Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática
Autor(a) principal: | |
---|---|
Data de Publicação: | 2014 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFS |
Texto Completo: | http://ri.ufs.br/jspui/handle/riufs/8906 |
Resumo: | The object of mathematical study titled function is present in several everyday situations, being used by several areas of knowledge. In this way, the acquisition of its concept becomes fundamental for the development of the individual’s cognitive that is in contact with the mathematics in and out of school. Thus, with the work presented here, it was aimed to analyze the mathematical representations mobilized by the students of the 1st year of high school from Colégio de Aplicação of the Universidade Federal de Sergipe (CODAP/UFS) during the teaching of affine and quadratic function. For this purpose, this study was based on Duval's theory of the registers of semiotic representation (2003, 2009, 2011) as well as the guidelines of the Parâmetros Curriculares Nacionais (BRASIL, 1999, 2002, 2006). In addition to that, it was taken as source the textbook Matemática: Contexto & Aplicações (DANTE, 2010), adopted by the participant groups of the research, as well as photocopies of the four (4) participating students' notebooks and 51 (fifty-one) protocols from a sequence of activities composed of 04 (four) problems that were developed with the students themselves. Among the obtained results, it was pointed out that, as in the 499 (four hundred and ninety-nine) activities categorized in the textbook as in the 108 (one hundred and eight) categorized in the students' notebooks, it was required the semiotic transformation of conversion in the majority of them, this is: 446 (four hundred and forty-six) activities, 89.38%, and 83 (eighty-three), 76.85%, respectively. In addition, the activities proposed by the textbook and those contained in the students' notebooks did not prioritize the back and forth feature of the registers among the conversions, disrupting, according to DUVAL (2003, 2009, 2011), the process of acquiring the concept of function. Moreover, in both research instruments it was noticed that, in conversions in which the graphic records were necessary, they were practically not presented, causing important losses in the process of acquisition of the concept of function. Therefore, among the main results obtained with this sequence of activities, it was highlighted that the vast majority of the individuals used in the research used algorithmization processes to perform most conversions. Finally, many of the students used case-by-case analysis and demonstrated that they were not able to identify and use the relevant visual variables to perform the conversions. |
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Meneses, Leonel Ricardo MachadoMariani, Rita de Cássia Pistóia2018-09-14T15:03:44Z2018-09-14T15:03:44Z2014-05-27MENESES, Leonel Ricardo Machado. Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática. 2014. 132 f. Dissertação (Mestrado em Ensino de Ciências e Matemática) - Universidade Federal de Sergipe, São Cristóvão, SE, 2014.http://ri.ufs.br/jspui/handle/riufs/8906The object of mathematical study titled function is present in several everyday situations, being used by several areas of knowledge. In this way, the acquisition of its concept becomes fundamental for the development of the individual’s cognitive that is in contact with the mathematics in and out of school. Thus, with the work presented here, it was aimed to analyze the mathematical representations mobilized by the students of the 1st year of high school from Colégio de Aplicação of the Universidade Federal de Sergipe (CODAP/UFS) during the teaching of affine and quadratic function. For this purpose, this study was based on Duval's theory of the registers of semiotic representation (2003, 2009, 2011) as well as the guidelines of the Parâmetros Curriculares Nacionais (BRASIL, 1999, 2002, 2006). In addition to that, it was taken as source the textbook Matemática: Contexto & Aplicações (DANTE, 2010), adopted by the participant groups of the research, as well as photocopies of the four (4) participating students' notebooks and 51 (fifty-one) protocols from a sequence of activities composed of 04 (four) problems that were developed with the students themselves. Among the obtained results, it was pointed out that, as in the 499 (four hundred and ninety-nine) activities categorized in the textbook as in the 108 (one hundred and eight) categorized in the students' notebooks, it was required the semiotic transformation of conversion in the majority of them, this is: 446 (four hundred and forty-six) activities, 89.38%, and 83 (eighty-three), 76.85%, respectively. In addition, the activities proposed by the textbook and those contained in the students' notebooks did not prioritize the back and forth feature of the registers among the conversions, disrupting, according to DUVAL (2003, 2009, 2011), the process of acquiring the