A study on the formal treatment of rational numbers
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Actio (Curitiba) |
Texto Completo: | https://periodicos.utfpr.edu.br/actio/article/view/11300 |
Resumo: | The objective of this paper is to present a study about the formal treatment of some concepts related to rational numbers, with discussions based on demonstrations. Our interest in the subject stems from own experience in the field of mathematics education both as teachers and researchers. For the present work, we assumed a phenomenological stance. This means that our considerations are not generalities, but interpretations and understandings of what we sought to study. The justification for writing this paper stems from the complexity of the theme, as there is no consensus among educators regarding when to start formal work on mathematics in a classroom context. The choice of theme is further justified by its importance, since these are mathematical demonstrations which underpin the theory of this science, thus ensuring its validity. We thread the path of the history of mathematics from the beginning, when mathematical truths were intuitively constituted, to be later intertwined by mathematical logic, to the present day, when they are defined by their logical-epistemological, rhetoric and heuristic characteristics. In this context, we were attracted to the study of rational numbers, due to the mathematical richness involved in the constitution of this numerical set, and their presence in elementary education. We focus on the formal treatment of rational numbers while, as educators, we try not to lose sight of the educational context. We state that it is not our intention to arbitrate on the formalization of mathematics or the teaching of this science in elementary education, but rather, we aim to introduce a theoretical study regarding some mathematical ideas involving rational numbers that synthesize our understandings. |
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A study on the formal treatment of rational numbersUm estudo sobre o tratamento formal dos números racionaisEducação/filosofia da Educação MatemáticaProva ou demonstração; Ensino de matemática; Números racionais.Proof or demonstration; Teaching of mathematics; Rational numbersThe objective of this paper is to present a study about the formal treatment of some concepts related to rational numbers, with discussions based on demonstrations. Our interest in the subject stems from own experience in the field of mathematics education both as teachers and researchers. For the present work, we assumed a phenomenological stance. This means that our considerations are not generalities, but interpretations and understandings of what we sought to study. The justification for writing this paper stems from the complexity of the theme, as there is no consensus among educators regarding when to start formal work on mathematics in a classroom context. The choice of theme is further justified by its importance, since these are mathematical demonstrations which underpin the theory of this science, thus ensuring its validity. We thread the path of the history of mathematics from the beginning, when mathematical truths were intuitively constituted, to be later intertwined by mathematical logic, to the present day, when they are defined by their logical-epistemological, rhetoric and heuristic characteristics. In this context, we were attracted to the study of rational numbers, due to the mathematical richness involved in the constitution of this numerical set, and their presence in elementary education. We focus on the formal treatment of rational numbers while, as educators, we try not to lose sight of the educational context. We state that it is not our intention to arbitrate on the formalization of mathematics or the teaching of this science in elementary education, but rather, we aim to introduce a theoretical study regarding some mathematical ideas involving rational numbers that synthesize our understandings.O seguinte artigo tem por objetivo apresentar um estudo sobre o tratamento formal para alguns conceitos referentes aos números racionais, discutidos a partir de demonstrações. Nosso interesse pelo assunto pauta-se em nossa experiência vivida, enquanto professores e pesquisadores da área de Educação Matemática. Assumimos para este trabalho uma postura fenomenológica. Isso significa que nossas considerações não são generalidades, mas sim, interpretações e compreensões do que nos propomos a pesquisar. Justificamos a escrita do texto pela complexidade envolvendo a temática, visto que não há consenso entre educadores sobre quando iniciar, no contexto da sala de aula, o trabalho com a matemática formal. E, ao mesmo tempo, a escolha do tema justifica-se também por sua importância, visto que são as demonstrações matemáticas que fundamentam as teorias desta Ciência, garantindo sua validade ou não. Partimos pelos caminhos da História da Matemática, que nos mostra que, em princípio, as verdades da matemática eram constituídas de modo intuitivo, depois foram entrelaçadas pela Lógica Matemática e, na atualidade, são definidas por suas características lógico-epistemológicas, retóricas e heurísticas. Nesse contexto, destaca-se para nós os números racionais, pela riqueza matemática envolvida na constituição desse conjunto numérico e por sua presença na Educação Básica. Assim, nos debruçamos sobre o tratamento formal deste conjunto numérico e, enquanto educadores, não perdemos de vista o contexto educacional. Anunciamos que nossa intenção não é arbitrar sobre a formalização da matemática em seu ensino na Educação Básica, mas sim, expor um estudo teórico sobre algumas ideias matemáticas envolvendo os números racionais que sintetizam nossas compreensões.Universidade Tecnológica Federal