Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra
Autor(a) principal: | |
---|---|
Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Biblioteca Digital de Teses e Dissertações do UFSM |
Texto Completo: | http://repositorio.ufsm.br/handle/1/13533 |
Resumo: | This research aimed to answer the following question: “How are the registers of semiotic representation mobilized in the approach of right triangle trigonometry with the help of the GeoGebra software, based on a sequence of activities with students of the 1st grade of high school?”. The sequence of activities was designed with an investigative conception, using the technological resource of GeoGebra, and was developed with a class of students of a public school in Erechim, in the state of Rio Grande do Sul, Brazil. This research is supported by the learning theory of registers of semiotic representation and constituted based on the Didactic Engineering methodology. Data collection was carried out through printed materials, files recorded with the software, and audio media containing the speeches of the students during the interventions. This material was analyzed considering the following categories: a) through mathematical experimentation and the consequent coordination of the various representations made possible by the dynamicity of GeoGebra resources, a program in which several semiotic representations were coordinated (natural language, figural, tabular, numerical, algebraic and symbolic), as well as the analysis of apprehensions (perceptual, discursive and operative); b) by proposing an exploratory approach in mathematics education, based on an environment of dynamic geometry and a sequence of activities with an investigative conception, in which the student‟s autonomy was verified in the accomplishment of the proposed activities, provided by the ease of manipulation of mathematical objects elaborated in GeoGebra; c) through the encouragement of mathematical communication in the classroom, through the preparation of written and verbal justifications, when the natural language register became evident, with the verification of the subjects‟ knowledge acquisition. In addition, the stages of Didactic Engineering, as well as its reflections, were recognized as fundamental for the development of this research and the elaboration of the sequence of activities. In the analysis of the results, it was verified that the students were able to acquire knowledge about the study of right triangle trigonometry. |
id |
UFSM_6f26b28e6aa4fded71e1787eef524245 |
---|---|
oai_identifier_str |
oai:repositorio.ufsm.br:1/13533 |
network_acronym_str |
UFSM |
network_name_str |
Biblioteca Digital de Teses e Dissertações do UFSM |
repository_id_str |
|
spelling |
2018-06-25T21:34:53Z2018-06-25T21:34:53Z2017-10-27http://repositorio.ufsm.br/handle/1/13533This research aimed to answer the following question: “How are the registers of semiotic representation mobilized in the approach of right triangle trigonometry with the help of the GeoGebra software, based on a sequence of activities with students of the 1st grade of high school?”. The sequence of activities was designed with an investigative conception, using the technological resource of GeoGebra, and was developed with a class of students of a public school in Erechim, in the state of Rio Grande do Sul, Brazil. This research is supported by the learning theory of registers of semiotic representation and constituted based on the Didactic Engineering methodology. Data collection was carried out through printed materials, files recorded with the software, and audio media containing the speeches of the students during the interventions. This material was analyzed considering the following categories: a) through mathematical experimentation and the consequent coordination of the various representations made possible by the dynamicity of GeoGebra resources, a program in which several semiotic representations were coordinated (natural language, figural, tabular, numerical, algebraic and symbolic), as well as the analysis of apprehensions (perceptual, discursive and operative); b) by proposing an exploratory approach in mathematics education, based on an environment of dynamic geometry and a sequence of activities with an investigative conception, in which the student‟s autonomy was verified in the accomplishment of the proposed activities, provided by the ease of manipulation of mathematical objects elaborated in GeoGebra; c) through the encouragement of mathematical communication in the classroom, through the preparation of written and verbal justifications, when the natural language register became evident, with the verification of the subjects‟ knowledge acquisition. In addition, the stages of Didactic Engineering, as well as its reflections, were recognized as fundamental for the development of this research and the elaboration of the sequence of activities. In the analysis of the results, it was verified that the students were able to acquire knowledge about the study of right triangle trigonometry.Esta pesquisa procurou responder a seguinte questão: “Como os registros de representação semiótica são mobilizados na abordagem de trigonometria no triângulo retângulo com o auxilio do software GeoGebra, a partir de uma sequência de atividades com alunos do 1º ano do ensino médio?”