Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental
Ano de defesa: | 2017 |
---|---|
Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | , |
Tipo de documento: | Dissertação |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas |
Programa de Pós-Graduação: |
Programa de Pós-Graduação em Educação Matemática e Ensino de Física
|
Departamento: |
Educação
|
País: |
Brasil
|
Palavras-chave em Português: | |
Palavras-chave em Inglês: | |
Área do conhecimento CNPq: | |
Link de acesso: | http://repositorio.ufsm.br/handle/1/13530 |
Resumo: | This research aims to analyze the registers of semiotic representation and the sequential, perceptual, discursive and operative apprehensions mobilized by students in 9th grade of Lower Secondary Education in the study of the area of the circle. Therefore, a qualitative research was carried out (LÜDKE; ANDRÉ, 1986) in a Municipal School of Primary and Lower Secondary Education of Erechim, in the state of Rio Grande do Sul, Brazil. The data was collected through two collections of textbooks (TB) adopted by the School in the academic year of 2016 – one destined to Primary Education, denominated Novo Girassol: saberes e fazeres do campo (Collection A), and another, to Lower Secondary Education, entitled Vontade de Saber Matemática (Collection B) –; notebooks of two students from each of the nine classes, from the 1st to the 9th grade, of the School; and a sequence of activities developed with the students in 9th grade at the School, consisting of 29 items about obtaining the area of the circle using the method of exhaustion, through manipulatives and the GeoGebra software. With the intention of establishing inferences about the study of the area of the circle in Primary and Lower Secondary Education, based on the principles of content analysis (BARDIN, 2016), it was found that the area of the circle was a subject discussed only in the 9th-grade TB, while, in the previous years, especially in Primary Education, the characteristics of the circle were explored, as well as its differences from other flat forms. The activities identified involved perceptual (72.55%), discursive (1.96%) and operative (37.25%) apprehensions, with mobilization of natural language register (NLR) and figural register (FgR) in the statements. Through the analysis of the notebooks, it was detected that the study of the area of the circle was developed in the 8th and 9th grades, mobilizing only the perceptual and operative apprehensions in exercises that were repeated in these two school years. The perceptual apprehension was employed in all activities, while the operative apprehension (50%), only to determine the area of the circular crown. With respect to the representations, it was found that, in these two data sources, except for one activity, the NLR was used only in the statements, and the approaches emphasized algebraic (AlR) and numerical (NmR) registers. The sequence of activities involved the reconfiguration of the area of the circle in the approximate form of a rectangle and the inclusion of polygons in the circle in order to manipulate different registers of semiotic representation, articulating, in particular, FgR and AlR. Still concerning the sequence, it was concluded that all apprehensions were mobilized, maintaining the prevalence of perceptual apprehension (95.24%), but with an expressive increase of discursive (34.52%) and operative (32.14%) apprehensions. In addition, the simultaneous mobilization of more than one apprehension was observed in several answers of the protocols (53.57%), mainly since they used NLR, accompanied concomitantly by more than one representation register, with emphasis on FgR, AlR and NmR, which characterizes the conversion. |
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2018-06-25T17:49:41Z2018-06-25T17:49:41Z2017-10-04http://repositorio.ufsm.br/handle/1/13530This research aims to analyze the registers of semiotic representation and the sequential, perceptual, discursive and operative apprehensions mobilized by students in 9th grade of Lower Secondary Education in the study of the area of the circle. Therefore, a qualitative research was carried out (LÜDKE; ANDRÉ, 1986) in a Municipal School of Primary and Lower Secondary Education of Erechim, in the state of Rio Grande do Sul, Brazil. The data was collected through two collections of textbooks (TB) adopted by the School in the academic year of 2016 – one destined to Primary Education, denominated Novo Girassol: saberes e fazeres do campo (Collection A), and another, to Lower Secondary Education, entitled Vontade de Saber Matemática (Collection B) –; notebooks of two students from each of the nine classes, from the 1st to the 9th grade, of the School; and a sequence of activities developed with the students in 9th grade at the School, consisting of 29 items about obtaining the area of the circle using the method of exhaustion, through manipulatives and the GeoGebra software. With the intention of establishing inferences about the study of the area of the circle in Primary and Lower Secondary Education, based on the principles of content analysis (BARDIN, 2016), it was found that the area of the circle was a subject discussed only in the 9th-grade TB, while, in the previous years, especially in Primary Education, the characteristics of the circle were explored, as well as its differences from other flat forms. The activities identified involved perceptual (72.55%), discursive (1.96%) and operative (37.25%) apprehensions, with mobilization of natural language register (NLR) and figural register (FgR) in the statements. Through the analysis of the notebooks, it was detected that the study of the area of the circle was developed in the 8th and 9th grades, mobilizing only the perceptual and operative