Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Tipo de documento: | Tese |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da PUC_SP |
Texto Completo: | https://tede2.pucsp.br/handle/handle/10914 |
Resumo: | This doctorate thesis aims to identify the characteristics and the dimensions of mathematical thinking in experimental and theoretical terms which may be useful to teachers with respect to teaching processes, development of mathematical ideas and the delineation of learning contexts. Our study began with a detailed analysis of the work of Krutetskii (1968). This book is very rich in theoretical examples and reflections. It is, however, a completely psychological work and provided few indications of the more general mathematic knowledge and thinking. For this reason we added detailed information about the work of other authors such as Gowers, Poincaré, Boutroux, Otte and Kurz, and this added other dimensions which assisted our understanding of the nature of mathematics. These authors were concerned with the problems of cognitive styles, cultural and historical differences, differences that are the results of mathematics itself and distinctive ways of representing mathematics. The experimental dimensions consisted of analysis of data obtained from qualitative research with students whereby one was taken from the literature (Krutetskii) and the other an exploratory survey which we carried out for the purposes of this thesis. Krutetskii carried out an experimental investigation involving 201 Russian students with different mathematic abilities, attending elementary school. These students were presented with a number of different series of mathematic problems and their mathematic abilities were observed during the problem solving process. In our survey we carried out case studies exploring mathematic problem solving involving 13 students from the Federal University of Mato Grosso with 9 students from the Mathematics/Education course and 4 students from the Computer Sciences Course. The exploratory survey was organized into 3 phases. The first was the completion of a questionnaire with subjective questions about Mathematics and preferred ways of thinking and dealing with this subject. The second phase was reserved for the solution of 13 varied mathematical problems. The final phase was the completion of another questionnaire with subjective questions which sought to obtain information about the experiences of the students when solving the problems set. With our exploratory survey we were able to document and verify several parameters and characteristics of mathematical thinking which were described in the theoretical chapters as well as being able identify the problems themselves and the experience of solving them also influenced mathematical thinking. As a general result we concluded that mathematical thinking must be considered in the light of different parameters since this can help to characterize more complete mathematical thinking |
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Otte, MichaelFranchi, AnnaWielewski, Gladys Denise2016-04-27T16:57:16Z2005-11-102005-11-11Wielewski, Gladys Denise. Aspects of the mathematical thought in the resolution of problems: a contextual presentation of the work of Krutetskii. 2005. 407 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2005.https://tede2.pucsp.br/handle/handle/10914This doctorate thesis aims to identify the characteristics and the dimensions of mathematical thinking in experimental and theoretical terms which may be useful to teachers with respect to teaching processes, development of mathematical ideas and the delineation of learning contexts. Our study began with a detailed analysis of the work of Krutetskii (1968). This book is very rich in theoretical examples and reflections. It is, however, a completely psychological work and provided few indications of the more general mathematic knowledge and thinking. For this reason we added detailed information about the work of other authors such as Gowers, Poincaré, Boutroux, Otte and Kurz, and this added other dimensions which assisted our understanding of the nature of mathematics. These authors were concerned with the problems of cognitive styles, cultural and historical differences, differences that are the results of mathematics itself and distinctive ways of representing mathematics. The experimental dimensions consisted of analysis of data obtained from qualitative research with students whereby one was taken from the literature (Krutetskii) and the other an exploratory survey which we carried out for the purposes of this thesis. Krutetskii carried out an experimental investigation involving 201 Russian students with different mathematic abilities, attending elementary school. These students were presented with a number of different series of mathematic problems and their mathematic abilities were observed during the problem solving process. In our survey we carried out case studies exploring mathematic problem solving involving 13 students from the Federal University of Mato Grosso with 9 students from the Mathematics/Education course and 4 students from the Computer Sciences Course. The exploratory survey was organized into 3 phases. The first was the completion of a questionnaire with subjective questions about Mathematics and preferred ways of thinking and dealing with this subject. The second phase was reserved for the solution of 13 varied mathematical problems. The final phase was the completion of another questionnaire with subjective questions which sought to obtain information about the experiences of the students when solving the problems set. With our exploratory survey