Fundamentals guiding mathematics education theories: perspectives and diversity

Detalhes bibliográficos
Autor(a) principal: Almouloud, Saddo Ag
Data de Publicação: 2017
Tipo de documento: Artigo
Idioma: por
Título da fonte: Amazônia (Universidade Federal do Pará. Online)
Texto Completo: https://periodicos.ufpa.br/index.php/revistaamazonia/article/view/5514
Resumo: The aim of the present text is to reflect on controversies about the plurality of theories that support the area of mathematics education and what is considered fundamental in its constitution as a scientific field. Furthermore, it brings to light some theoretical bases of mathematics education, in order to compare the diversity of its approaches. We divide the text in three parts to provide a better insight into the central ideas of each one of them. The first deals with mathematics education as a field of knowledge. In the second part, we discuss the fundamentals of mathematics education and the diversity in approaches. In the third part, we present a discussion and a synthesis of the different theoretical constructs discussed in the first two parts, focusing, at the end of the text, on some aspects of the Didactic Anthropological Theory. This study, although not exhaustive, allows a comprehensive view of the various existing theories related to mathematics teaching and learning. The diversity of theories and the specificities of each of them confirm the idea that a single theory, or a single model, can hardly explain and reveal all the phenomena involved in the processes of teaching and learning mathematics. The researcher should pursue sound knowledge of the main ideas of the different theories so that they can identify which of them they can use to refer theoretically their research.
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spelling Fundamentals guiding mathematics education theories: perspectives and diversityFundamentos norteadores das teorias da Educação Matemática: perspectivas e diversidademathematics education; teaching and learning; plurality of theories in mathematics educationeducação matemática; ensino e aprendizagem; pluralidade de teorias da educação matemáticaThe aim of the present text is to reflect on controversies about the plurality of theories that support the area of mathematics education and what is considered fundamental in its constitution as a scientific field. Furthermore, it brings to light some theoretical bases of mathematics education, in order to compare the diversity of its approaches. We divide the text in three parts to provide a better insight into the central ideas of each one of them. The first deals with mathematics education as a field of knowledge. In the second part, we discuss the fundamentals of mathematics education and the diversity in approaches. In the third part, we present a discussion and a synthesis of the different theoretical constructs discussed in the first two parts, focusing, at the end of the text, on some aspects of the Didactic Anthropological Theory. This study, although not exhaustive, allows a comprehensive view of the various existing theories related to mathematics teaching and learning. The diversity of theories and the specificities of each of them confirm the idea that a single theory, or a single model, can hardly explain and reveal all the phenomena involved in the processes of teaching and learning mathematics. The researcher should pursue sound knowledge of the main ideas of the different theories so that they can identify which of them they can use to refer theoretically their research.O presente texto tem por objetivo tecer reflexões acerca de controvérsias sobre a pluralidade de teorias que veem sustentando a área de Educação Matemática e o que é considerado fundamental em sua constituição como campo científico. Além disso, traz à luz alguns fundamentos teóricos da Educação Matemática, com o intuito de comparar a diversidade de seus enfoques. Dividimos o texto em três partes a fim de proporcionar uma melhor visão das ideias centrais de cada uma. A primeira tratamos da Educação Matemática como campo de conhecimento, na segunda parte, discutimos os fundamentos da Educação Matemática e a diversidade nos enfoques. Na terceira parte apresentamos uma discussão e uma síntese dos diferentes construtos teóricos discutidos nas duas primeiras partes, focando no final do texto alguns aspectos da Teoria Antropológica do Didático. Este estudo, apesar de não exaustivo, permite obter uma visão abrangente das diversas teorias existentes, relacionadas ao ensino e à aprendizagem de matemática. A diversidade de teorias e as especificidades de cada uma delas vêm confirmar a ideia de que uma única teoria, ou um único modelo, dificilmente dá conta de explicar e explicitar todos os fenômenos envolvidos nos processos de ensino e de aprendizagem de matemática. O pesquisador deve procurar conhecer bem as ideias principais das diversas