concept of function. Moreover, in both research instruments it was noticed that, in conversions in which the graphic records were necessary, they were practically not presented, causing important losses in the process of acquisition of the concept of function. Therefore, among the main results obtained with this sequence of activities, it was highlighted that the vast majority of the individuals used in the research used algorithmization processes to perform most conversions. Finally, many of the students used case-by-case analysis and demonstrated that they were not able to identify and use the relevant visual variables to perform the conversions.O objeto de estudo matemático intitulado função está presente em várias situações do cotidiano, sendo o mesmo utilizado por diversas áreas do conhecimento. Dessa forma, a aquisição de seu conceito torna-se algo fundamental para o desenvolvimento do cognitivo do indivíduo que esteja em contato com a matemática dentro e fora da escola. Assim, com o trabalho ora apresentado, objetivou-se analisar as representações matemáticas mobilizadas pelos alunos do 1º ano do ensino médio do Colégio de Aplicação da Universidade Federal de Sergipe (CODAP/UFS) durante o ensino de função afim e quadrática. Para tal efeito, o estudo embasou-se na teoria dos registros de representação semiótica de Duval (2003, 2009, 2011) bem como nas orientações dos Parâmetros Curriculares Nacionais (BRASIL, 1999, 2002, 2006). Além disso, tomou-se como fonte o livro didático Matemática: Contexto & Aplicações (DANTE, 2010), adotado nas turmas participantes da pesquisa bem como fotocópias dos cadernos de 04 (quatro) alunos participantes e 51 (cinquenta e um) protocolos de uma sequência de atividades compostas por 04 (quatro) problemas as quais foram desenvolvidas com os próprios alunos. Entre os resultados obtidos, destacou-se que tanto nas 499 (quatrocentas e noventa e nove) atividades categorizadas no livro didático quanto nas 108 (cento e oito) categorizadas nos cadernos dos alunos foram requeridas nelas, majoritariamente, a transformação semiótica de conversão, a saber: 446 (quatrocentas e quarenta e seis) atividades, 89,38%, e 83 (oitenta e três), 76,85%, respectivamente. Somado a isso, as atividades propostas pelo livro didático e as contidas nos cadernos dos alunos não priorizavam a característica de ida e volta de registros entre as conversões, prejudicando, segundo DUVAL (2003, 2009, 2011), o processo de aquisição do conceito de função. Ademais, em ambos os instrumentos de pesquisa notou-se que, em conversões em que eram necessários os registros gráficos, praticamente não foram apresentadas, proporcionando importantes perdas no processo de aquisição do conceito de função. Dessa forma, entre os principais resultados obtidos com essa sequência de atividades destacou-se que a grande maioria dos sujeitos usados na pesquisa recorreu a processos de algoritimização para executar a maioria das conversões realizadas. Por fim, muitos dos alunos usaram análise pontual e demonstraram não saber identificar e usar as variáveis visuais pertinentes para realizar as conversões.São Cristóvão, SEporEstudo de matemáticaEnsino de matemáticaFunções quadráticasLivros didáticosSemióticaRegistros de representação semióticaFunção afimFunção quadráticaRegisters of semiotic representationTextbookAffine functionQuadratic functionCIENCIAS HUMANAS::EDUCACAORepresentações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadráticainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPós-Graduação em Ensino de Ciências e MatemáticaUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessTEXTLEONEL_RICARDO_MACHADO_MENESES.pdf.txtLEONEL_RICARDO_MACHADO_MENESES.pdf.txtExtracted texttext/plain287962https://ri.ufs.br/jspui/bitstream/riufs/8906/3/LEONEL_RICARDO_MACHADO_MENESES.pdf.txt783bbc4ca83256c315dd16f4dc85bd5aMD53THUMBNAILLEONEL_RICARDO_MACHADO_MENESES.pdf.jpgLEONEL_RICARDO_MACHADO_MENESES.pdf.jpgGenerated Thumbnailimage/jpeg1322https://ri.ufs.br/jspui/bitstream/riufs/8906/4/LEONEL_RICARDO_MACHADO_MENESES.pdf.jpgadb3db8be7ac4f9ea565bb2e8c2403ddMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/8906/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALLEONEL_RICARDO_MACHADO_MENESES.pdfLEONEL_RICARDO_MACHADO_MENESES.pdfapplication/pdf4454383https://ri.ufs.br/jspui/bitstream/riufs/8906/2/LEONEL_RICARDO_MACHADO_MENESES.pdf02a49c868238d36428fea6fdb1827864MD52riufs/89062018-09-14 12:03:49.942oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2018-09-14T15:03:49Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false |
dc.title.pt_BR.fl_str_mv |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
title |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
spellingShingle |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática Meneses, Leonel Ricardo Machado Estudo de matemática Ensino de matemática Funções quadráticas Livros didáticos Semiótica Registros de representação semiótica Função afim Função quadrática Registers of semiotic representation Textbook Affine function Quadratic function CIENCIAS HUMANAS::EDUCACAO |
