Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática
Autor(a) principal: | |
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Data de Publicação: | 2016 |
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/19214 |
Resumo: | This study aims to understand and analyze how the communication, the student explaining how thought to solve the activity in math class you will be able to contribute to the development of algebraic thinking. To this end, we look for evidence of the development of some elements of algebraic thinking that can be attributed to the understanding of the equal sign with the sense of equivalence. To guide this study have formulated the following research question: how communication in math class you will be able to contribute to the construction of algebraic thinking? To perform this qualitative interpretive research, developed a string of activities based on the assumptions of the theory of Didactic Situations and records of Semiotic Representation, with 7th grade students of a State school, located in a traditional neighbourhood in the city of São Paulo. The students were placed in a situation of communication so that they could act, formulate their conjectures and validate their hypotheses. At first, the students in pairs decided activities producing a collective sense the equal sign and communicated their ideas through writing and orality. After that first time, the teams were swapped so that they could validate their responses or produce a new sense to the equal sign. The data were collected by means of audio recordings, video and some written observations in field journal. For the analysis, the transcript of some of the students ' dialogues in order to identify: (i) the different meanings of equal sign presented by the students and how it can interfere in the development of algebraic thinking; (ii) contributions to the development of algebraic thought attributed to interaction, communication, with fellow; (iii) the record of the natural language, as a first record of semiotics of equal representation and liaison with the other records of semiotic representation. From these analyses, we have seen the development of relational thinking and algebraic thinking, which were facilitated by communication between the students and the negotiation of meanings. Most of the students, at first, the meaning of the equal sign as an operator, that is, immediately after the equal sign should be writing the result of the operation, before the equal sign. Students who showed the significance of the sign as an operator, presented difficulty to address activities and, at times, were not knowing how to complete the proposed activity. In some cases, we observe that students, at first, showed the operational meaning, but, with the interaction with the partner and with the activity, managed to mobilise the expertise to assign a new sense to the equal sign as equivalence. The latter has overcome the activities so as to leave the sentences true. Communication in math class can help students produce sense of equivalence of the equal sign by facilitating the development of algebraic thinking, emphasizing the important role of the teacher, as a mediator of this interaction |
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Bianchini, Barbara Lutaifhttp://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K8505594Z3Cruz, Patrícia de Souza Ferreira da2016-10-20T17:22:52Z2016-08-03Cruz, Patrícia de Souza Ferreira da. Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática. 2016. 122 f. Dissertação (Mestrado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2016.https://tede2.pucsp.br/handle/handle/19214This study aims to understand and analyze how the communication, the student explaining how thought to solve the activity in math class you will be able to contribute to the development of algebraic thinking. To this end, we look for evidence of the development of some elements of algebraic thinking that can be attributed to the understanding of the equal sign with the sense of equivalence. To guide this study have formulated the following research question: how communication in math class you will be able to contribute to the construction of algebraic thinking? To perform this qualitative interpretive research, developed a string of activities based on the assumptions of the theory of Didactic Situations and records of Semiotic Representation, with 7th grade students of a State school, located in a traditional neighbourhood in the city of São Paulo. The students were placed in a situation of communication so that they could act, formulate their conjectures and validate their hypotheses. At first, the students in pairs decided activities producing a collective sense the equal sign and communicated their ideas through writing and orality. After that first time, the teams were swapped so that they could validate their responses or produce a new sense to the equal sign. The data were collected by means of audio recordings, video and some written observations in field journal. For the analysis, the transcript of some of the students ' dialogues in order to identify: (i) the different meanings of equal sign presented by the students and how it can interfere in the development of algebraic thinking; (ii) contributions to the development of algebraic thought attributed to interaction, communication, with fellow; (iii) the record of the natural language, as a first record of semiotics of equal representation and liaison with the other records of semiotic representation. From these analyses, we have seen the development of relational thinking and algebraic thinking, which were facilitated by communication between the students and the negotiation of meanings. Most of the students, at first, the meaning of the equal sign as an operator, that is, immediately after the equal sign should be writing the result of the operation, before the equal sign. Students