teorias, de modo a poder identificar quais delas poderá usar para referenciar teoricamente sua pesquisa.Universidade Federal do ParáAlmouloud, Saddo Ag2017-09-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufpa.br/index.php/revistaamazonia/article/view/551410.18542/amazrecm.v13i27.5514Amazônia: Revista de Educação em Ciências e Matemáticas; v. 13, n. 27 (2017): Especial Teoria Antropológica do Didático; 5-35Amazônia - Journal of Science and Mathematics Education; v. 13, n. 27 (2017): Especial Teoria Antropológica do Didático; 5-352317-51251980-5128reponame:Amazônia (Universidade Federal do Pará. Online)instname:Universidade Federal do Pará (UFPA)instacron:UFPAporhttps://periodicos.ufpa.br/index.php/revistaamazonia/article/view/5514/4561/*ref*/ALMOULOUD, Saddo Ag. Fundamentos da didática da matemática. Curitiba: Ed. UFPR, 2007./*ref*/ARTAUD, M ( ) Introduction à l’approche écologique du didactique, L’écologie des organisation mathématiques et didactiques. InC. Comitictal. ( ) Actes de la IXè école d’été de didactique des mathématiques, Houlgate, pp. 101-119./*ref*/BAGES, Sébastien. Qu’est-ce qu’une Théorie Scientifique ? (in http://civilisation2.org/questce-quune-theorie-scientifique/ , acessado no dia 12/12/2014), 13 de março de 2012./*ref*/BARQUERO, B., BOSCH, M. e GASCÓN, J. Ecología de la modelización matemática: Restricciones transpositivas en las instituciones universitarias. communication au 2e congrès TAD, Uzès 2007./*ref*/BARQUERO, B., BOSCH, M. e GASCÓN, J. Ecología de la Modelización Matemática: los Recorridos de Estudio e Investigación - III International Conference on the Anthropological Theory of the Didactic, 2010./*ref*/BARQUERO, B., BOSCH, M. e GASCÓN, J. Las tres dimensiones del problema didáctico de la modelización matemática. Educação Matemática e Pesquisa, São Paulo, v.15, n.1, pp.1-28, 2013./*ref*/BOSCH, Marianna; GASCON, Josep. Las prácticas docentes del profesor de matemáticas. XIème École d'Été de Didactique des Mathématiques. Agosto de 2001./*ref*/BOSCH, Marianna. CHEVALLARD, Yves e GASCÓN, Josep. Science or magic? The use of models and theories in didactics of mathematics. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 2006./*ref*/BOSCH, Marianna. Un Punto de Vista Antropológico: la evolución de los “instrumentos de representación” en la actividad matemática. Cuarto Simposio de la Sociedad Española de Investigación en Educación Matemática. pp. 15-28. Espanha, 2001./*ref*/BOSCH, Marianna; FONSECA, Cecílio; GASCÓN, Josep. Incompletitud de las organizaciones matemáticas locales em las instituciones escolares. In: Recherches en Didactique des Mathématiques, v. 24/2.3, Grenoble, França: La Pensée Sauvage, 2004, p. 205-250./*ref*/BOSCH, Marianna, CHEVALLARD, Yves. La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique. Recherches en Didactique des Mathématiques. Grenoble : La Pensée Sauvage-Éditions, v.19, n°1, p.77-124, 1999./*ref*/BROUSSEAU, Guy. Fondements et méthodes de la didactique des mathématiques. Recherches en Didactique des Mathématiques. Grenoble : La Pensée Sauvage, v.7, n°2, p.33-115, 1986./*ref*/BROUSSEAU, Guy. Théorie des situations didactiques. Textes rassemblés et préparés par Nicolas Balacheff, Martin Cooper, Rosamund Sutherland, Virginia Warflied, Grenoble : La Pensée Sauvage éditions, 1998./*ref*/CHEVALLARD, Yves. L´analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques. Grenoble: La Pensée SauvageÉditions, v. 19.2, p.221-265, 1999./*ref*/CHEVALLARD, Yves. Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques. Grenoble : La Pensée Sauvage-Éditions, v. 12.1, p.73-112, 1992./*ref*/CHEVALLARD, Yves. Organiser l´étude. 1. Structures & Fonctions. Actes de la 11 École d´Été de Didactique des Mathématiques. France : La Pensée Sauvage. 2002. Versão eletronica./*ref*/CHEVALLARD, Yves. Organiser l´étude. 3. Ecologie & régulation. Actes de la 11 École d´Été de Didactique des Mathématiques. France : La Pensée Sauvage. p. 41-55, 2002./*ref*/CHEVALLARD, Yves, JOHSUA, M. A. La transposition didactique. Grenoble : La Pensée Sauvage-Éditions, 1991./*ref*/ENGLISH, L.; SRIRAMAN, B. (coord.) RF04: Theories of Mathematics Education. In: Chick, H. L. & Vincent, J. L. (Eds.) Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 170-202. Melbourne: PME, 2003. Disponível em: http://www.emis.de/proceedings/PME29/PME29CompleteProc/PME29Vol1Complete.pdf (Acesso em: 25 jun. 2012.)/*ref*/LERMAN, S. Theories of Mathematics Education: Is Plurality a Problem?. In: SRIRAMAN, B.; ENGLISH, L. Theories of Mathematics Education Advances in Mathematics Education. SPRINGER, 2010, pp. 97-117./*ref*/PEGG, J.; TALL, D. The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks. In: SRIRAMAN, B.; ENGLISH, L. Theories of Mathematics Education Advances in Mathematics Education. SPRINGER, 2010, pp.173-192./*ref*/PERRIN-GLORIAN, M.J. (1994). Théorie des situations didactiques: naissance, développement, perspectives, in Artigue, M. & al.