A cognitive approach to mental representation in mathematical problem solving
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | , |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRJ |
Texto Completo: | http://hdl.handle.net/11422/1897 |
Resumo: | In this paper we investigate mental-representation strategies applied to solve contextual problerns that involve mathematical calculus. We are interested in formal procedures, algorithrms, and strategies that could be used by three groups of peoples: with specific mathematical knowledge (the expert group); without this knowledge (the control group); and without this specific knowledge but acquainted with the designed problem context (the familiar group ). Our investigation demonstrates that the reasoning developments of these three groups are quite different from one to another: in the expert group the reasoning is only based on algorithmic operations; in the control group the reasoning combines algorithm with other mathematical strategies; and the familiar group uses a more intuitive reasoning. probably influenced by their familiarity with the problem context and by their special mental strategies. In this research we aim to come through with Cognitive Science studies on the nature of human knowledge. Mathematical problem resolutions in general and arithmetic calculus in particular are tools very interesting to recognize the difference between expert and beginner knowledge and reasoning. |
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Soares, AdrianaPourbaix, MaridelmaLima, Cabral2017-05-08T15:10:37Z2023-11-30T03:00:27Z2004-12-30SOARES, A.; POURBAIX, M.; LIMA, C. A cognitive approach to mental representation in mathematical problem solving. Rio de Janeiro: NCE/UFRJ, 2002. 5 p. (Relatório Técnico, 10/02)http://hdl.handle.net/11422/1897In this paper we investigate mental-representation strategies applied to solve contextual problerns that involve mathematical calculus. We are interested in formal procedures, algorithrms, and strategies that could be used by three groups of peoples: with specific mathematical knowledge (the expert group); without this knowledge (the control group); and without this specific knowledge but acquainted with the designed problem context (the familiar group ). Our investigation demonstrates that the reasoning developments of these three groups are quite different from one to another: in the expert group the reasoning is only based on algorithmic operations; in the control group the reasoning combines algorithm with other mathematical strategies; and the familiar group uses a more intuitive reasoning. probably influenced by their familiarity with the problem context and by their special mental strategies. In this research we aim to come through with Cognitive Science studies on the nature of human knowledge. Mathematical problem resolutions in general and arithmetic calculus in particular are tools very interesting to recognize the difference between expert and beginner knowledge and reasoning.Submitted by Raquel Porto (raquel@nce.ufrj.br) on 2017-05-08T15:10:37Z No. of bitstreams: 1 10_02_000613394.pdf: 613439 bytes, checksum: c9ac06f24d248c7b943474fe51589e78 (MD5)Made available in DSpace on 2017-05-08T15:10:37Z (GMT). No. of bitstreams: 1 10_02_000613394.pdf: 613439 bytes, checksum: c9ac06f24d248c7b943474fe51589e78 (MD5) Previous issue date: 2004-12-30engRelatório Técnico NCECNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAOCiência cognitivaRepresentação mentalMental representationMathematical reasoningCognitive scienceA cognitive approach to mental representation in mathematical problem solvinginfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/report1002abertoBrasilInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionaisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJORIGINAL10_02_000613394.pdf10_02_000613394.pdfapplication/pdf343830http://pantheon.ufrj.br:80/bitstream/11422/1897/4/10_02_000613394.pdf7820f9d5d29315e956cc36d19f3cd57aMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81853http://pantheon.ufrj.br:80/bitstream/11422/1897/3/license.txtdd32849f2bfb22da963c3aac6e26e255MD53TEXT10_02_000613394.pdf.txt10_02_000613394.pdf.txtExtracted texttext/plain10030http://pantheon.ufrj.br:80/bitstream/11422/1897/5/10_02_000613394.pdf.txt3380e57d645032c9027d2d92eb7c7a28MD5511422/18972023-11-30 00:00:27.61oai:pantheon.ufrj.br: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Repositório de PublicaçõesPUBhttp://www.pantheon.ufrj.br/oai/requestopendoar:2023-11-30T03:00:27Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
dc.title.pt_BR.fl_str_mv |
A cognitive approach to mental representation in mathematical problem solving |
title |
A cognitive approach to mental representation in mathematical problem solving |
spellingShingle |
A cognitive approach to mental representation in mathematical problem solving Soares, Adriana CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Ciência cognitiva Representação mental Mental representation Mathematical reasoning Cognitive science |
title_short |
A cognitive approach to mental representation in mathematical problem solving |
title_full |
A cognitive approach to mental representation in mathematical problem solving |
title_fullStr |
A cognitive approach to mental representation in mathematical problem solving |
title_full_unstemmed |
A cognitive approach to mental representation in mathematical problem solving |
title_sort |
A cognitive approach to mental representation in mathematical problem solving |
author |
Soares, Adriana |
author_facet |
Soares, Adriana Pourbaix, Maridelma Lima, Cabral |
author_role |
author |
author2 |
Pourbaix, Maridelma Lima, Cabral |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Soares, Adriana Pourbaix, Maridelma Lima, Cabral |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Ciência cognitiva Representação mental Mental representation Mathematical reasoning Cognitive science |
dc.subject.por.fl_str_mv |
Ciência cognitiva Representação mental |
dc.subject.eng.fl_str_mv |
Mental representation Mathematical reasoning Cognitive science |
description |
In this paper we investigate mental-representation strategies applied to solve contextual problerns that involve mathematical calculus. We are interested in formal procedures, algorithrms, and strategies that could be used by three groups of peoples: with specific mathematical knowledge (the expert group); without this knowledge (the control group); and without this specific knowledge but acquainted with the designed problem context (the familiar group ). Our investigation demonstrates that the reasoning developments of these three groups are quite different from one to another: in the expert group the reasoning is only based on algorithmic operations; in the control group the reasoning combines algorithm with other mathematical strategies; and the familiar group uses a more intuitive reasoning. probably influenced by their familiarity with the problem context and by their special mental strategies. In this research we aim to come through with Cognitive Science studies on the nature of human knowledge. Mathematical problem resolutions in general and arithmetic calculus in particular are tools very interesting to recognize the difference between expert and beginner knowledge and reasoning. |
publishDate |
2004 |
dc.date.issued.fl_str_mv |
2004-12-30 |
dc.date.accessioned.fl_str_mv |
2017-05-08T15:10:37Z |
dc.date.available.fl_str_mv |
2023-11-30T03:00:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/report |
format |
report |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
SOARES, A.; POURBAIX, M.; LIMA, C. A cognitive approach to mental representation in mathematical problem solving. Rio de Janeiro: NCE/UFRJ, 2002. 5 p. (Relatório Técnico, 10/02) |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11422/1897 |
identifier_str_mv |
SOARES, A.; POURBAIX, M.; LIMA, C. A cognitive approach to mental representation in mathematical problem solving. Rio de Janeiro: NCE/UFRJ, 2002. 5 p. (Relatório Técnico, 10/02) |
url |
http://hdl.handle.net/11422/1897 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Relatório Técnico NCE |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRJ instname:Universidade Federal do Rio de Janeiro (UFRJ) instacron:UFRJ |
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Universidade Federal do Rio de Janeiro (UFRJ) |
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UFRJ |
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UFRJ |
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