title_short |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
title_full |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
title_fullStr |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
title_full_unstemmed |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
title_sort |
Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática |
author |
Meneses, Leonel Ricardo Machado |
author_facet |
Meneses, Leonel Ricardo Machado |
author_role |
author |
dc.contributor.author.fl_str_mv |
Meneses, Leonel Ricardo Machado |
dc.contributor.advisor1.fl_str_mv |
Mariani, Rita de Cássia Pistóia |
contributor_str_mv |
Mariani, Rita de Cássia Pistóia |
dc.subject.por.fl_str_mv |
Estudo de matemática Ensino de matemática Funções quadráticas Livros didáticos Semiótica Registros de representação semiótica Função afim Função quadrática |
topic |
Estudo de matemática Ensino de matemática Funções quadráticas Livros didáticos Semiótica Registros de representação semiótica Função afim Função quadrática Registers of semiotic representation Textbook Affine function Quadratic function CIENCIAS HUMANAS::EDUCACAO |
dc.subject.eng.fl_str_mv |
Registers of semiotic representation Textbook Affine function Quadratic function |
dc.subject.cnpq.fl_str_mv |
CIENCIAS HUMANAS::EDUCACAO |
description |
The object of mathematical study titled function is present in several everyday situations, being used by several areas of knowledge. In this way, the acquisition of its concept becomes fundamental for the development of the individual’s cognitive that is in contact with the mathematics in and out of school. Thus, with the work presented here, it was aimed to analyze the mathematical representations mobilized by the students of the 1st year of high school from Colégio de Aplicação of the Universidade Federal de Sergipe (CODAP/UFS) during the teaching of affine and quadratic function. For this purpose, this study was based on Duval's theory of the registers of semiotic representation (2003, 2009, 2011) as well as the guidelines of the Parâmetros Curriculares Nacionais (BRASIL, 1999, 2002, 2006). In addition to that, it was taken as source the textbook Matemática: Contexto & Aplicações (DANTE, 2010), adopted by the participant groups of the research, as well as photocopies of the four (4) participating students' notebooks and 51 (fifty-one) protocols from a sequence of activities composed of 04 (four) problems that were developed with the students themselves. Among the obtained results, it was pointed out that, as in the 499 (four hundred and ninety-nine) activities categorized in the textbook as in the 108 (one hundred and eight) categorized in the students' notebooks, it was required the semiotic transformation of conversion in the majority of them, this is: 446 (four hundred and forty-six) activities, 89.38%, and 83 (eighty-three), 76.85%, respectively. In addition, the activities proposed by the textbook and those contained in the students' notebooks did not prioritize the back and forth feature of the registers among the conversions, disrupting, according to DUVAL (2003, 2009, 2011), the process of acquiring the concept of function. Moreover, in both research instruments it was noticed that, in conversions in which the graphic records were necessary, they were practically not presented, causing important losses in the process of acquisition of the concept of function. Therefore, among the main results obtained with this sequence of activities, it was highlighted that the vast majority of the individuals used in the research used algorithmization processes to perform most conversions. Finally, many of the students used case-by-case analysis and demonstrated that they were not able to identify and use the relevant visual variables to perform the conversions. |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014-05-27 |
dc.date.accessioned.fl_str_mv |
2018-09-14T15:03:44Z |
dc.date.available.fl_str_mv |
2018-09-14T15:03:44Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
MENESES, Leonel Ricardo Machado. Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática. 2014. 132 f. Dissertação (Mestrado em Ensino de Ciências e Matemática) - Universidade Federal de Sergipe, São Cristóvão, SE, 2014. |
dc.identifier.uri.fl_str_mv |
http://ri.ufs.br/jspui/handle/riufs/8906 |
identifier_str_mv |
MENESES, Leonel Ricardo Machado. Representações mobilizadas nas turmas de 1º ano do Colégio de Aplicação da Universidade Federal de Sergipe no ensino de função afim e quadrática. 2014. 132 f. Dissertação (Mestrado em Ensino de Ciências e Matemática) - Universidade Federal de Sergipe, São Cristóvão, SE, 2014. |
url |
http://ri.ufs.br/jspui/handle/riufs/8906 |
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Pós-Graduação em Ensino de Ciências e Matemática |
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Universidade Federal de Sergipe |
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