(org.): Vingt ans de didactique des mathématiques en France. Recherches en Didactiques des Mathématiques. Grenoble: La Pensée Sauvage Editions, p.96-147./*ref*/PERRIN-GLORIAN, M.J (1995). Utilisation de la notion de obstacule en didatique des mathematiques. Grenoble: Séminaire de l’IUFM de Grenoble./*ref*/PERRIN-GLORIAN, M.J (1986). Représentation des fractions et des nombres décimaux chez les élèves du CM2 et du collège, Cahier de Didactique des Mathématiques. Paris: IREM Paris 7, v.24./*ref*/ROBERT, A. Les recherches surl es pratiques des enseignants et contraintes de l´exercice du métier d´enseignant. Recherches en Didactique des Mathématiques. 2001, 21/1.2, p. 5780./*ref*/SFARD, A. On the dual nature of Mathematical Conceptions: Reflections on Process and Objects as Different Sides of The Same Coin. Netherlands: Kluwer Academic Publishers. Educational Studies in Mathematics 22, pp. 1-36, 1991./*ref*/SRIRAMAN, B.; ENGLISH, L. Surveying Theories and Philosophies of Mathematics Education. In: SRIRAMAN, B.; ENGLISH, L. Theories of Mathematics Education Advances in Mathematics Education. SPRINGER, 2010, pp. 3-32./*ref*/TALL, D. Reflections on APOS theory in Elementary and Advanced Mathematical Thinking. PME 23, Haifa, Israel, julho, 1999. Disponível em: (Acesso em: 26 junho 2012 )/*ref*/WIKIPÉDIA. Teoria cientifica (In http://pt.wikipedia.org/wiki/Teoria, acessado no dia 12/12/2014).Direitos autorais 2017 Amazônia: Revista de Educação em Ciências e Matemáticashttp://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccess2021-01-21T13:24:06Zoai:ojs.periodicos.ufpa.br:article/5514Revistahttp://www.periodicos.ufpa.br/index.php/revistaamazoniaPUBhttps://periodicos.ufpa.br/index.php/revistaamazonia/oaiamazrecm@ufpa.br||brabo@ufpa.br||amazoniaeducimat@yahoo.com.br2317-51251980-5128opendoar:2021-01-21T13:24:06Amazônia (Universidade Federal do Pará. Online) - Universidade Federal do Pará (UFPA)false
dc.title.none.fl_str_mv Fundamentals guiding mathematics education theories: perspectives and diversity
Fundamentos norteadores das teorias da Educação Matemática: perspectivas e diversidade
title Fundamentals guiding mathematics education theories: perspectives and diversity
spellingShingle Fundamentals guiding mathematics education theories: perspectives and diversity
Almouloud, Saddo Ag
mathematics education; teaching and learning; plurality of theories in mathematics education
educação matemática; ensino e aprendizagem; pluralidade de teorias da educação matemática
title_short Fundamentals guiding mathematics education theories: perspectives and diversity
title_full Fundamentals guiding mathematics education theories: perspectives and diversity
title_fullStr Fundamentals guiding mathematics education theories: perspectives and diversity
title_full_unstemmed Fundamentals guiding mathematics education theories: perspectives and diversity
title_sort Fundamentals guiding mathematics education theories: perspectives and diversity
author Almouloud, Saddo Ag
author_facet Almouloud, Saddo Ag
author_role author
dc.contributor.none.fl_str_mv

dc.contributor.author.fl_str_mv Almouloud, Saddo Ag
dc.subject.por.fl_str_mv mathematics education; teaching and learning; plurality of theories in mathematics education
educação matemática; ensino e aprendizagem; pluralidade de teorias da educação matemática
topic mathematics education; teaching and learning; plurality of theories in mathematics education
educação matemática; ensino e aprendizagem; pluralidade de teorias da educação matemática
description The aim of the present text is to reflect on controversies about the plurality of theories that support the area of mathematics education and what is considered fundamental in its constitution as a scientific field. Furthermore, it brings to light some theoretical bases of mathematics education, in order to compare the diversity of its approaches. We divide the text in three parts to provide a better insight into the central ideas of each one of them. The first deals with mathematics education as a field of knowledge. In the second part, we discuss the fundamentals of mathematics education and the diversity in approaches. In the third part, we present a discussion and a synthesis of the different theoretical constructs discussed in the first two parts, focusing, at the end of the text, on some aspects of the Didactic Anthropological Theory. This study, although not exhaustive, allows a comprehensive view of the various existing theories related to mathematics teaching and learning. The diversity of theories and the specificities of each of them confirm the idea that a single theory, or a single model, can hardly explain and reveal all the phenomena involved in the processes of teaching and learning mathematics. The researcher should pursue sound knowledge of the main ideas of the different theories so that they can identify which of them they can use to refer theoretically their research.
