Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students

Detalhes bibliográficos
Autor(a) principal: Frizzarini, Silvia Teresinha
Data de Publicação: 2020
Outros Autores: Cargnin, Claudete, Waideman, Adriele Carolini, Guedes, Luciane
Tipo de documento: Artigo
Idioma: por
Título da fonte: Revista de Ensino de Ciências e Matemática - REnCiMa
Texto Completo: https://revistapos.cruzeirodosul.edu.br/rencima/article/view/2605
Resumo: This paper aims to analyze which congruence criteria are conserved in the study of limits and to reflect on the influence of conserved criteria in the clippings of productions made by students attending University Higher Education Federal University of Technology – Parana. The methodology used is the bibliographical analysis of the books used by these students and some of their documentary productions with problems that involve limits. For this, we use the theoretical assumptions of Duval representation records, in particular the semantic congruence, for the analysis of the limit concept. Transformations of the different representations, by treatment and conversion, of the rules used in the calculation of limits, graphical representation, numerical approximation and algebraic representation are considered. The results presented were that, although the criteria conserved in the algebraic calculations by substitution are mathematically verifiable, when applicable, they are semantically non-congruent, that is, there is no semantic univocity between the respective significant units of numerical and graphical records. Therefore, other methodologies are needed to interpret the concept boundaries of a function through different representations.
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spelling Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education studentsA congruência semântica na definição de limites: uma análise dos critérios conservados por alunos no Ensino SuperiorEducação MatemáticaCongruência SemânticaLimitesMathematical EducationSemantic CongruenceLimitsThis paper aims to analyze which congruence criteria are conserved in the study of limits and to reflect on the influence of conserved criteria in the clippings of productions made by students attending University Higher Education Federal University of Technology – Parana. The methodology used is the bibliographical analysis of the books used by these students and some of their documentary productions with problems that involve limits. For this, we use the theoretical assumptions of Duval representation records, in particular the semantic congruence, for the analysis of the limit concept. Transformations of the different representations, by treatment and conversion, of the rules used in the calculation of limits, graphical representation, numerical approximation and algebraic representation are considered. The results presented were that, although the criteria conserved in the algebraic calculations by substitution are mathematically verifiable, when applicable, they are semantically non-congruent, that is, there is no semantic univocity between the respective significant units of numerical and graphical records. Therefore, other methodologies are needed to interpret the concept boundaries of a function through different representations.O trabalho objetiva analisar quais critérios de congruência são conservados no estudo de limites e tecer reflexões sobre a influência dos critérios conservados nos recortes de produções realizadas por alunos que cursam o Ensino Superior da Universidade Tecnológica Federal do Paraná. A metodologia utilizada é a análise bibliográfica dos livros utilizados por esses alunos e algumas de suas produções documentais com problemas que envolvem limites. Para isso, são utilizados os pressupostos teóricos dos registros de representação de Duval, em específico a congruência semântica, para a análise do conceito de limite. São consideradas as transformações das diferentes representações, por tratamento e conversão, das regras utilizadas no cálculo de limites, representação gráfica, aproximação numérica e representação algébrica.  Os resultados apresentados foram que, apesar dos critérios conservados nos cálculos algébricos por substituição sejam matematicamente comprováveis, nos casos em que se aplica, eles são semanticamente não congruentes, ou seja, não há univocidade semântica entre as unidades significantes respectivas dos registros numérico e gráfico. Portanto, outras metodologias são necessárias para se interpretar o conceito limites de uma função, por meio de diferentes representações.Editora Cruzeiro do Sul2020-10-18info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistapos.cruzeirodosul.edu.br/rencima/article/view/260510.26843/rencima.v11i6.2605Revista de Ensino de Ciências e Matemática; v. 11 n. 6 (2020): out./dez.; 18-332179-426Xreponame:Revista de Ensino de Ciências e Matemática - REnCiMainstname:Universidade de Caxias do Sul (UCS)instacron:UCSporhttps://revistapos.cruzeirodosul.edu.br/rencima/article/view/2605/1359https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BRinfo:eu-repo/semantics/openAccessFrizzarini, Silvia TeresinhaCargnin, ClaudeteWaideman, Adriele CaroliniGuedes, Luciane2023-04-21T21:24:09Zoai:ojs.pkp.sfu.ca:article/2605Revistahttps://revistapos.cruzeirodosul.edu.br/index.php/rencima/indexPRIhttps://revistapos.cruzeirodosul.edu.br/index.php/rencima/oai||rencima@cruzeirodosul.edu.br2179-426X2179-426Xopendoar:2023-04-21T21:24:09Revista de Ensino de Ciências e Matemática - REnCiMa - Universidade de Caxias do Sul (UCS)false
