O design e o uso de um micromundo musical para explorar relações multiplicativas
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da PUC_SP |
Texto Completo: | https://tede2.pucsp.br/handle/handle/11244 |
Resumo: | The aim of this work was to design and evaluate a musical microworld, created to enable users to explore concepts related to multiplication. Inspired by the constructionist perspective of Papert, the study evolved from the conjecture that by engaging in the construction of a musical rhythm, learners could interact with various aspects of the multiplicative field. To investigate this conjecture, a teaching experiment of two phases was conceived. The analyses in both these phases were based on the distinction made in the research of Confrey between the world of counting and the world of splitting. In the design phase, attention was given to the aspects of the microworld that might permit learners to construct conceptions that go beyond a vision of multiplication as repeated addition. The experimentation phase involved two groups of six students of the 5th Grade of a school within the public education system in the city of São Paulo. Using as their bases the interactions of students during the construction of their own rhythmic compositions, the analyses explored the different ways through which the learners made use of tools of the microworld and, in particular, the ways they chose to represent and express ideas related to notions such as ratio and proportion. The results suggest that, with the support of these tools, the learners gradually came to associate their musical activities with mathematical properties and concepts. They also showed how, during the experiment, the learners were enabled to explore the relations half and double within a perspective coherent with the world of splitting, as well as to use a diverse set of representations of these two relations |
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Healy, Siobhan VictoriaRibeiro, Edith Valladão Campos2016-04-27T16:58:23Z2008-01-072007-05-25Ribeiro, Edith Valladão Campos. O design e o uso de um micromundo musical para explorar relações multiplicativas. 2007. 225 f. Dissertação (Mestrado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2007.https://tede2.pucsp.br/handle/handle/11244The aim of this work was to design and evaluate a musical microworld, created to enable users to explore concepts related to multiplication. Inspired by the constructionist perspective of Papert, the study evolved from the conjecture that by engaging in the construction of a musical rhythm, learners could interact with various aspects of the multiplicative field. To investigate this conjecture, a teaching experiment of two phases was conceived. The analyses in both these phases were based on the distinction made in the research of Confrey between the world of counting and the world of splitting. In the design phase, attention was given to the aspects of the microworld that might permit learners to construct conceptions that go beyond a vision of multiplication as repeated addition. The experimentation phase involved two groups of six students of the 5th Grade of a school within the public education system in the city of São Paulo. Using as their bases the interactions of students during the construction of their own rhythmic compositions, the analyses explored the different ways through which the learners made use of tools of the microworld and, in particular, the ways they chose to represent and express ideas related to notions such as ratio and proportion. The results suggest that, with the support of these tools, the learners gradually came to associate their musical activities with mathematical properties and concepts. They also showed how, during the experiment, the learners were enabled to explore the relations half and double within a perspective coherent with the world of splitting, as well as to use a diverse set of representations of these two relationsEste trabalho tem como objetivo o design e a avaliação de um micromundo musical para a exploração de conceitos multiplicativos. Dentro de uma perspectiva construcionista, partiu-se da hipótese de que, no contexto da construção de um ritmo musical, os aprendizes possam interagir com diferentes aspectos do campo multiplicativo. Foi elaborado um experimento de ensino composto por duas fases: a fase de design do micromundo e a fase de experimentação. As análises em ambas as fases foram baseadas na distinção feita nas pesquisas de Confrey entre o mundo da contagem e o mundo de splitting. Na fase de design, a atenção foi dada aos aspetos do micromundo que permitissem os aprendizes ampliar as concepções do campo multiplicativo, indo além de uma visão de multiplicação como adição repetida. A fase de experimentação contou com dois grupos de seis alunos da 5.ª série do Ensino Fundamental de uma escola pública localizada na cidade de São Paulo. Por meio das interações dos estudantes durante a construção de suas próprias composições rítmicas, as análises exploraram as diferentes maneiras pelas quais os aprendizes interagiram com as ferramentas do micromundo e em particular as formas utilizadas para expressar concepções relativas a noções, tais como razão e proporção. Como resultado, foi observado que, com o apoio destas ferramentas, os alunos gradualmente associaram suas atividades musicais com propriedades e conceitos matemáticos. Em particular, todos os alunos conseguiram, ao longo do experimento, explorar as relações de dobro e metade em uma perspectiva coerente com o mundo de splitting e utilizaram uma variedade de formas para representar estas relaçõesapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/23191/edith%20desp.