do Paraná (UTFPR)Santos, Joel Gonçalves dosMondini, Fabiane2020-07-26info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionestudo teóricoapplication/pdfhttps://periodicos.utfpr.edu.br/actio/article/view/1130010.3895/actio.v5n2.11300ACTIO: Teaching in Sciences; v. 5, n. 2 (2020); 1-15ACTIO: Docência em Ciências; v. 5, n. 2 (2020); 1-152525-892310.3895/actio.v5n2reponame:Actio (Curitiba)instname:Universidade Tecnológica Federal do Paraná (UTFPR)instacron:UTFPRporhttps://periodicos.utfpr.edu.br/actio/article/view/11300/7599Direitos autorais 2020 ACTIO: Docência em Ciênciashttp://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccess2022-10-18T23:53:36Zoai:periodicos.utfpr:article/11300Revistahttps://periodicos.utfpr.edu.br/actio/PUBhttps://periodicos.utfpr.edu.br/actio/oaimarcelolambach@utfpr.edu.br||actio-ct@utfpr.edu.br||periodicos@utfpr.edu.br2525-89232525-8923opendoar:2022-10-18T23:53:36Actio (Curitiba) - Universidade Tecnológica Federal do Paraná (UTFPR)false |
dc.title.none.fl_str_mv |
A study on the formal treatment of rational numbers Um estudo sobre o tratamento formal dos números racionais |
title |
A study on the formal treatment of rational numbers |
spellingShingle |
A study on the formal treatment of rational numbers Santos, Joel Gonçalves dos Educação/filosofia da Educação Matemática Prova ou demonstração; Ensino de matemática; Números racionais. Proof or demonstration; Teaching of mathematics; Rational numbers |
title_short |
A study on the formal treatment of rational numbers |
title_full |
A study on the formal treatment of rational numbers |
title_fullStr |
A study on the formal treatment of rational numbers |
title_full_unstemmed |
A study on the formal treatment of rational numbers |
title_sort |
A study on the formal treatment of rational numbers |
author |
Santos, Joel Gonçalves dos |
author_facet |
Santos, Joel Gonçalves dos Mondini, Fabiane |
author_role |
author |
author2 |
Mondini, Fabiane |
author2_role |
author |
dc.contributor.none.fl_str_mv |
|
dc.contributor.author.fl_str_mv |
Santos, Joel Gonçalves dos Mondini, Fabiane |
dc.subject.por.fl_str_mv |
Educação/filosofia da Educação Matemática Prova ou demonstração; Ensino de matemática; Números racionais. Proof or demonstration; Teaching of mathematics; Rational numbers |
topic |
Educação/filosofia da Educação Matemática Prova ou demonstração; Ensino de matemática; Números racionais. Proof or demonstration; Teaching of mathematics; Rational numbers |
description |
The objective of this paper is to present a study about the formal treatment of some concepts related to rational numbers, with discussions based on demonstrations. Our interest in the subject stems from own experience in the field of mathematics education both as teachers and researchers. For the present work, we assumed a phenomenological stance. This means that our considerations are not generalities, but interpretations and understandings of what we sought to study. The justification for writing this paper stems from the complexity of the theme, as there is no consensus among educators regarding when to start formal work on mathematics in a classroom context. The choice of theme is further justified by its importance, since these are mathematical demonstrations which underpin the theory of this science, thus ensuring its validity. We thread the path of the history of mathematics from the beginning, when mathematical truths were intuitively constituted, to be later intertwined by mathematical logic, to the present day, when they are defined by their logical-epistemological, rhetoric and heuristic characteristics. In this context, we were attracted to the study of rational numbers, due to the mathematical richness involved in the constitution of this numerical set, and their presence in elementary education. We focus on the formal treatment of rational numbers while, as educators, we try not to lose sight of the educational context. We state that it is not our intention to arbitrate on the formalization of mathematics or the teaching of this science in elementary education, but rather, we aim to introduce a theoretical study regarding some mathematical ideas involving rational numbers that synthesize our understandings. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-07-26 |
dc.type.none.fl_str_mv |
|
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion estudo teórico |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.utfpr.edu.br/actio/article/view/11300 10.3895/actio.v5n2.11300 |
url |
https://periodicos.utfpr.edu.br/actio/article/view/11300 |
identifier_str_mv |
10.3895/actio.v5n2.11300 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.utfpr.edu.br/actio/article/view/11300/7599 |
dc.rights.driver.fl_str_mv |
Direitos autorais 2020 ACTIO: Docência em Ciências http://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Direitos autorais 2020 ACTIO: Docência em Ciências http://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Universidade Tecnológica Federal do Paraná (UTFPR) |
publisher.none.fl_str_mv |
Universidade Tecnológica Federal do Paraná (UTFPR) |
dc.source.none.fl_str_mv |
ACTIO: Teaching in Sciences; v. 5, n. 2 (2020); 1-15 ACTIO: Docência em Ciências; v. 5, n. 2 (2020); 1-15 2525-8923 10.3895/actio.v5n2 reponame:Actio (Curitiba) instname:Universidade Tecnológica Federal do Paraná (UTFPR) instacron:UTFPR |
instname_str |
Universidade Tecnológica Federal do Paraná (UTFPR) |
instacron_str |
UTFPR |
institution |
UTFPR |
reponame_str |
Actio (Curitiba) |
collection |
Actio (Curitiba) |
repository.name.fl_str_mv |
Actio (Curitiba) - Universidade Tecnológica Federal do Paraná (UTFPR) |
repository.mail.fl_str_mv |
marcelolambach@utfpr.edu.br||actio-ct@utfpr.edu.br||periodicos@utfpr.edu.br |
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1797239983697821696 |