publishDate 2017
dc.date.none.fl_str_mv 2017-09-30
dc.type.none.fl_str_mv
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info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.ufpa.br/index.php/revistaamazonia/article/view/5514
10.18542/amazrecm.v13i27.5514
url https://periodicos.ufpa.br/index.php/revistaamazonia/article/view/5514
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dc.language.iso.fl_str_mv por
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dc.relation.none.fl_str_mv https://periodicos.ufpa.br/index.php/revistaamazonia/article/view/5514/4561
/*ref*/ALMOULOUD, Saddo Ag. Fundamentos da didática da matemática. Curitiba: Ed. UFPR, 2007.
/*ref*/ARTAUD, M ( ) Introduction à l’approche écologique du didactique, L’écologie des organisation mathématiques et didactiques. InC. Comitictal. ( ) Actes de la IXè école d’été de didactique des mathématiques, Houlgate, pp. 101-119.
/*ref*/BAGES, Sébastien. Qu’est-ce qu’une Théorie Scientifique ? (in http://civilisation2.org/questce-quune-theorie-scientifique/ , acessado no dia 12/12/2014), 13 de março de 2012.
/*ref*/BARQUERO, B., BOSCH, M. e GASCÓN, J. Ecología de la modelización matemática: Restricciones transpositivas en las instituciones universitarias. communication au 2e congrès TAD, Uzès 2007.
/*ref*/BARQUERO, B., BOSCH, M. e GASCÓN, J. Ecología de la Modelización Matemática: los Recorridos de Estudio e Investigación - III International Conference on the Anthropological Theory of the Didactic, 2010.
/*ref*/BARQUERO, B., BOSCH, M. e GASCÓN, J. Las tres dimensiones del problema didáctico de la modelización matemática. Educação Matemática e Pesquisa, São Paulo, v.15, n.1, pp.1-28, 2013.
/*ref*/BOSCH, Marianna; GASCON, Josep. Las prácticas docentes del profesor de matemáticas. XIème École d'Été de Didactique des Mathématiques. Agosto de 2001.
/*ref*/BOSCH, Marianna. CHEVALLARD, Yves e GASCÓN, Josep. Science or magic? The use of models and theories in didactics of mathematics. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 2006.
/*ref*/BOSCH, Marianna. Un Punto de Vista Antropológico: la evolución de los “instrumentos de representación” en la actividad matemática. Cuarto Simposio de la Sociedad Española de Investigación en Educación Matemática. pp. 15-28. Espanha, 2001.
/*ref*/BOSCH, Marianna; FONSECA, Cecílio; GASCÓN, Josep. Incompletitud de las organizaciones matemáticas locales em las instituciones escolares. In: Recherches en Didactique des Mathématiques, v. 24/2.3, Grenoble, França: La Pensée Sauvage, 2004, p. 205-250.
/*ref*/BOSCH, Marianna, CHEVALLARD, Yves. La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique. Recherches en Didactique des Mathématiques. Grenoble : La Pensée Sauvage-Éditions, v.19, n°1, p.77-124, 1999.
/*ref*/BROUSSEAU, Guy. Fondements et méthodes de la didactique des mathématiques. Recherches en Didactique des Mathématiques. Grenoble : La Pensée Sauvage, v.7, n°2, p.33-115, 1986.
/*ref*/BROUSSEAU, Guy. Théorie des situations didactiques. Textes rassemblés et préparés par Nicolas Balacheff, Martin Cooper, Rosamund Sutherland, Virginia Warflied, Grenoble : La Pensée Sauvage éditions, 1998.
