Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Manancial - Repositório Digital da UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/6769 |
Resumo: | The aim of this research is to investigate whether and how the semiotic representation registers are employed in the strict sense research produced by Brazilian institutions that address the development of combinatory reasoning through educational activities that had the participation of high school students. The study is based on qualitative meta-analysis, which can be understood as the realization of a systematic review of a body of research intended to culminate in an interpretive synthesis through analysis and primary data from these (BICUDO, 2014). Therefore, we adopted the semiotic representation registers based on Duval (2003, 2009, 2011) as a theoretical framework. The screening took place on the websites of postgraduate programs of Brazilian universities (Multidisciplinary Teaching of Mathematics area) and the Bank of Theses and Dissertations of Higher Education Personnel Improvement Coordination (CAPES). In search it was used keywords "combinatorics", "combinatorial" and "permutations". It was found that 43 research emphasized the combinatorial reasoning; 35 made explicit in its documentary corpus educational activities in basic education, higher education or training of teachers who teach mathematics. From these, 12 focused on high school, both in regular schools and in the form of Youth and Adult Education. To accomplish the data analysis it was selected four dissertations that analyze and propose activities resolved by high school students and have theoretical support in solving problems. Thus, using descriptors drawn from solving strategies of combinatorial nature of activities presented by Batanero et al (1996, 1997, 2001 and 2003). It sought these evidence activities that have identified the representation registers mobilized in the solutions presented by the participants of the selected studies. The data analysis it was concluded that the use of array formulas, combination and permutation is not the strategy adopted by the students, but rather the product rule (Cartesian product or multiplicative principle). This rule mainly symbolic mobilizes records and, therefore, poses treatments in the same record type. However, when the activities are developed through formulas, that is, the product rule, the sum or quotient, were also employed symbolic records and their treatments. Additionally, these tasks were further evidence of the modification of the starting record in natural language to the intermediary, symbolic record. In other strategies such as enumerating the requested settings, recursion, subdividing the problem, set variables and translation problem the equivalent there was a greater diversity of records, namely: natural language, figural, tabular and tree. Therefore a variety in most types of conversion. Finally, it was also noted that the mobilization of semiotic representation registers in solving combinatorial nature of activities are not aimed at only the seizure of mathematical objects, but mainly a support for solving such problems. |
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Raciocínio combinatório: uma meta-análise a partir dos registros de representação semióticaCombinatorial reasoning: a meta-analysis from the register of semiotic representationsRaciocínio combinatórioMeta-análiseRegistros de representaçãoCombinatorial reasoningMeta-analysisRegister of representationCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAThe aim of this research is to investigate whether and how the semiotic representation registers are employed in the strict sense research produced by Brazilian institutions that address the development of combinatory reasoning through educational activities that had the participation of high school students. The study is based on qualitative meta-analysis, which can be understood as the realization of a systematic review of a body of research intended to culminate in an interpretive synthesis through analysis and primary data from these (BICUDO, 2014). Therefore, we adopted the semiotic representation registers based on Duval (2003, 2009, 2011) as a theoretical framework. The screening took place on the websites of postgraduate programs of Brazilian universities (Multidisciplinary Teaching of Mathematics area) and the Bank of Theses and Dissertations of Higher Education Personnel Improvement Coordination (CAPES). In search it was used keywords "combinatorics", "combinatorial" and "permutations". It was found that 43 research emphasized the combinatorial reasoning; 35 made explicit in its documentary corpus educational activities in basic education, higher education or training of teachers who teach mathematics. From these, 12 focused on high school, both in regular schools and in the form of Youth and Adult Education. To accomplish the data analysis it was selected four dissertations that analyze and propose activities resolved by high school students and have theoretical support in solving problems. Thus, using descriptors drawn from solving strategies of combinatorial nature of activities presented by Batanero et al (1996, 1997, 2001 and 2003). It sought these evidence activities that have identified the representation registers mobilized in the solutions presented by the participants of the selected studies. The data analysis it was concluded that the use of array formulas, combination and permutation is not the strategy adopted by the students, but rather the product rule (Cartesian product or multiplicative principle). This rule mainly symbolic mobilizes records and, therefore, poses treatments in the same record type. However, when the activities are developed through formulas, that is, the product