Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Actio (Curitiba) |
Texto Completo: | https://periodicos.utfpr.edu.br/actio/article/view/10603 |
Resumo: | This article presents the results of a study that analyzed the conceptual approach of the multiplicative structure in didactic manuals, because in our view, concepts should be formed and developed from a set of problem situations that consider the representation and the concept itself. With this premise, this study aimed to classify different problem situations of the multiplicative structure of natural numbers in a collection of textbooks used in the early years of elementary school from the perspective of the Theory of Conceptual Fields developed by Gérard Vergnaud. This study is linked to the Research Group on Science and Mathematics Teaching (Grupo de Pesquisa em Ensino de Ciências e Matemática - GPECMA). This is a qualitative study with characteristics of documentary analysis and is methodologically based on content analysis. This analysis considered selecting, exploring, and treating data as necessary steps to meet the objective of the study and allowed us to identify and analyze the mathematical and didactic organization adopted in teaching the multiplicative structure in the collection of textbooks analyzed. When preparing and analyzing data, five types of multiplicative situations emerged. The algorithm of multiplication and division was formalized in the last volume of the collection. Among the problem situations identified were multiplication as the sum of equal parcels, rectangular arrangement, combination of possibilities, and dividing equally and determining how many fit. These problem situations were presented in three recorded units that differed by the representation used, in natural and figural language, and manipulable materials. It should be noted that most of the problem situations presented mobilized concepts of isomorphism of measures. The reasoning involved in the product of measures class was contemplated in multiplicative situations, excluding division situations, which indicated the need to propose to students more situations that organized the multiplicative thinking in different aspects, addressing multiplication and division in the product of measures class. It also implied the need to approach several multiplicative situations within different contexts and degrees of difficulty, since textbooks are often the main material used by teachers to prepare their lessons. |
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Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary schoolEstrutura multiplicativa de números naturais: um olhar para o livro didático de matemática dos anos iniciais do ensino fundamentalEnsinoIsomorfismo de medidas; Produto de medidas; Campos Conceituais; Livro didático de Matemática.Isomorphism of measures; Product of measures; Conceptual Fields; Mathematical LiteracyThis article presents the results of a study that analyzed the conceptual approach of the multiplicative structure in didactic manuals, because in our view, concepts should be formed and developed from a set of problem situations that consider the representation and the concept itself. With this premise, this study aimed to classify different problem situations of the multiplicative structure of natural numbers in a collection of textbooks used in the early years of elementary school from the perspective of the Theory of Conceptual Fields developed by Gérard Vergnaud. This study is linked to the Research Group on Science and Mathematics Teaching (Grupo de Pesquisa em Ensino de Ciências e Matemática - GPECMA). This is a qualitative study with characteristics of documentary analysis and is methodologically based on content analysis. This analysis considered selecting, exploring, and treating data as necessary steps to meet the objective of the study and allowed us to identify and analyze the mathematical and didactic organization adopted in teaching the multiplicative structure in the collection of textbooks analyzed. When preparing and analyzing data, five types of multiplicative situations emerged. The algorithm of multiplication and division was formalized in the last volume of the collection. Among the problem situations identified were multiplication as the sum of equal parcels, rectangular arrangement, combination of possibilities, and dividing equally and determining how many fit. These problem situations were presented in three recorded units that differed by the representation used, in natural and figural language, and manipulable materials. It should be noted that most of the problem situations presented mobilized concepts of isomorphism of measures. The reasoning involved in the product of measures class was contemplated in multiplicative situations, excluding division situations, which indicated the need to propose to