Crianças, algoritmos e sistema de numeração decimal

Detalhes bibliográficos
Autor(a) principal: Signorini, Marcela Boccoli
Data de Publicação: 2007
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)
Texto Completo: http://repositorio.uem.br:8080/jspui/handle/1/4436
Resumo: Although many studies in Mathematics Education (in the national as well as in the international sphere) approach possible problems about an "incorrect" introduction of formal educational procedures in the arithmetic's teaching during the beginning stages of learning, it is important to recognize that these discussions haven't emerged completely in the scholars limits to provoke an important rupture on the present scholar practices, which remains taking priority to repetition instead of the mathematical knowledge construction. In this sense, the present research proposed to investigate if the arithmetical teaching, with emphasis in algorithm, contributes to the mathematical knowledge construction. It was decided to analyze only the additives structures - addition operation and/or subtraction - as these structures make possible to investigate: a) if the conventional operations techniques (the algorithms) utilization, in addition and subtraction operations solving, allow the flexibility of the child's thinking and; b) if the child, while using the formal addition and subtraction algorithms, perceives the principles and properties of the Decimal Numeration System which are implicit in this procedure. Aiming to achieve the proposed objectives, it was interviewed, through Piaget's Clinical Method, twenty children of a public school of Maringá, being that, ten children belonged to the third grade of the basic cycle and the other ten to the fifth grade of the Fundamental Education. Each one of these two groups were subdivided into other two smaller groups, composed by five children who, according to their teachers, had a good performance and five children who had an insufficient performance in mathematical learning. The results analysis indicates that children from both educational stages reproduce mechanically the conventional operations techniques, without a real comprehension of the actions executed by them. While using the conventional algorithms of addition and subtraction, they make it automatically, repeating rules that they were taught to without realizing the existing relation between this mechanism and the principles and properties of the Decimal Numeration System. Regarding the learning performance in the subject (good or insufficient), it is not possible to affirm if it is related to the Decimal Numeration System comprehension, it seems that these classifications point toward to other variables of the educative process.
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spelling Crianças, algoritmos e sistema de numeração decimalEducação matemáticaAlgoritmo de adição e subtraçãoSistema de Numeração DecimalEnsino e aprendizagemPráticas educativasAritméticaBrasil.Mathematics EducationAddiction and Subtraction AlgorithmsDecimal Numeration SystemBrazil.Ciências Exatas e da TerraMatemáticaAlthough many studies in Mathematics Education (in the national as well as in the international sphere) approach possible problems about an "incorrect" introduction of formal educational procedures in the arithmetic's teaching during the beginning stages of learning, it is important to recognize that these discussions haven't emerged completely in the scholars limits to provoke an important rupture on the present scholar practices, which remains taking priority to repetition instead of the mathematical knowledge construction. In this sense, the present research proposed to investigate if the arithmetical teaching, with emphasis in algorithm, contributes to the mathematical knowledge construction. It was decided to analyze only the additives structures - addition operation and/or subtraction - as these structures make possible to investigate: a) if the conventional operations techniques (the algorithms) utilization, in addition and subtraction operations solving, allow the flexibility of the child's thinking and; b) if the child, while using the formal addition and subtraction algorithms, perceives the principles and properties of the Decimal Numeration System which are implicit in this procedure. Aiming to achieve the proposed objectives, it was interviewed, through Piaget's Clinical Method, twenty children of a public school of Maringá, being that, ten children belonged to the third grade of the basic cycle and the other ten to the fifth grade of the