dc.title.none.fl_str_mv Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
A congruência semântica na definição de limites: uma análise dos critérios conservados por alunos no Ensino Superior
title Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
spellingShingle Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
Frizzarini, Silvia Teresinha
Educação Matemática
Congruência Semântica
Limites
Mathematical Education
Semantic Congruence
Limits
title_short Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
title_full Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
title_fullStr Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
title_full_unstemmed Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
title_sort Semantic congruence in definition of limits: an analysis of the criteria conserved by Higher Education students
author Frizzarini, Silvia Teresinha
author_facet Frizzarini, Silvia Teresinha
Cargnin, Claudete
Waideman, Adriele Carolini
Guedes, Luciane
author_role author
author2 Cargnin, Claudete
Waideman, Adriele Carolini
Guedes, Luciane
author2_role author
author
author
dc.contributor.author.fl_str_mv Frizzarini, Silvia Teresinha
Cargnin, Claudete
Waideman, Adriele Carolini
Guedes, Luciane
dc.subject.por.fl_str_mv Educação Matemática
Congruência Semântica
Limites
Mathematical Education
Semantic Congruence
Limits
topic Educação Matemática
Congruência Semântica
Limites
Mathematical Education
Semantic Congruence
Limits
description This paper aims to analyze which congruence criteria are conserved in the study of limits and to reflect on the influence of conserved criteria in the clippings of productions made by students attending University Higher Education Federal University of Technology – Parana. The methodology used is the bibliographical analysis of the books used by these students and some of their documentary productions with problems that involve limits. For this, we use the theoretical assumptions of Duval representation records, in particular the semantic congruence, for the analysis of the limit concept. Transformations of the different representations, by treatment and conversion, of the rules used in the calculation of limits, graphical representation, numerical approximation and algebraic representation are considered. The results presented were that, although the criteria conserved in the algebraic calculations by substitution are mathematically verifiable, when applicable, they are semantically non-congruent, that is, there is no semantic univocity between the respective significant units of numerical and graphical records. Therefore, other methodologies are needed to interpret the concept boundaries of a function through different representations.
publishDate 2020
dc.date.none.fl_str_mv 2020-10-18
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://revistapos.cruzeirodosul.edu.br/rencima/article/view/2605
10.26843/rencima.v11i6.2605
url https://revistapos.cruzeirodosul.edu.br/rencima/article/view/2605
identifier_str_mv 10.26843/rencima.v11i6.2605
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://revistapos.cruzeirodosul.edu.br/rencima/article/view/2605/1359
dc.rights.driver.fl_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BR
info:eu-repo/semantics/openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/4.0/deed.pt_BR
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Editora Cruzeiro do Sul
publisher.none.fl_str_mv Editora Cruzeiro do Sul
dc.source.none.fl_str_mv Revista de Ensino de Ciências e Matemática; v. 11 n. 6 (2020): out./dez.; 18-33
2179-426X
reponame:Revista de Ensino de Ciências e Matemática - REnCiMa
instname:Universidade de Caxias do Sul (UCS)
instacron:UCS
instname_str Universidade de Caxias do Sul (UCS)
instacron_str UCS
institution UCS
reponame_str Revista de Ensino de Ciências e Matemática - REnCiMa
collection Revista de Ensino de Ciências e Matemática - REnCiMa
repository.name.fl_str_mv Revista de Ensino de Ciências e Matemática - REnCiMa - Universidade de Caxias do Sul (UCS)
repository.mail.fl_str_mv ||rencima@cruzeirodosul.edu.br
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