rule, the sum or quotient, were also employed symbolic records and their treatments. Additionally, these tasks were further evidence of the modification of the starting record in natural language to the intermediary, symbolic record. In other strategies such as enumerating the requested settings, recursion, subdividing the problem, set variables and translation problem the equivalent there was a greater diversity of records, namely: natural language, figural, tabular and tree. Therefore a variety in most types of conversion. Finally, it was also noted that the mobilization of semiotic representation registers in solving combinatorial nature of activities are not aimed at only the seizure of mathematical objects, but mainly a support for solving such problems.O objetivo desta pesquisa é investigar se e como são empregados os registros de representação semiótica nas investigações stricto sensu produzidas por instituições brasileiras que abordam o desenvolvimento do raciocínio combinatório por meio de atividades didáticas que tiveram a participação de alunos do ensino médio. O estudo está baseado na meta-análise qualitativa, que pode ser entendida como a realização de uma revisão sistemática de um conjunto de pesquisas com a intenção de culminar em uma síntese interpretativa por meio da análise e dos dados primários destas (BICUDO, 2014). Para tanto, adotamos os registros de representação semiótica de Duval (2003, 2009, 2011) como referencial teórico. A triagem se deu nos sites dos programas de pós-graduação de universidades brasileiras (grande área Multidisciplinar, área de Ensino de Matemática) e no Banco de Teses e Dissertações da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). Nas buscas utilizou-se as palavras-chave análise combinatória , combinatória e permutações . Constatou-se que 43 pesquisas enfatizaram o raciocínio combinatório e 35 delas explicitaram em seu corpus documental atividades didáticas na educação básica, no ensino superior ou na formação de professores que ensinam Matemática. Dessas, 12 centraram-se no ensino médio, tanto no ensino regular quanto na modalidade de Educação de Jovens e Adultos. Para realizar a análise dos dados selecionou-se quatro dissertações que propõem e analisam atividades resolvidas por estudantes do ensino médio e que têm aporte teórico na resolução de problemas. Diante disso, por meio de descritores elaborados a partir das estratégias de resolução de atividades de cunho combinatório apresentadas por Batanero et al (1996, 1997, 2001 e 2003), buscou-se nestas atividades indícios que permitiram identificar os registros de representação mobilizados nas soluções apresentadas pelos participantes dos estudos selecionados. Das análises dos dados conclui-se que o emprego das fórmulas de arranjo, combinação e permutação não é a estratégia mais adotada pelos estudantes, mas sim, a regra do produto (produto cartesiano ou princípio multiplicativo). Esta regra mobiliza principalmente registros simbólicos e, sendo assim, suscita tratamentos nesse mesmo tipo de registro. De modo semelhante, quando as atividades são desenvolvidas por meio de fórmulas, ou seja, pela regra do produto, da soma ou do quociente, também foram empregados registros simbólicos e seus tratamentos. Além disso, nestas tarefas houve uma maior evidência das modificações do registro de partida, em língua natural, para o intermediário, registro simbólico. Nas demais estratégias como enumerar as configurações solicitadas, recursividade, subdividir o problema, fixar variáveis e tradução do problema a outro equivalente identificou-se uma diversidade maior de registros, a saber: língua natural, figural, tabular e em árvore e, por conseguinte, uma variedade maior nos tipos de mudanças entre eles. Por fim, observou-se que a mobilização dos registros de representação semiótica na resolução de atividades de cunho combinatório não visam somente à apreensão dos objetos matemáticos, mas, principalmente, um suporte para a resolução desse tipo de problemas.Universidade Federal de Santa MariaBREducação Matemática e Ensino de FísicaUFSMPrograma de Pós-Graduação em Educação Matemática e Ensino de FísicaMariani, Rita de Cássia Pistóiahttp://lattes.cnpq.br/8330933788557081Fioreze, Leandra Anversahttp://lattes.cnpq.br/9910618131721810Fajardo, Ricardohttp://lattes.cnpq.br/4796609278630063Schmidt, Wilian2017-01-052017-01-052016-08-24info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfapplication/pdfSCHMIDT, Wilian. COMBINATORIAL REASONING: A META-ANALYSIS FROM THE REGISTER OF SEMIOTIC REPRESENTATIONS. 2016. 148 f. Dissertação (Mestrado em Educação Matemática e Ensino de Física) - Universidade Federal de Santa Maria, Santa Maria, 2016.http://repositorio.ufsm.br/handle/1/6769porinfo:eu-repo/semantics/openAccessreponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSM2020-11-03T15:16:35Zoai:repositorio.ufsm.br:1/6769Biblioteca Digital de Teses e Dissertaçõeshttps://repositorio.ufsm.br/ONGhttps://repositorio.ufsm.br/oai/requestatendimento.sib@ufsm.br||tedebc@gmail.comopendoar:2020-11-03T15:16:35Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.none.fl_str_mv |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica Combinatorial reasoning: a meta-analysis from the register of semiotic representations |
title |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica |
spellingShingle |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica Schmidt, Wilian Raciocínio combinatório Meta-análise Registros de representação Combinatorial reasoning Meta-analysis Register of representation CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica |
title_full |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica |
title_fullStr |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica |
title_full_unstemmed |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica |