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBREducaçãoMicromundo musicalConceitos multiplicativosConstrucionismoExperimento de ensinoEducacao matematicaMatematica -- Estudo e ensinoMusical microworldMultiplicative conceptsConstructionismTeaching experimentCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO design e o uso de um micromundo musical para explorar relações multiplicativasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da PUC_SPinstname:Pontifícia Universidade Católica de São Paulo (PUC-SP)instacron:PUC_SPTEXTedith desp.pdf.txtedith desp.pdf.txtExtracted texttext/plain268315https://repositorio.pucsp.br/xmlui/bitstream/handle/11244/3/edith%20desp.pdf.txt28e3fa052e5f1d8ee9aa6bc78c88150aMD53ORIGINALedith desp.pdfapplication/pdf9443168https://repositorio.pucsp.br/xmlui/bitstream/handle/11244/1/edith%20desp.pdf373751b634881d1df27b702d1636cc5aMD51THUMBNAILedith desp.pdf.jpgedith desp.pdf.jpgGenerated Thumbnailimage/jpeg3481https://repositorio.pucsp.br/xmlui/bitstream/handle/11244/2/edith%20desp.pdf.jpgb4d71e6869f06ca50901e0a6b74c8513MD52handle/112442022-04-28 05:35:54.398oai:repositorio.pucsp.br:handle/11244Biblioteca Digital de Teses e Dissertaçõeshttps://sapientia.pucsp.br/https://sapientia.pucsp.br/oai/requestbngkatende@pucsp.br||rapassi@pucsp.bropendoar:2022-04-28T08:35:54Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP)false |
dc.title.por.fl_str_mv |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
title |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
spellingShingle |
O design e o uso de um micromundo musical para explorar relações multiplicativas Ribeiro, Edith Valladão Campos Micromundo musical Conceitos multiplicativos Construcionismo Experimento de ensino Educacao matematica Matematica -- Estudo e ensino Musical microworld Multiplicative concepts Constructionism Teaching experiment CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
title_full |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
title_fullStr |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
title_full_unstemmed |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
title_sort |
O design e o uso de um micromundo musical para explorar relações multiplicativas |
author |
Ribeiro, Edith Valladão Campos |
author_facet |
Ribeiro, Edith Valladão Campos |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Healy, Siobhan Victoria |
dc.contributor.author.fl_str_mv |
Ribeiro, Edith Valladão Campos |
contributor_str_mv |
Healy, Siobhan Victoria |
dc.subject.por.fl_str_mv |
Micromundo musical Conceitos multiplicativos Construcionismo Experimento de ensino Educacao matematica Matematica -- Estudo e ensino |
topic |
Micromundo musical Conceitos multiplicativos Construcionismo Experimento de ensino Educacao matematica Matematica -- Estudo e ensino Musical microworld Multiplicative concepts Constructionism Teaching experiment CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Musical microworld Multiplicative concepts Constructionism Teaching experiment |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
The aim of this work was to design and evaluate a musical microworld, created to enable users to explore concepts related to multiplication. Inspired by the constructionist perspective of Papert, the study evolved from the conjecture that by engaging in the construction of a musical rhythm, learners could interact with various aspects of the multiplicative field. To investigate this conjecture, a teaching experiment of two phases was conceived. The analyses in both these phases were based on the distinction made in the research of Confrey between the world of counting and the world of splitting. In the design phase, attention was given to the aspects of the microworld that might permit learners to construct conceptions that go beyond a vision of multiplication as repeated addition. The experimentation phase involved two groups of six students of the 5th Grade of a school within the public education system in the city of São Paulo. Using as their bases the interactions of students during the construction of their own rhythmic compositions, the analyses explored the different ways through which the learners made use of tools of the microworld and, in particular, the ways they chose to represent and express ideas related to notions such as ratio and proportion. The results suggest that, with the support of these tools, the learners gradually came to associate their musical activities with mathematical properties and concepts. They also showed how, during the experiment, the learners were enabled to explore the relations half and double within a perspective coherent with the world of splitting, as well as to use a diverse set of representations of these two relations |
publishDate |
2007 |
dc.date.issued.fl_str_mv |
2007-05-25 |
dc.date.available.fl_str_mv |
2008-01-07 |
dc.date.accessioned.fl_str_mv |
2016-04-27T16:58:23Z |
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.citation.fl_str_mv |
Ribeiro, Edith Valladão Campos. O design e o uso de um micromundo musical para explorar relações multiplicativas. 2007. 225 f. Dissertação (Mestrado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2007. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/11244 |
identifier_str_mv |
Ribeiro, Edith Valladão Campos. O design e o uso de um micromundo musical para explorar relações multiplicativas. 2007. 225 f. Dissertação (Mestrado em Educação) - Pontifícia Universidade Católica de São Paulo, São Paulo, 2007. |
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Pontifícia Universidade Católica de São Paulo |
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Programa de Estudos Pós-Graduados em Educação Matemática |
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PUC-SP |
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BR |
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Educação |
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Pontifícia Universidade Católica de São Paulo |
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