who showed the significance of the sign as an operator, presented difficulty to address activities and, at times, were not knowing how to complete the proposed activity. In some cases, we observe that students, at first, showed the operational meaning, but, with the interaction with the partner and with the activity, managed to mobilise the expertise to assign a new sense to the equal sign as equivalence. The latter has overcome the activities so as to leave the sentences true. Communication in math class can help students produce sense of equivalence of the equal sign by facilitating the development of algebraic thinking, emphasizing the important role of the teacher, as a mediator of this interactionEste estudo tem como objetivo compreender e analisar de que forma a comunicação, o aluno explicando como pensou para resolver a atividade na aula de matemática poderá contribuir para o desenvolvimento do pensamento algébrico. Para tanto, buscamos indícios do desenvolvimento de alguns elementos do pensamento algébrico que podem ser atribuídos à compreensão do sinal de igualdade com o sentido de equivalência. Para nortear este estudo formulamos a seguinte questão de pesquisa: De que forma a comunicação na aula de matemática poderá contribuir para a construção do pensamento algébrico? Para realizar esta investigação de natureza qualitativa interpretativa, foi desenvolvida uma sequência de atividades fundamentadas nos pressupostos da Teoria das Situações Didáticas e dos Registros de Representação Semiótica, com alunos do 7º ano de uma escola estadual, localizada em um bairro tradicional da cidade de São Paulo. Os alunos foram colocados em situação de comunicação para que pudessem agir, formular suas conjecturas e validar suas hipóteses. Em um primeiro momento, os alunos em duplas resolveram as atividades produzindo um sentido coletivo ao sinal de igualdade e comunicaram suas ideias, por meio da escrita e da oralidade. Após esse primeiro momento, as duplas foram trocadas para que pudessem validar suas respostas ou produzir um novo sentido ao sinal de igualdade. A coleta de dados foi realizada por meio de gravações de áudio, vídeo e algumas observações escritas em diário de campo. Para a análise, fez-se a transcrição de alguns dos diálogos dos alunos com o intuito de identificar: (i) os diferentes significados do sinal de igualdade apresentados pelos alunos e de que modo podem interferir no desenvolvimento do pensamento algébrico; (ii) as contribuições para o desenvolvimento do pensamento algébrico atribuídas à interação, comunicação, com o colega; (iii) o registro da língua natural, como um primeiro registro de representação semiótica da igualdade e a articulação com os outros registros de representação semiótica. A partir destas análises, pudemos constatar o desenvolvimento do pensamento relacional e do pensamento algébrico, que foram facilitados pela comunicação entre os alunos e a negociação de significados. A maior parte dos alunos, a princípio, evidenciou o significado do sinal de igualdade como operador, ou seja, logo após o sinal de igualdade deveria estar escrito o resultado da operação localizada, antes do sinal de igualdade. Os alunos que mostraram o significado do sinal como operador, apresentaram dificuldade para resolver as atividades e, em alguns momentos, ficaram sem saber como concluir a atividade proposta. Em alguns casos, observamos que os alunos, em um primeiro momento, evidenciaram o significado operacional, mas, com a interação com o colega e com a atividade, conseguiram mobilizar os conhecimentos necessários para atribuir um novo sentido ao sinal de igualdade como equivalência. Estes últimos, conseguiram resolver as atividades de modo a deixar as sentenças verdadeiras. A comunicação na aula de Matemática pode contribuir para que os alunos produzam sentido de equivalência do sinal de igualdade facilitando o desenvolvimento do pensamento algébrico, destacando-se o importante papel do professor, como mediador dessa interaçãoCoordenação de Aperfeiçoamento de Pessoal de Nível Superiorapplication/pdfhttp://tede2.pucsp.br/tede/retrieve/39927/Patr%c3%adcia%20de%20Souza%20Ferreira%20da%20Cruz.pdf.jpgporPontifícia Universidade Católica de São PauloPrograma de Estudos Pós-Graduados em Educação MatemáticaPUC-SPBrasilFaculdade de Ciências Exatas e TecnologiaEducação algébricaComunicação na aulaOralidade na aulaAlgebraic educationCommunication in classOrality in classCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAPensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemáticaAlgebraic thinking and the meanings of equal sign: the use of Orality and Storytelling in the math classesinfo: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_SPTEXTPatrícia de Souza Ferreira da Cruz.pdf.txtPatrícia de Souza Ferreira da Cruz.pdf.txtExtracted texttext/plain233099https://repositorio.pucsp.br/xmlui/bitstream/handle/19214/4/Patr%c3%adcia%20de%20Souza%20Ferreira%20da%20Cruz.pdf.txtfe1abbccbc8c231de0393bcba3deb744MD54ORIGINALPatrícia de Souza Ferreira da Cruz.pdfPatrícia de Souza Ferreira da Cruz.pdfapplication/pdf2081308https://repositorio.pucsp.br/xmlui/bitstream/handle/19214/2/Patr%c3%adcia%20de%20Souza%20Ferreira%20da%20Cruz.pdff1fc829c7e70d17f8ded2ccc59e0f7b7MD52LICENSElicense.txtlicense.txttext/plain; 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dc.title.por.fl_str_mv |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
dc.title.alternative.eng.fl_str_mv |
Algebraic thinking and the meanings of equal sign: the use of Orality and Storytelling in the math classes |
title |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
spellingShingle |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática Cruz, Patrícia de Souza Ferreira da Educação algébrica Comunicação na aula Oralidade na aula Algebraic education Communication in class Orality in class CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
title_short |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