apprehensions in exercises that were repeated in these two school years. The perceptual apprehension was employed in all activities, while the operative apprehension (50%), only to determine the area of the circular crown. With respect to the representations, it was found that, in these two data sources, except for one activity, the NLR was used only in the statements, and the approaches emphasized algebraic (AlR) and numerical (NmR) registers. The sequence of activities involved the reconfiguration of the area of the circle in the approximate form of a rectangle and the inclusion of polygons in the circle in order to manipulate different registers of semiotic representation, articulating, in particular, FgR and AlR. Still concerning the sequence, it was concluded that all apprehensions were mobilized, maintaining the prevalence of perceptual apprehension (95.24%), but with an expressive increase of discursive (34.52%) and operative (32.14%) apprehensions. In addition, the simultaneous mobilization of more than one apprehension was observed in several answers of the protocols (53.57%), mainly since they used NLR, accompanied concomitantly by more than one representation register, with emphasis on FgR, AlR and NmR, which characterizes the conversion.Esta pesquisa objetiva analisar os registros de representação semiótica e as apreensões sequencial, perceptiva, discursiva e operatória mobilizadas por estudantes do 9° ano do Ensino Fundamental no estudo da área do círculo. Para tanto, realizou-se uma pesquisa qualitativa (LÜDKE; ANDRÉ, 1986) em uma Escola Municipal de Ensino Fundamental de Erechim/RS. A produção dos dados ocorreu por meio de duas coleções de livros didáticos (LD) adotadas pela Escola no ano letivo de 2016 – uma destinada aos anos iniciais do Ensino Fundamental, denominada Novo Girassol: saberes e fazeres do campo (Coleção A), e outra, aos anos finais, intitulada Vontade de Saber Matemática (Coleção B) –; do caderno de dois alunos de cada uma das nove turmas, do 1º ao 9º ano, da Escola; e de uma sequência de atividades desenvolvida com os alunos do 9º ano da Escola, constituída por 29 itens versando sobre a obtenção da área do círculo a partir do princípio da exaustão, com a utilização de material manipulável e do software GeoGebra. Na intenção de estabelecer inferências acerca do estudo da área do círculo no Ensino Fundamental, com base nos preceitos da análise de conteúdo (BARDIN, 2016), constatou-se que a área do círculo foi trabalhada apenas no LD do 9º ano, enquanto, nos anos anteriores, principalmente nos anos iniciais, exploravam-se as características do círculo e buscava-se diferenciá-lo das demais formas planas. As atividades identificadas envolveram as apreensões perceptiva (72,55%), discursiva (1,96%) e operatória (37,25%), com mobilização de registro em língua natural (RLN) e registro figural (RFg) nos enunciados. Por meio da análise dos cadernos, detectou-se que a área do círculo foi desenvolvida no 8º e 9º anos, mobilizando apenas a apreensão perceptiva e operatória em questões que se repetiam nesses dois anos escolares. A perceptiva foi empregada em todas as atividades, enquanto a operatória (50%), apenas para determinar a área da coroa circular. No que se refere às representações, verificou-se que, nessas duas fontes de dados, com exceção de uma atividade, o RLN foi empregado apenas nos enunciados, e os tratamentos enfatizaram registros algébricos (RAl) e numéricos (RNm). A sequência de atividades envolveu a reconfiguração da área do círculo na forma aproximada de retângulo e a inscrição de polígonos no círculo, a fim de manipular diferentes registros de representação semiótica, articulando especialmente o RFg e o RAl. Ainda no que tange à sequência, concluiu-se que todas as apreensões foram mobilizadas, mantendo a prevalência da perceptiva (95,24%), mas com aumento expressivo da discursiva (34,52%) e da operatória (32,14%). Além disso, observou-se a mobilização simultânea de mais de uma apreensão em várias respostas dos protocolos (53,57%), sobretudo pelo fato de empregarem o RLN, acompanhado concomitantemente por mais de um registro de representação, com destaque ao RFg, RAl e RNm, o que caracteriza a conversão.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/openAccessRegistros de representação semióticaApreensõesEnsino de geometriaÁrea do círculoEnsino fundamentalRegisters of semiotic representationApprehensionsTeaching geometryArea of circlePrimary and lower secondary educationCNPQ::CIENCIAS HUMANAS::EDUCACAORepresentações semióticas mobilizadas no estudo da área do círculo no ensino fundamentalSemiotic representations mobilized in the study of the area of a circle in primary and lower secondary educationinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMariani, Rita de Cássia Pistóiahttp://lattes.cnpq.br/8330933788557081Leivas, José Carlos Pintohttp://lattes.cnpq.br/0314545667166824Ferreira, Inês Fariashttp://lattes.cnpq.br/0979050331045936http://lattes.cnpq.br/5464206574872671Arcego, Priscila7008000000066001587a7ea-0877-496d-a629-7a9c40ad00dd5023e6cb-9b3a-40f8-8d5c-6da67e04eca117afd4fb-2a9e-4dc5-9d6e-c0af0e90a167e78b036b-026e-45b2-abfa-a84a7b637dd1reponame:Biblioteca Digital de Teses e Dissertações do UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
dc.title.alternative.eng.fl_str_mv |
Semiotic representations mobilized in the study of the area of a circle in primary and lower secondary education |
title |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
spellingShingle |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental Arcego, Priscila Registros de representação semiótica Apreensões Ensino de geometria Área do círculo Ensino fundamental Registers of semiotic representation Apprehensions Teaching geometry Area of circle Primary and lower secondary education CNPQ::CIENCIAS HUMANAS::EDUCACAO |