we were able to document and verify several parameters and characteristics of mathematical thinking which were described in the theoretical chapters as well as being able identify the problems themselves and the experience of solving them also influenced mathematical thinking. As a general result we concluded that mathematical thinking must be considered in the light of different parameters since this can help to characterize more complete mathematical thinkingA presente Tese de Doutorado pretende indicar características e dimensões do pensamento matemático, em termos teóricos e experimentais, que podem ser úteis aos professores no que se refere aos processos de ensino, ao desenvolvimento de idéias matemáticas e ao delineamento de contextos de aprendizagem. Nosso estudo começou com uma análise detalhada do trabalho de Krutetskii (1968). Esse livro é muito rico em exemplos e reflexões teóricas. No entanto, é um trabalho completamente psicológico e forneceu poucas indicações a respeito dos aspectos mais gerais do conhecimento matemático e do pensamento matemático. Por esse motivo, adicionamos informações detalhadas sobre o trabalho de outros autores como Gowers, Poincaré, Boutroux, Otte e Kurz que acrescentaram outras dimensões que auxiliaram a nossa compreensão da natureza da Matemática. Esses autores se preocuparam com problemas de estilos cognitivos, de diferenças culturais e históricas, de diferenças que são resultados das várias áreas da própria Matemática e distintas formas de representação na Matemática. As dimensões experimentais consistiram na análise de dados obtidos em pesquisas qualitativas com estudantes, sendo uma da literatura (Krutetskii) e outra uma pesquisa exploratória realizada por nós para a presente Tese. Krutetskii realizou uma investigação experimental envolvendo 201 estudantes russos do Ensino Fundamental, com diferentes habilidades matemáticas. A esses estudantes foram propostas diversas séries de problemas matemáticos, em que foram observadas suas habilidades matemáticas durante o processo de resolução. Na nossa pesquisa, realizamos estudos de caso exploratório na resolução de problemas matemáticos envolvendo 13 estudantes da Universidade Federal de Mato Grosso, sendo 09 do Curso de Licenciatura Plena em Matemática e 04 do Curso de Ciências da Computação. A pesquisa exploratória foi organizada em três momentos. O primeiro foi destinado a responder um questionário com perguntas subjetivas acerca da Matemática e de preferências na forma de pensar e de lidar com a mesma. O segundo momento foi reservado para a resolução de 13 problemas matemáticos variados. E o último momento foi destinado para responder a outro questionário com perguntas subjetivas que procurava obter informações sobre a experiência dos estudantes na atividade de resolução dos problemas propostos. Com a nossa pesquisa exploratória pudemos documentar e verificar vários parâmetros e características do pensamento matemático que foram descritos nos capítulos teóricos, bem como identificar que os próprios problemas e as experiências com a resolução dos mesmos também influenciam o pensamento matemático. Como resultado geral, concluímos que o pensamento matemático deve ser considerado sob diferentes parâmetros, pois eles podem auxiliar na caracterização mais completa do pensamento matemáticoCoordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/24138/Aspectos%20do%20Pens%20Matematico%20na%20RP-Segurity%20printing.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBREducaçãoEpistemologiaHistória da Matemáticapensamento matemáticoresolução de problemasrepresentação matemáticaKrutetskii, Vadim Andreevich, 1917-1989 - Crítica e interpretaçãoEducação matemáticaMatemática - Estudo e ensinoEpistemologyMathematic Historymathematical thinkingproblem solvingmathematical representationCNPQ::CIENCIAS HUMANAS::FILOSOFIA::EPISTEMOLOGIAAspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de KrutetskiiAspects of the mathematical thought in the resolution of problems: a contextual presentation of the work of Krutetskiiinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da PUC_SPinstname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPTEXTAspectos do Pens Matematico na RP-Segurity printing.pdf.txtAspectos do Pens Matematico na RP-Segurity printing.pdf.txtExtracted texttext/plain750795https://repositorio.pucsp.br/xmlui/bitstream/handle/10914/3/Aspectos%20do%20Pens%20Matematico%20na%20RP-Segurity%20printing.pdf.txt3e37662d5db8ef9877c39ec6b6bc980fMD53ORIGINALAspectos do Pens Matematico na RP-Segurity printing.pdfapplication/pdf2060132https://repositorio.pucsp.br/xmlui/bitstream/handle/10914/1/Aspectos%20do%20Pens%20Matematico%20na%20RP-Segurity%20printing.pdfc0711be8b2de82245dd639a3d704a6beMD51THUMBNAILAspectos do Pens Matematico na RP-Segurity printing.pdf.jpgAspectos do Pens Matematico na RP-Segurity printing.pdf.jpgGenerated Thumbnailimage/jpeg1943https://repositorio.pucsp.br/xmlui/bitstream/handle/10914/2/Aspectos%20do%20Pens%20Matematico%20na%20RP-Segurity%20printing.pdf.jpgcc73c4c239a4c332d642ba1e7c7a9fb2MD52handle/109142022-04-27 13:03:51.481oai:repositorio.pucsp.br:handle/10914Biblioteca Digital de Teses e Dissertaçõeshttps://sapientia.pucsp.br/https://sapientia.pucsp.br/oai/requestbngkatende@pucsp.br||rapassi@pucsp.bropendoar:2022-04-27T16:03:51Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.por.fl_str_mv |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
dc.title.alternative.eng.fl_str_mv |
Aspects of the mathematical thought in the resolution of problems: a contextual presentation of the work of Krutetskii |
title |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