students more situations that organized the multiplicative thinking in different aspects, addressing multiplication and division in the product of measures class. It also implied the need to approach several multiplicative situations within different contexts and degrees of difficulty, since textbooks are often the main material used by teachers to prepare their lessons.Este artigo apresenta os resultados de uma pesquisa que analisa a abordagem conceitual da estrutura multiplicativa em manuais didáticos, pois consideramos que a formação e o desenvolvimento dos conceitos devem emergir a partir de um conjunto de situações- problemas que levem em consideração a representação e o próprio conceito. Com esta premissa, este estudo teve por objetivo classificar tipos de situações-problemas da estrutura multiplicativa de Números Naturais em uma coleção de livros didáticos dos anos iniciais do Ensino Fundamental sob a perspectiva da Teoria dos Campos Conceituais, desenvolvida por Gerard Vergnaud. Este trabalho é vinculado ao Grupo de Pesquisa em Ensino de Ciências e Matemática (GPECMA). A pesquisa, de caráter qualitativo, apresenta características da análise documental, baseando-se metodologicamente na análise de conteúdo, a qual considera necessário selecionar, explorar e tratar os dados com vistas a abordar o objetivo, que nos permitiu identificar e analisar as escolhas referentes à organização matemática e didática presente no ensino da estrutura multiplicativa na coleção de livros didáticos analisada. A partir da produção e análise de dados notamos que emergiram cinco tipos de situações multiplicativas. A formalização do algoritmo da multiplicação e divisão é apresentada no último volume da coleção. Dentre as situações identificamos a multiplicação entendida como soma de parcelas iguais, disposição retangular, combinação de possibilidades, repartir igualmente e quantos cabem, apresentados em três unidades de registro que se diferenciam pela representação utilizada em língua natural, figural e materiais manipuláveis. Destaca-se que a maioria das situações apresentadas mobilizam conceitos do isomorfismo de medidas. O raciocínio envolvido na classe de produto de medidas é contemplado em situações multiplicativas, deixando relegadas situações envolvendo divisão, o que indica a necessidade de propor aos estudantes mais situações que organizam o pensamento multiplicativo em diferentes aspectos, em que se trabalhe a multiplicação e a divisão na classe do produto de medidas. Depreende-se também a necessidade de abordar diversificadas situações multiplicativas, em diferentes contextos e grau de dificuldade, visto que muitas vezes o livro didático é o principal material utilizado pelo professor no preparo de suas aulas.Universidade Tecnológica Federal do Paraná (UTFPR)Schmitt Zanella, MarliKrachinscki, João Marcos de AraújoZanella, Idelmar André2019-12-31info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionDossiê TemáticoPesquisa documentalapplication/pdftext/htmlhttps://periodicos.utfpr.edu.br/actio/article/view/1060310.3895/actio.v4n3.10603ACTIO: Teaching in Sciences; v. 4, n. 3 (2019); 465-487ACTIO: Docência em Ciências; v. 4, n. 3 (2019); 465-4872525-892310.3895/actio.v4n3reponame:Actio (Curitiba)instname:Universidade Tecnológica Federal do Paraná (UTFPR)instacron:UTFPRporhttps://periodicos.utfpr.edu.br/actio/article/view/10603/7041https://periodicos.utfpr.edu.br/actio/article/view/10603/7394Direitos autorais 2020 ACTIO: Docência em Ciênciashttp://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccess2022-10-18T23:53:45Zoai:periodicos.utfpr:article/10603Revistahttps://periodicos.utfpr.edu.br/actio/PUBhttps://periodicos.utfpr.edu.br/actio/oaimarcelolambach@utfpr.edu.br||actio-ct@utfpr.edu.br||periodicos@utfpr.edu.br2525-89232525-8923opendoar:2022-10-18T23:53:45Actio (Curitiba) - Universidade Tecnológica Federal do Paraná (UTFPR)false |
dc.title.none.fl_str_mv |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school Estrutura multiplicativa de números naturais: um olhar para o livro didático de matemática dos anos iniciais do ensino fundamental |
title |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school |
spellingShingle |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school Schmitt Zanella, Marli Ensino Isomorfismo de medidas; Produto de medidas; Campos Conceituais; Livro didático de Matemática. Isomorphism of measures; Product of measures; Conceptual Fields; Mathematical Literacy |
title_short |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school |
title_full |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school |
title_fullStr |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school |
title_full_unstemmed |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school |
title_sort |
Multiplicative structure of natural numbers: an analysis of mathematics textbooks used in the early years of elementary school |