title_short |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
title_full |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
title_fullStr |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
title_full_unstemmed |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
title_sort |
Representações semióticas mobilizadas no estudo da área do círculo no ensino fundamental |
author |
Arcego, Priscila |
author_facet |
Arcego, Priscila |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Mariani, Rita de Cássia Pistóia |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/8330933788557081 |
dc.contributor.referee1.fl_str_mv |
Leivas, José Carlos Pinto |
dc.contributor.referee1Lattes.fl_str_mv |
http://lattes.cnpq.br/0314545667166824 |
dc.contributor.referee2.fl_str_mv |
Ferreira, Inês Farias |
dc.contributor.referee2Lattes.fl_str_mv |
http://lattes.cnpq.br/0979050331045936 |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/5464206574872671 |
dc.contributor.author.fl_str_mv |
Arcego, Priscila |
contributor_str_mv |
Mariani, Rita de Cássia Pistóia Leivas, José Carlos Pinto Ferreira, Inês Farias |
dc.subject.por.fl_str_mv |
Registros de representação semiótica Apreensões Ensino de geometria Área do círculo Ensino fundamental |
topic |
Registros de representação semiótica Apreensões Ensino de geometria Área do círculo Ensino fundamental Registers of semiotic representation Apprehensions Teaching geometry Area of circle Primary and lower secondary education CNPQ::CIENCIAS HUMANAS::EDUCACAO |
dc.subject.eng.fl_str_mv |
Registers of semiotic representation Apprehensions Teaching geometry Area of circle Primary and lower secondary education |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS HUMANAS::EDUCACAO |
description |
This research aims to analyze the registers of semiotic representation and the sequential, perceptual, discursive and operative apprehensions mobilized by students in 9th grade of Lower Secondary Education in the study of the area of the circle. Therefore, a qualitative research was carried out (LÜDKE; ANDRÉ, 1986) in a Municipal School of Primary and Lower Secondary Education of Erechim, in the state of Rio Grande do Sul, Brazil. The data was collected through two collections of textbooks (TB) adopted by the School in the academic year of 2016 – one destined to Primary Education, denominated Novo Girassol: saberes e fazeres do campo (Collection A), and another, to Lower Secondary Education, entitled Vontade de Saber Matemática (Collection B) –; notebooks of two students from each of the nine classes, from the 1st to the 9th grade, of the School; and a sequence of activities developed with the students in 9th grade at the School, consisting of 29 items about obtaining the area of the circle using the method of exhaustion, through manipulatives and the GeoGebra software. With the intention of establishing inferences about the study of the area of the circle in Primary and Lower Secondary Education, based on the principles of content analysis (BARDIN, 2016), it was found that the area of the circle was a subject discussed only in the 9th-grade TB, while, in the previous years, especially in Primary Education, the characteristics of the circle were explored, as well as its differences from other flat forms. The activities identified involved perceptual (72.55%), discursive (1.96%) and operative (37.25%) apprehensions, with mobilization of natural language register (NLR) and figural register (FgR) in the statements. Through the analysis of the notebooks, it was detected that the study of the area of the circle was developed in the 8th and 9th grades, mobilizing only the perceptual and operative apprehensions in exercises that were repeated in these two school years. The perceptual apprehension was employed in all activities, while the operative apprehension (50%), only to determine the area of the circular crown. With respect to the representations, it was found that, in these two data sources, except for one activity, the NLR was used only in the statements, and the approaches emphasized algebraic (AlR) and numerical (NmR) registers. The sequence of activities involved the reconfiguration of the area of the circle in the approximate form of a rectangle and the inclusion of polygons in the circle in order to manipulate different registers of semiotic representation, articulating, in particular, FgR and AlR. Still concerning the sequence, it was concluded that all apprehensions were mobilized, maintaining the prevalence of perceptual apprehension (95.24%), but with an expressive increase of discursive (34.52%) and operative (32.14%) apprehensions. In addition, the simultaneous mobilization of more than one apprehension was observed in several answers of the protocols (53.57%), mainly since they used NLR, accompanied concomitantly by more than one representation register, with emphasis on FgR, AlR and NmR, which characterizes the conversion. |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-10-04 |
dc.date.accessioned.fl_str_mv |
2018-06-25T17:49:41Z |
dc.date.available.fl_str_mv |
2018-06-25T17:49:41Z |
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/1/13530 |
url |
http://repositorio.ufsm.br/handle/1/13530 |
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 |
1587a7ea-0877-496d-a629-7a9c40ad00dd 5023e6cb-9b3a-40f8-8d5c-6da67e04eca1 17afd4fb-2a9e-4dc5-9d6e-c0af0e90a167 e78b036b-026e-45b2-abfa-a84a7b637dd1 |
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 |
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bitstream.checksum.fl_str_mv |
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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 |
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1793240042168123392 |