spellingShingle |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii Wielewski, Gladys Denise Epistemologia História da Matemática pensamento matemático resolução de problemas representação matemática Krutetskii, Vadim Andreevich, 1917-1989 - Crítica e interpretação Educação matemática Matemática - Estudo e ensino Epistemology Mathematic History mathematical thinking problem solving mathematical representation CNPQ::CIENCIAS HUMANAS::FILOSOFIA::EPISTEMOLOGIA |
title_short |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
title_full |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
title_fullStr |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
title_full_unstemmed |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
title_sort |
Aspectos do pensamento matemático na resolução de problemas: uma apresentação contextualizada da obra de Krutetskii |
author |
Wielewski, Gladys Denise |
author_facet |
Wielewski, Gladys Denise |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Otte, Michael |
dc.contributor.advisor-co1.fl_str_mv |
Franchi, Anna |
dc.contributor.author.fl_str_mv |
Wielewski, Gladys Denise |
contributor_str_mv |
Otte, Michael Franchi, Anna |
dc.subject.por.fl_str_mv |
Epistemologia História da Matemática pensamento matemático resolução de problemas representação matemática Krutetskii, Vadim Andreevich, 1917-1989 - Crítica e interpretação Educação matemática Matemática - Estudo e ensino |
topic |
Epistemologia História da Matemática pensamento matemático resolução de problemas representação matemática Krutetskii, Vadim Andreevich, 1917-1989 - Crítica e interpretação Educação matemática Matemática - Estudo e ensino Epistemology Mathematic History mathematical thinking problem solving mathematical representation CNPQ::CIENCIAS HUMANAS::FILOSOFIA::EPISTEMOLOGIA |
dc.subject.eng.fl_str_mv |
Epistemology Mathematic History mathematical thinking problem solving mathematical representation |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS HUMANAS::FILOSOFIA::EPISTEMOLOGIA |
description |
This doctorate thesis aims to identify the characteristics and the dimensions of mathematical thinking in experimental and theoretical terms which may be useful to teachers with respect to teaching processes, development of mathematical ideas and the delineation of learning contexts. Our study began with a detailed analysis of the work of Krutetskii (1968). This book is very rich in theoretical examples and reflections. It is, however, a completely psychological work and provided few indications of the more general mathematic knowledge and thinking. For this reason we added detailed information about the work of other authors such as Gowers, Poincaré, Boutroux, Otte and Kurz, and this added other dimensions which assisted our understanding of the nature of mathematics. These authors were concerned with the problems of cognitive styles, cultural and historical differences, differences that are the results of mathematics itself and distinctive ways of representing mathematics. The experimental dimensions consisted of analysis of data obtained from qualitative research with students whereby one was taken from the literature (Krutetskii) and the other an exploratory survey which we carried out for the purposes of this thesis. Krutetskii carried out an experimental investigation involving 201 Russian students with different mathematic abilities, attending elementary school. These students were presented with a number of different series of mathematic problems and their mathematic abilities were observed during the problem solving process. In our survey we carried out case studies exploring mathematic problem solving involving 13 students from the Federal University of Mato Grosso with 9 students from the Mathematics/Education course and 4 students from the Computer Sciences Course. The exploratory survey was organized into 3 phases. The first was the completion of a questionnaire with subjective questions about Mathematics and preferred ways of thinking and dealing with this subject. The second phase was reserved for the solution of 13 varied mathematical problems. The final phase was the completion of another questionnaire with subjective questions which sought to obtain information about the experiences of the students when solving the problems set. With our exploratory survey we were able to document and verify several parameters and characteristics of mathematical thinking which were described in the theoretical chapters as well as being able identify the problems themselves and the experience of solving them also influenced mathematical thinking. As a general result we concluded that mathematical thinking must be considered in the light of different parameters since this can help to characterize more complete mathematical thinking |
publishDate |
2005 |
dc.date.available.fl_str_mv |
2005-11-10 |
dc.date.issued.fl_str_mv |
2005-11-11 |
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2016-04-27T16:57:16Z |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/doctoralThesis |
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Wielewski, Gladys Denise. Aspects of the mathematical thought in the resolution of problems: a contextual presentation of the work of Krutetskii. 2005. 407 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2005. |
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https://tede2.pucsp.br/handle/handle/10914 |
identifier_str_mv |
Wielewski, Gladys Denise. Aspects of the mathematical thought in the resolution of problems: a contextual presentation of the work of Krutetskii. 2005. 407 f. Tese (Doutorado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2005. |
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