados da pesquisa de Pessoa (2009) e propostos pelos alunos. Conclui-se que a proposta metodológica da Resolução, Exploração e Proposição de Problemas contribui para a promoção da aprendizagem combinatória dos alunos, possibilitando o desenvolvimento de um processo educativo reflexivo. Constatou-se que as problematizações provocadas durante o processo de Resolução, Exploração e Proposição de Problemas potencializaram o trabalho de reflexão sobre os invariantes dos problemas combinatórios, o que favoreceu o desenvolvimento do raciocínio combinatório, generalizante e lógico dos alunos, além de também ter possibilitado a exploração de diferentes dimensões dos problemas propostos.Sociedade Brasileira de Educação Matemática (SBEM)2020-05-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/29310.37001/remat25269062v17id293Revista de Educação Matemática; Vol. 17 (2020): Publicação Contínua; e020030Revista de Educação Matemática; ##issue.vol## 17 (2020): Publicação Contínua; e020030Revista de Educação Matemática; Vol. 17 (2020): Publicação Contínua; e020030Revista de Educação Matemática; v. 17 (2020): Publicação Contínua; e0200302526-9062reponame:Revista de Educação Matemática (Online)instname:Sociedade Brasileira de Educação Matemática (SBEM)instacron:SBEMporhttps://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/293/pdfCopyright (c) 2020 Emily Vasconcelos Santos, Silvanio Andradeinfo:eu-repo/semantics/openAccessSantos, Emily VasconcelosAndrade, Silvanio2021-05-05T18:50:19ZRevistahttps://www.revistasbemsp.com.br/index.php/REMat-SPONG |
dc.title.none.fl_str_mv |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics Resolución, Exploración y Proposición de Problemas en los primeros años de la educación fundamental: contribuciones a la enseñanza y aprendizaje de la combinación Resolução, Exploração e Proposição de Problemas nos anos iniciais do ensino fundamental: contribuições para o ensino e aprendizagem da combinatória |
title |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics |
spellingShingle |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics Santos, Emily Vasconcelos Problem Exploration Combinatorial Analysis Elementary School Exploración de Problemas Análisis Combinatoria Enseñanza Primaria Exploração de Problemas Análise Combinatória Ensino Fundamental. |
title_short |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics |
title_full |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics |
title_fullStr |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics |
title_full_unstemmed |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics |
title_sort |
Problem Solving, Exploration, and Posing in the elementary school: contributions to the teaching and learning of combinatorics |
author |
Santos, Emily Vasconcelos |
author_facet |
Santos, Emily Vasconcelos Andrade, Silvanio |
author_role |
author |
author2 |
Andrade, Silvanio |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Santos, Emily Vasconcelos Andrade, Silvanio |
dc.subject.por.fl_str_mv |
Problem Exploration Combinatorial Analysis Elementary School Exploración de Problemas Análisis Combinatoria Enseñanza Primaria Exploração de Problemas Análise Combinatória Ensino Fundamental. |
topic |
Problem Exploration Combinatorial Analysis Elementary School Exploración de Problemas Análisis Combinatoria Enseñanza Primaria Exploração de Problemas Análise Combinatória Ensino Fundamental. |
description |
The present study aims to investigate the contributions of the Problem Solving, Exploration and Posing to the teaching and learning process of Combinatorics in the initial years of Elementary School, based on studies related to the teaching-learning methodology of Problem Solving and Combinatory Education. It`s a qualitative research, dedicated to describing and analyzing in detail the data collected through observations, field notes, written records made by the students and audio recordings. As subjects of the research, we adopted 16 students from a 5th grade classroom from an Elementary School in the municipal public network of Paraíba State, Brazil. The pedagogical actions carried out in a classroom context were supported by the classroom methodological perspective of Problem Solving, Exploration and Posing defended by Andrade (1998, 2017), as well as in studies that discuss the teaching and learning process of Combinatorics. In the opportunity, the four types of combinatorial problems (combination, arrangement, permutation and Cartesian product) that need to be approached in the initial years of Elementary School, based on combinatorial problems drawn from Pessoa's research (2009) and proposed by the students were worked out. It was concluded that the methodological proposal of the Problem Solving, Exploration and Posing contributes to the promotion of the combinatorial learning of the students, enabling the development of a reflective educational process. It was verified that the problematizations provoked during the Problem Solving, Exploration and Posing process potentiated the work of reflection on the invariants of the combinatorial problems, which favored the development of the combinatorial, generalizing and logical reasoning of the students, besides enabling the researchers to explore different dimensions of the proposed problems. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-05-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/293 10.37001/remat25269062v17id293 |
url |
https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/293 |
identifier_str_mv |
10.37001/remat25269062v17id293 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/293/pdf |
dc.rights.driver.fl_str_mv |
Copyright (c) 2020 Emily Vasconcelos Santos, Silvanio Andrade info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2020 Emily Vasconcelos Santos, Silvanio Andrade |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Educação Matemática (SBEM) |
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Sociedade Brasileira de Educação Matemática (SBEM) |
dc.source.none.fl_str_mv |
Revista de Educação Matemática; Vol. 17 (2020): Publicação Contínua; e020030 Revista de Educação Matemática; ##issue.vol## 17 (2020): Publicação Contínua; e020030 Revista de Educação Matemática; Vol. 17 (2020): Publicação Contínua; e020030 Revista de Educação Matemática; v. 17 (2020): Publicação Contínua; e020030 2526-9062 reponame:Revista de Educação Matemática (Online) instname:Sociedade Brasileira de Educação Matemática (SBEM) instacron:SBEM |
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Sociedade Brasileira de Educação Matemática (SBEM) |
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SBEM |
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SBEM |
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Revista de Educação Matemática (Online) |
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Revista de Educação Matemática (Online) |
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