title_sort |
Raciocínio combinatório: uma meta-análise a partir dos registros de representação semiótica |
author |
Schmidt, Wilian |
author_facet |
Schmidt, Wilian |
author_role |
author |
dc.contributor.none.fl_str_mv |
Mariani, Rita de Cássia Pistóia http://lattes.cnpq.br/8330933788557081 Fioreze, Leandra Anversa http://lattes.cnpq.br/9910618131721810 Fajardo, Ricardo http://lattes.cnpq.br/4796609278630063 |
dc.contributor.author.fl_str_mv |
Schmidt, Wilian |
dc.subject.por.fl_str_mv |
Raciocínio combinatório Meta-análise Registros de representação Combinatorial reasoning Meta-analysis Register of representation CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
topic |
Raciocínio combinatório Meta-análise Registros de representação Combinatorial reasoning Meta-analysis Register of representation CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
The aim of this research is to investigate whether and how the semiotic representation registers are employed in the strict sense research produced by Brazilian institutions that address the development of combinatory reasoning through educational activities that had the participation of high school students. The study is based on qualitative meta-analysis, which can be understood as the realization of a systematic review of a body of research intended to culminate in an interpretive synthesis through analysis and primary data from these (BICUDO, 2014). Therefore, we adopted the semiotic representation registers based on Duval (2003, 2009, 2011) as a theoretical framework. The screening took place on the websites of postgraduate programs of Brazilian universities (Multidisciplinary Teaching of Mathematics area) and the Bank of Theses and Dissertations of Higher Education Personnel Improvement Coordination (CAPES). In search it was used keywords "combinatorics", "combinatorial" and "permutations". It was found that 43 research emphasized the combinatorial reasoning; 35 made explicit in its documentary corpus educational activities in basic education, higher education or training of teachers who teach mathematics. From these, 12 focused on high school, both in regular schools and in the form of Youth and Adult Education. To accomplish the data analysis it was selected four dissertations that analyze and propose activities resolved by high school students and have theoretical support in solving problems. Thus, using descriptors drawn from solving strategies of combinatorial nature of activities presented by Batanero et al (1996, 1997, 2001 and 2003). It sought these evidence activities that have identified the representation registers mobilized in the solutions presented by the participants of the selected studies. The data analysis it was concluded that the use of array formulas, combination and permutation is not the strategy adopted by the students, but rather the product rule (Cartesian product or multiplicative principle). This rule mainly symbolic mobilizes records and, therefore, poses treatments in the same record type. However, when the activities are developed through formulas, that is, the product rule, the sum or quotient, were also employed symbolic records and their treatments. Additionally, these tasks were further evidence of the modification of the starting record in natural language to the intermediary, symbolic record. In other strategies such as enumerating the requested settings, recursion, subdividing the problem, set variables and translation problem the equivalent there was a greater diversity of records, namely: natural language, figural, tabular and tree. Therefore a variety in most types of conversion. Finally, it was also noted that the mobilization of semiotic representation registers in solving combinatorial nature of activities are not aimed at only the seizure of mathematical objects, but mainly a support for solving such problems. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-08-24 2017-01-05 2017-01-05 |
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 |
SCHMIDT, Wilian. COMBINATORIAL REASONING: A META-ANALYSIS FROM THE REGISTER OF SEMIOTIC REPRESENTATIONS. 2016. 148 f. Dissertação (Mestrado em Educação Matemática e Ensino de Física) - Universidade Federal de Santa Maria, Santa Maria, 2016. http://repositorio.ufsm.br/handle/1/6769 |
identifier_str_mv |
SCHMIDT, Wilian. COMBINATORIAL REASONING: A META-ANALYSIS FROM THE REGISTER OF SEMIOTIC REPRESENTATIONS. 2016. 148 f. Dissertação (Mestrado em Educação Matemática e Ensino de Física) - Universidade Federal de Santa Maria, Santa Maria, 2016. |
url |
http://repositorio.ufsm.br/handle/1/6769 |
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.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria BR Educação Matemática e Ensino de Física UFSM Programa de Pós-Graduação em Educação Matemática e Ensino de Física |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria BR Educação Matemática e Ensino de Física UFSM Programa de Pós-Graduação em Educação Matemática e Ensino de Física |
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reponame:Manancial - Repositório Digital da UFSM instname:Universidade Federal de Santa Maria (UFSM) instacron:UFSM |
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Universidade Federal de Santa Maria (UFSM) |
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UFSM |
institution |
UFSM |
reponame_str |
Manancial - Repositório Digital da UFSM |
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Manancial - Repositório Digital da UFSM |
repository.name.fl_str_mv |
Manancial - Repositório Digital da UFSM - Universidade Federal de Santa Maria (UFSM) |
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atendimento.sib@ufsm.br||tedebc@gmail.com |
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