/*ref*/CHEVALLARD, Yves. L´analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques. Grenoble: La Pensée SauvageÉditions, v. 19.2, p.221-265, 1999.
/*ref*/CHEVALLARD, Yves. Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques. Grenoble : La Pensée Sauvage-Éditions, v. 12.1, p.73-112, 1992.
/*ref*/CHEVALLARD, Yves. Organiser l´étude. 1. Structures & Fonctions. Actes de la 11 École d´Été de Didactique des Mathématiques. France : La Pensée Sauvage. 2002. Versão eletronica.
/*ref*/CHEVALLARD, Yves. Organiser l´étude. 3. Ecologie & régulation. Actes de la 11 École d´Été de Didactique des Mathématiques. France : La Pensée Sauvage. p. 41-55, 2002.
/*ref*/CHEVALLARD, Yves, JOHSUA, M. A. La transposition didactique. Grenoble : La Pensée Sauvage-Éditions, 1991.
/*ref*/ENGLISH, L.; SRIRAMAN, B. (coord.) RF04: Theories of Mathematics Education. In: Chick, H. L. & Vincent, J. L. (Eds.) Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 170-202. Melbourne: PME, 2003. Disponível em: http://www.emis.de/proceedings/PME29/PME29CompleteProc/PME29Vol1Complete.pdf (Acesso em: 25 jun. 2012.)
/*ref*/LERMAN, S. Theories of Mathematics Education: Is Plurality a Problem?. In: SRIRAMAN, B.; ENGLISH, L. Theories of Mathematics Education Advances in Mathematics Education. SPRINGER, 2010, pp. 97-117.
/*ref*/PEGG, J.; TALL, D. The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks. In: SRIRAMAN, B.; ENGLISH, L. Theories of Mathematics Education Advances in Mathematics Education. SPRINGER, 2010, pp.173-192.
/*ref*/PERRIN-GLORIAN, M.J. (1994). Théorie des situations didactiques: naissance, développement, perspectives, in Artigue, M. & al.(org.): Vingt ans de didactique des mathématiques en France. Recherches en Didactiques des Mathématiques. Grenoble: La Pensée Sauvage Editions, p.96-147.
/*ref*/PERRIN-GLORIAN, M.J (1995). Utilisation de la notion de obstacule en didatique des mathematiques. Grenoble: Séminaire de l’IUFM de Grenoble.
/*ref*/PERRIN-GLORIAN, M.J (1986). Représentation des fractions et des nombres décimaux chez les élèves du CM2 et du collège, Cahier de Didactique des Mathématiques. Paris: IREM Paris 7, v.24.
/*ref*/ROBERT, A. Les recherches surl es pratiques des enseignants et contraintes de l´exercice du métier d´enseignant. Recherches en Didactique des Mathématiques. 2001, 21/1.2, p. 5780.
/*ref*/SFARD, A. On the dual nature of Mathematical Conceptions: Reflections on Process and Objects as Different Sides of The Same Coin. Netherlands: Kluwer Academic Publishers. Educational Studies in Mathematics 22, pp. 1-36, 1991.
/*ref*/SRIRAMAN, B.; ENGLISH, L. Surveying Theories and Philosophies of Mathematics Education. In: SRIRAMAN, B.; ENGLISH, L. Theories of Mathematics Education Advances in Mathematics Education. SPRINGER, 2010, pp. 3-32.
/*ref*/TALL, D. Reflections on APOS theory in Elementary and Advanced Mathematical Thinking. PME 23, Haifa, Israel, julho, 1999. Disponível em: (Acesso em: 26 junho 2012 )
/*ref*/WIKIPÉDIA. Teoria cientifica (In http://pt.wikipedia.org/wiki/Teoria, acessado no dia 12/12/2014).
dc.rights.driver.fl_str_mv Direitos autorais 2017 Amazônia: Revista de Educação em Ciências e Matemáticas
http://creativecommons.org/licenses/by/4.0
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rights_invalid_str_mv Direitos autorais 2017 Amazônia: Revista de Educação em Ciências e Matemáticas
http://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Universidade Federal do Pará
publisher.none.fl_str_mv Universidade Federal do Pará
dc.source.none.fl_str_mv Amazônia: Revista de Educação em Ciências e Matemáticas; v. 13, n. 27 (2017): Especial Teoria Antropológica do Didático; 5-35
Amazônia - Journal of Science and Mathematics Education; v. 13, n. 27 (2017): Especial Teoria Antropológica do Didático; 5-35
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