. A sequência de atividades foi elaborada com um caráter investigativo, tendo sido utilizado o recurso tecnológico GeoGebra e dinamizada junto a uma turma de alunos de uma escola da rede pública estadual do município de Erechim, RS. Esta pesquisa está amparada pela teoria de aprendizagem de registros de representação semiótica e constituída a partir da metodologia da Engenharia Didática. A coleta de dados foi realizada por meio de material impresso, arquivos gravados com o software e mídias de áudios contendo as falas dos estudantes durante as intervenções. Este material, foi analisado considerando-se as seguintes categorias: a) Por meio da experimentação matemática e consequente coordenação das diversas representações viabilizadas pela dinamicidade oportunizada pelos recursos do GeoGebra, onde ocorreu a coordenação de diversas representações semióticas: língua natural, figural, tabular, numérica, algébrica e simbólica; além da análise de apreensões: perceptivas, discursivas e operatórias; b) Mediante a proposição de uma abordagem exploratória no ensino de matemática, pautada em um ambiente de geometria dinâmica e numa sequência de atividades com caráter investigativo, onde constatou-se a autonomia dos alunos na realização das atividades propostas, proporcionadas pela facilidade de manipulação dos objetos matemáticos elaborados no GeoGebra; c) Por meio do incentivo a comunicação matemática em sala de aula mediante a elaboração de justificativas escritas e verbais, ficando evidente o registro em língua natural onde ocorreu a verificação da obtenção do conhecimento do assunto. Também, reconheceu-se como fundamental para o desenvolvimento desta pesquisa e da elaboração da sequência de atividades as etapas presentes na engenharia didática junto de suas reflexões. Sendo que, na análise dos resultados constatou-se que foi viabilizada aos alunos a aquisição de conhecimentos relativos ao estudo de trigonometria no triângulo retângulo.porUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em Educação Matemática e Ensino de FísicaUFSMBrasilEducaçãoAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessTrigonometria no triângulo retânguloGeoGebraRegistros de representação semióticaEngenharia didáticaRight triangle trigonometryGeoGebraRegisters of semiotic representationDidactic engineeringCNPQ::CIENCIAS HUMANAS::EDUCACAOMobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebraMobilizations of records of semiotic representation in the study of trigonometry in triangle rectangle with the aid of GeoGebra softwareinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisFerreira, Inês Fariashttp://lattes.cnpq.br/0979050331045936Richit, Adrianahttp://lattes.cnpq.br/2107707592550055Mariani, Rita de Cássia Pistóiahttp://lattes.cnpq.br/8330933788557081http://lattes.cnpq.br/5574153702944501Berlanda, Juliane Carla70080000000660089989312-533f-4ac1-9df1-25251e908367093d8a10-0205-4c77-b634-e4b67095f7fa4510bd7f-4e33-402f-a937-9f34ae6c7ff2cdaf48f6-d0d6-4dac-a0d5-dcc6949d13f9reponame:Biblioteca Digital de Teses e Dissertações do UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGEMEF_2017_BERLANDA_JULIANE.pdfDIS_PPGEMEF_2017_BERLANDA_JULIANE.pdfDissertação de Mestradoapplication/pdf3808604http://repositorio.ufsm.br/bitstream/1/13533/1/DIS_PPGEMEF_2017_BERLANDA_JULIANE.pdfe3d85cd2fd27d00ce484ea8f406ea0f5MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8804http://repositorio.ufsm.br/bitstream/1/13533/2/license_rdfc1efe8e24d7281448e873be30ea326ffMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81956http://repositorio.ufsm.br/bitstream/1/13533/3/license.txt2f0571ecee68693bd5cd3f17c1e075dfMD53TEXTDIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.txtDIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.txtExtracted texttext/plain334757http://repositorio.ufsm.br/bitstream/1/13533/4/DIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.txt9584fada5c11eddb82d22c8065c7d984MD54THUMBNAILDIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.jpgDIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.jpgIM Thumbnailimage/jpeg4425http://repositorio.ufsm.br/bitstream/1/13533/5/DIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.jpgf0d2dd3dbbf8086f04a7d7fd404b7f8eMD551/135332022-04-13 08:24:53.527oai:repositorio.ufsm.br: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 Digital de Teses e Dissertaçõeshttps://repositorio.ufsm.br/ONGhttps://repositorio.ufsm.br/oai/requestatendimento.sib@ufsm.br||tedebc@gmail.comopendoar:2022-04-13T11:24:53Biblioteca Digital de Teses e Dissertações do UFSM - Universidade Federal de Santa Maria (UFSM)false |
dc.title.por.fl_str_mv |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
dc.title.alternative.eng.fl_str_mv |
Mobilizations of records of semiotic representation in the study of trigonometry in triangle rectangle with the aid of GeoGebra software |
title |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
spellingShingle |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra Berlanda, Juliane Carla Trigonometria no triângulo retângulo GeoGebra Registros de representação semiótica Engenharia didática Right triangle trigonometry GeoGebra Registers of semiotic representation Didactic engineering CNPQ::CIENCIAS HUMANAS::EDUCACAO |
title_short |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
title_full |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
title_fullStr |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
title_full_unstemmed |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
title_sort |
Mobilizações de registros de representação semiótica no estudo de trigonometria no triângulo retângulo com o auxílio do software GeoGebra |
author |
Berlanda, Juliane Carla |
author_facet |