Fundamental Education. Each one of these two groups were subdivided into other two smaller groups, composed by five children who, according to their teachers, had a good performance and five children who had an insufficient performance in mathematical learning. The results analysis indicates that children from both educational stages reproduce mechanically the conventional operations techniques, without a real comprehension of the actions executed by them. While using the conventional algorithms of addition and subtraction, they make it automatically, repeating rules that they were taught to without realizing the existing relation between this mechanism and the principles and properties of the Decimal Numeration System. Regarding the learning performance in the subject (good or insufficient), it is not possible to affirm if it is related to the Decimal Numeration System comprehension, it seems that these classifications point toward to other variables of the educative process.Embora vários estudos em Educação Matemática (tanto no âmbito nacional quanto internacional) abordem possíveis problemas na inserção "incorreta" de procedimentos formais no ensino de aritmética nas séries iniciais, é necessário reconhecer que essas discussões ainda não adentraram por completo nos limites escolares a ponto de romper significativamente com as práticas escolares que priorizam a repetição em detrimento da construção do conhecimento matemático. Nessa perspectiva, a presente pesquisa teve como proposta investigar se o ensino da aritmética, com ênfase no algoritmo contribui para a construção do conhecimento matemático. Optou-se por analisar apenas as estruturas aditivas - operação de adição e/ou subtração - pois elas permitem investigar: a) se a utilização das técnicas operatórias convencionais (os algoritmos), na resolução das operações de adição e subtração, permite a flexibilidade do pensamento da criança e; b) se a criança, ao utilizar os algoritmos formais de adição e subtração, percebe os princípios e as propriedades do Sistema de Numeração Decimal implícitos nesse procedimento. Para alcançar os objetivos almejados, foram entrevistadas, mediante o Método Clínico de Jean Piaget, vinte crianças de uma escola pública de Maringá, sendo que, dez pertencia à terceira série do ciclo básico e dez cursavam a quinta série do Ensino Fundamental. Estes dois grupos foram subdivididos ainda em outros dois grupos menores composto por cinco crianças que, segundo suas professoras, apresentavam bom desempenho de aprendizagem em Matemática e cinco que apresentavam desempenho tido com insuficiente. A análise dos resultados indica que tanto as crianças de terceira como as de quinta série reproduzem mecanicamente as técnicas operatórias convencionais, sem compreensão real das ações que realizam. Ao utilizar o algoritmo convencional de adição e subtração o fazem de forma automática, repetindo regras que lhes foram ensinadas e sem perceber a relação existente entre esse dispositivo e os princípios e as propriedades do Sistema de Numeração Decimal. Quanto ao desempenho na aprendizagem da disciplina (bom ou insuficiente), não é possível afirmar que ele esteja relacionado com a compreensão do Sistema de Numeração Decimal, o que nos parece é que essas classificações estão voltadas para outras variáveis do processo educativo.124 fUniversidade Estadual de MaringáBrasilPrograma de Pós-Graduação em Educação para a Ciência e o Ensino de MatemáticaUEMMaringáCentro de Ciências ExatasClélia Maria Ignatius NogueiraRuy César Pietropaulo - UEMLuzia Marta Bellini - UEMSignorini, Marcela Boccoli2018-04-23T19:21:45Z2018-04-23T19:21:45Z2007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesishttp://repositorio.uem.br:8080/jspui/handle/1/4436porinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)instname:Universidade Estadual de Maringá (UEM)instacron:UEM2018-04-23T19:21:45Zoai:localhost:1/4436Repositório InstitucionalPUBhttp://repositorio.uem.br:8080/oai/requestopendoar:2024-04-23T14:57:36.012956Repositório Institucional da Universidade Estadual de Maringá (RI-UEM) - Universidade Estadual de Maringá (UEM)false
dc.title.none.fl_str_mv Crianças, algoritmos e sistema de numeração decimal
title Crianças, algoritmos e sistema de numeração decimal
spellingShingle Crianças, algoritmos e sistema de numeração decimal
Signorini, Marcela Boccoli
Educação matemática
Algoritmo de adição e subtração
Sistema de Numeração Decimal
Ensino e aprendizagem
Práticas educativas
Aritmética
Brasil.
Mathematics Education
Addiction and Subtraction Algorithms
Decimal Numeration System
Brazil.