title_full |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
title_fullStr |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
title_full_unstemmed |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
title_sort |
Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática |
author |
Cruz, Patrícia de Souza Ferreira da |
author_facet |
Cruz, Patrícia de Souza Ferreira da |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Bianchini, Barbara Lutaif |
dc.contributor.authorLattes.fl_str_mv |
http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K8505594Z3 |
dc.contributor.author.fl_str_mv |
Cruz, Patrícia de Souza Ferreira da |
contributor_str_mv |
Bianchini, Barbara Lutaif |
dc.subject.por.fl_str_mv |
Educação algébrica Comunicação na aula Oralidade na aula |
topic |
Educação algébrica Comunicação na aula Oralidade na aula Algebraic education Communication in class Orality in class CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
dc.subject.eng.fl_str_mv |
Algebraic education Communication in class Orality in class |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA |
description |
This study aims to understand and analyze how the communication, the student explaining how thought to solve the activity in math class you will be able to contribute to the development of algebraic thinking. To this end, we look for evidence of the development of some elements of algebraic thinking that can be attributed to the understanding of the equal sign with the sense of equivalence. To guide this study have formulated the following research question: how communication in math class you will be able to contribute to the construction of algebraic thinking? To perform this qualitative interpretive research, developed a string of activities based on the assumptions of the theory of Didactic Situations and records of Semiotic Representation, with 7th grade students of a State school, located in a traditional neighbourhood in the city of São Paulo. The students were placed in a situation of communication so that they could act, formulate their conjectures and validate their hypotheses. At first, the students in pairs decided activities producing a collective sense the equal sign and communicated their ideas through writing and orality. After that first time, the teams were swapped so that they could validate their responses or produce a new sense to the equal sign. The data were collected by means of audio recordings, video and some written observations in field journal. For the analysis, the transcript of some of the students ' dialogues in order to identify: (i) the different meanings of equal sign presented by the students and how it can interfere in the development of algebraic thinking; (ii) contributions to the development of algebraic thought attributed to interaction, communication, with fellow; (iii) the record of the natural language, as a first record of semiotics of equal representation and liaison with the other records of semiotic representation. From these analyses, we have seen the development of relational thinking and algebraic thinking, which were facilitated by communication between the students and the negotiation of meanings. Most of the students, at first, the meaning of the equal sign as an operator, that is, immediately after the equal sign should be writing the result of the operation, before the equal sign. Students who showed the significance of the sign as an operator, presented difficulty to address activities and, at times, were not knowing how to complete the proposed activity. In some cases, we observe that students, at first, showed the operational meaning, but, with the interaction with the partner and with the activity, managed to mobilise the expertise to assign a new sense to the equal sign as equivalence. The latter has overcome the activities so as to leave the sentences true. Communication in math class can help students produce sense of equivalence of the equal sign by facilitating the development of algebraic thinking, emphasizing the important role of the teacher, as a mediator of this interaction |
publishDate |
2016 |
dc.date.accessioned.fl_str_mv |
2016-10-20T17:22:52Z |
dc.date.issued.fl_str_mv |
2016-08-03 |
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 |
Cruz, Patrícia de Souza Ferreira da. Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática. 2016. 122 f. Dissertação (Mestrado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2016. |
dc.identifier.uri.fl_str_mv |
https://tede2.pucsp.br/handle/handle/19214 |
identifier_str_mv |
Cruz, Patrícia de Souza Ferreira da. Pensamento algébrico e os significados do sinal de igualdade: o uso da oralidade e da narrativa nas aulas de matemática. 2016. 122 f. Dissertação (Mestrado em Educação Matemática) - Programa de Estudos Pós-Graduados em Educação Matemática, Pontifícia Universidade Católica de São Paulo, São Paulo, 2016. |
url |
https://tede2.pucsp.br/handle/handle/19214 |
dc.language.iso.fl_str_mv |
por |
language |
por |
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info:eu-repo/semantics/openAccess |
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openAccess |
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application/pdf |
dc.publisher.none.fl_str_mv |
Pontifícia Universidade Católica de São Paulo |
dc.publisher.program.fl_str_mv |
Programa de Estudos Pós-Graduados em Educação Matemática |
dc.publisher.initials.fl_str_mv |
PUC-SP |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Faculdade de Ciências Exatas e Tecnologia |
publisher.none.fl_str_mv |
Pontifícia Universidade Católica de São Paulo |
dc.source.none.fl_str_mv |
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repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da PUC_SP - Pontifícia Universidade Católica de São Paulo (PUC-SP) |
repository.mail.fl_str_mv |
bngkatende@pucsp.br||rapassi@pucsp.br |
_version_ |
1809277888045776896 |