author |
Schmitt Zanella, Marli |
author_facet |
Schmitt Zanella, Marli Krachinscki, João Marcos de Araújo Zanella, Idelmar André |
author_role |
author |
author2 |
Krachinscki, João Marcos de Araújo Zanella, Idelmar André |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
|
dc.contributor.author.fl_str_mv |
Schmitt Zanella, Marli Krachinscki, João Marcos de Araújo Zanella, Idelmar André |
dc.subject.por.fl_str_mv |
Ensino Isomorfismo de medidas; Produto de medidas; Campos Conceituais; Livro didático de Matemática. Isomorphism of measures; Product of measures; Conceptual Fields; Mathematical Literacy |
topic |
Ensino Isomorfismo de medidas; Produto de medidas; Campos Conceituais; Livro didático de Matemática. Isomorphism of measures; Product of measures; Conceptual Fields; Mathematical Literacy |
description |
This article presents the results of a study that analyzed the conceptual approach of the multiplicative structure in didactic manuals, because in our view, concepts should be formed and developed from a set of problem situations that consider the representation and the concept itself. With this premise, this study aimed to classify different problem situations of the multiplicative structure of natural numbers in a collection of textbooks used in the early years of elementary school from the perspective of the Theory of Conceptual Fields developed by Gérard Vergnaud. This study is linked to the Research Group on Science and Mathematics Teaching (Grupo de Pesquisa em Ensino de Ciências e Matemática - GPECMA). This is a qualitative study with characteristics of documentary analysis and is methodologically based on content analysis. This analysis considered selecting, exploring, and treating data as necessary steps to meet the objective of the study and allowed us to identify and analyze the mathematical and didactic organization adopted in teaching the multiplicative structure in the collection of textbooks analyzed. When preparing and analyzing data, five types of multiplicative situations emerged. The algorithm of multiplication and division was formalized in the last volume of the collection. Among the problem situations identified were multiplication as the sum of equal parcels, rectangular arrangement, combination of possibilities, and dividing equally and determining how many fit. These problem situations were presented in three recorded units that differed by the representation used, in natural and figural language, and manipulable materials. It should be noted that most of the problem situations presented mobilized concepts of isomorphism of measures. The reasoning involved in the product of measures class was contemplated in multiplicative situations, excluding division situations, which indicated the need to propose to students more situations that organized the multiplicative thinking in different aspects, addressing multiplication and division in the product of measures class. It also implied the need to approach several multiplicative situations within different contexts and degrees of difficulty, since textbooks are often the main material used by teachers to prepare their lessons. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-12-31 |
dc.type.none.fl_str_mv |
|
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Dossiê Temático Pesquisa documental |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.utfpr.edu.br/actio/article/view/10603 10.3895/actio.v4n3.10603 |
url |
https://periodicos.utfpr.edu.br/actio/article/view/10603 |
identifier_str_mv |
10.3895/actio.v4n3.10603 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.utfpr.edu.br/actio/article/view/10603/7041 https://periodicos.utfpr.edu.br/actio/article/view/10603/7394 |
dc.rights.driver.fl_str_mv |
Direitos autorais 2020 ACTIO: Docência em Ciências http://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Direitos autorais 2020 ACTIO: Docência em Ciências http://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf text/html |
dc.publisher.none.fl_str_mv |
Universidade Tecnológica Federal do Paraná (UTFPR) |
publisher.none.fl_str_mv |
Universidade Tecnológica Federal do Paraná (UTFPR) |
dc.source.none.fl_str_mv |
ACTIO: Teaching in Sciences; v. 4, n. 3 (2019); 465-487 ACTIO: Docência em Ciências; v. 4, n. 3 (2019); 465-487 2525-8923 10.3895/actio.v4n3 reponame:Actio (Curitiba) instname:Universidade Tecnológica Federal do Paraná (UTFPR) instacron:UTFPR |
instname_str |
Universidade Tecnológica Federal do Paraná (UTFPR) |
instacron_str |
UTFPR |
institution |
UTFPR |
reponame_str |
Actio (Curitiba) |
collection |
Actio (Curitiba) |
repository.name.fl_str_mv |
Actio (Curitiba) - Universidade Tecnológica Federal do Paraná (UTFPR) |
repository.mail.fl_str_mv |
marcelolambach@utfpr.edu.br||actio-ct@utfpr.edu.br||periodicos@utfpr.edu.br |
_version_ |
1797239983656927232 |