Ciências Exatas e da Terra
Matemática
title_short Crianças, algoritmos e sistema de numeração decimal
title_full Crianças, algoritmos e sistema de numeração decimal
title_fullStr Crianças, algoritmos e sistema de numeração decimal
title_full_unstemmed Crianças, algoritmos e sistema de numeração decimal
title_sort Crianças, algoritmos e sistema de numeração decimal
author Signorini, Marcela Boccoli
author_facet Signorini, Marcela Boccoli
author_role author
dc.contributor.none.fl_str_mv Clélia Maria Ignatius Nogueira
Ruy César Pietropaulo - UEM
Luzia Marta Bellini - UEM
dc.contributor.author.fl_str_mv Signorini, Marcela Boccoli
dc.subject.por.fl_str_mv Educação matemática
Algoritmo de adição e subtração
Sistema de Numeração Decimal
Ensino e aprendizagem
Práticas educativas
Aritmética
Brasil.
Mathematics Education
Addiction and Subtraction Algorithms
Decimal Numeration System
Brazil.
Ciências Exatas e da Terra
Matemática
topic Educação matemática
Algoritmo de adição e subtração
Sistema de Numeração Decimal
Ensino e aprendizagem
Práticas educativas
Aritmética
Brasil.
Mathematics Education
Addiction and Subtraction Algorithms
Decimal Numeration System
Brazil.
Ciências Exatas e da Terra
Matemática
description Although many studies in Mathematics Education (in the national as well as in the international sphere) approach possible problems about an "incorrect" introduction of formal educational procedures in the arithmetic's teaching during the beginning stages of learning, it is important to recognize that these discussions haven't emerged completely in the scholars limits to provoke an important rupture on the present scholar practices, which remains taking priority to repetition instead of the mathematical knowledge construction. In this sense, the present research proposed to investigate if the arithmetical teaching, with emphasis in algorithm, contributes to the mathematical knowledge construction. It was decided to analyze only the additives structures - addition operation and/or subtraction - as these structures make possible to investigate: a) if the conventional operations techniques (the algorithms) utilization, in addition and subtraction operations solving, allow the flexibility of the child's thinking and; b) if the child, while using the formal addition and subtraction algorithms, perceives the principles and properties of the Decimal Numeration System which are implicit in this procedure. Aiming to achieve the proposed objectives, it was interviewed, through Piaget's Clinical Method, twenty children of a public school of Maringá, being that, ten children belonged to the third grade of the basic cycle and the other ten to the fifth grade of the Fundamental Education. Each one of these two groups were subdivided into other two smaller groups, composed by five children who, according to their teachers, had a good performance and five children who had an insufficient performance in mathematical learning. The results analysis indicates that children from both educational stages reproduce mechanically the conventional operations techniques, without a real comprehension of the actions executed by them. While using the conventional algorithms of addition and subtraction, they make it automatically, repeating rules that they were taught to without realizing the existing relation between this mechanism and the principles and properties of the Decimal Numeration System. Regarding the learning performance in the subject (good or insufficient), it is not possible to affirm if it is related to the Decimal Numeration System comprehension, it seems that these classifications point toward to other variables of the educative process.
publishDate 2007
dc.date.none.fl_str_mv 2007
2018-04-23T19:21:45Z
2018-04-23T19:21:45Z
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 http://repositorio.uem.br:8080/jspui/handle/1/4436
url http://repositorio.uem.br:8080/jspui/handle/1/4436
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Estadual de Maringá
Brasil
Programa de Pós-Graduação em Educação para a Ciência e o Ensino de Matemática
UEM
Maringá
Centro de Ciências Exatas
publisher.none.fl_str_mv Universidade Estadual de Maringá
Brasil
Programa de Pós-Graduação em Educação para a Ciência e o Ensino de Matemática
UEM
Maringá
Centro de Ciências Exatas
dc.source.none.fl_str_mv reponame:Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)
instname:Universidade Estadual de Maringá (UEM)
instacron:UEM
instname_str Universidade Estadual de Maringá (UEM)
instacron_str UEM
institution UEM
reponame_str Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)
collection Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)
repository.name.fl_str_mv Repositório Institucional da Universidade Estadual de Maringá (RI-UEM) - Universidade Estadual de Maringá (UEM)
repository.mail.fl_str_mv
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