Berlanda, Juliane Carla |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Ferreira, Inês Farias |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/0979050331045936 |
dc.contributor.referee1.fl_str_mv |
Richit, Adriana |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/2107707592550055 |
dc.contributor.referee2.fl_str_mv |
Mariani, Rita de Cássia Pistóia |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/8330933788557081 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5574153702944501 |
dc.contributor.author.fl_str_mv |
Berlanda, Juliane Carla |
contributor_str_mv |
Ferreira, Inês Farias Richit, Adriana Mariani, Rita de Cássia Pistóia |
dc.subject.por.fl_str_mv |
Trigonometria no triângulo retângulo GeoGebra Registros de representação semiótica Engenharia didática |
topic |
Trigonometria no triângulo retângulo GeoGebra Registros de representação semiótica Engenharia didática Right triangle trigonometry GeoGebra Registers of semiotic representation Didactic engineering CNPQ::CIENCIAS HUMANAS::EDUCACAO |
dc.subject.eng.fl_str_mv |
Right triangle trigonometry GeoGebra Registers of semiotic representation Didactic engineering |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS HUMANAS::EDUCACAO |
description |
This research aimed to answer the following question: “How are the registers of semiotic representation mobilized in the approach of right triangle trigonometry with the help of the GeoGebra software, based on a sequence of activities with students of the 1st grade of high school?”. The sequence of activities was designed with an investigative conception, using the technological resource of GeoGebra, and was developed with a class of students of a public school in Erechim, in the state of Rio Grande do Sul, Brazil. This research is supported by the learning theory of registers of semiotic representation and constituted based on the Didactic Engineering methodology. Data collection was carried out through printed materials, files recorded with the software, and audio media containing the speeches of the students during the interventions. This material was analyzed considering the following categories: a) through mathematical experimentation and the consequent coordination of the various representations made possible by the dynamicity of GeoGebra resources, a program in which several semiotic representations were coordinated (natural language, figural, tabular, numerical, algebraic and symbolic), as well as the analysis of apprehensions (perceptual, discursive and operative); b) by proposing an exploratory approach in mathematics education, based on an environment of dynamic geometry and a sequence of activities with an investigative conception, in which the student‟s autonomy was verified in the accomplishment of the proposed activities, provided by the ease of manipulation of mathematical objects elaborated in GeoGebra; c) through the encouragement of mathematical communication in the classroom, through the preparation of written and verbal justifications, when the natural language register became evident, with the verification of the subjects‟ knowledge acquisition. In addition, the stages of Didactic Engineering, as well as its reflections, were recognized as fundamental for the development of this research and the elaboration of the sequence of activities. In the analysis of the results, it was verified that the students were able to acquire knowledge about the study of right triangle trigonometry. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-10-27 |
dc.date.accessioned.fl_str_mv |
2018-06-25T21:34:53Z |
dc.date.available.fl_str_mv |
2018-06-25T21:34:53Z |
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 |
http://repositorio.ufsm.br/handle/1/13533 |
url |
http://repositorio.ufsm.br/handle/1/13533 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.cnpq.fl_str_mv |
700800000006 |
dc.relation.confidence.fl_str_mv |
600 |
dc.relation.authority.fl_str_mv |
89989312-533f-4ac1-9df1-25251e908367 093d8a10-0205-4c77-b634-e4b67095f7fa 4510bd7f-4e33-402f-a937-9f34ae6c7ff2 cdaf48f6-d0d6-4dac-a0d5-dcc6949d13f9 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Educação Matemática e Ensino de Física |
dc.publisher.initials.fl_str_mv |
UFSM |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Educação |
publisher.none.fl_str_mv |
Universidade Federal de Santa Maria Centro de Ciências Naturais e Exatas |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações do UFSM instname:Universidade Federal de Santa Maria (UFSM) instacron:UFSM |
instname_str |
Universidade Federal de Santa Maria (UFSM) |
instacron_str |
UFSM |
institution |
UFSM |
reponame_str |
Biblioteca Digital de Teses e Dissertações do UFSM |
collection |
Biblioteca Digital de Teses e Dissertações do UFSM |
bitstream.url.fl_str_mv |
http://repositorio.ufsm.br/bitstream/1/13533/1/DIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf http://repositorio.ufsm.br/bitstream/1/13533/2/license_rdf http://repositorio.ufsm.br/bitstream/1/13533/3/license.txt http://repositorio.ufsm.br/bitstream/1/13533/4/DIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.txt http://repositorio.ufsm.br/bitstream/1/13533/5/DIS_PPGEMEF_2017_BERLANDA_JULIANE.pdf.jpg |
bitstream.checksum.fl_str_mv |
e3d85cd2fd27d00ce484ea8f406ea0f5 c1efe8e24d7281448e873be30ea326ff 2f0571ecee68693bd5cd3f17c1e075df 9584fada5c11eddb82d22c8065c7d984 f0d2dd3dbbf8086f04a7d7fd404b7f8e |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações do UFSM - Universidade Federal de Santa Maria (UFSM) |
repository.mail.fl_str_mv |
atendimento.sib@ufsm.br||tedebc@gmail.com |
_version_ |
1801485338384793600 |