Teaching exponential functions through robotics gears
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Texto livre |
Texto Completo: | https://periodicos.ufmg.br/index.php/textolivre/article/view/24890 |
Resumo: | The central theme of this work is the exponential function and the exponential type through interactions between gears of the LEGO® Mindstorms NXT Kit. For this, we used the construction of a cart with parts from the kit, composed of a 4-speed gearbox, which works under an exponential rate of change. The motivation of this work was to discover if it would be possible or not to abstract this function, from interactions between gears that, in the great majority, are only associated with the proportionality issues and, consequently, with linear functions. But, with analyzes and studies made on materials already obtained, both on interactions between gears and on gear changes made of LEGO® pieces, we could carry out the construction of the proposed gear. We use gears reductions, which, in sequence, form a geometric progression, which, in turn, was associated with the exponential type function. Thus, this exchange is used as an object of study of a didactic sequence and content, both with regard to its construction and its functioning. And as a result of this work, first it is possible to glimpse the great mathematical collection existing in the interactions between gears, which, when associated with Educational Robotics, allows us to fully work on the integral development of students, and second, a didactic sequence for teaching exponential function, which starts from the concrete construction of something, for mathematical abstraction. |
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Teaching exponential functions through robotics gearsO ensino de funções exponenciais por engrenagens robóticasEngrenagensFunção exponencialLEGO®Sequência didáticaRobótica educacionalGearsExponential functionLEGO®Didactic sequenceEducational roboticsThe central theme of this work is the exponential function and the exponential type through interactions between gears of the LEGO® Mindstorms NXT Kit. For this, we used the construction of a cart with parts from the kit, composed of a 4-speed gearbox, which works under an exponential rate of change. The motivation of this work was to discover if it would be possible or not to abstract this function, from interactions between gears that, in the great majority, are only associated with the proportionality issues and, consequently, with linear functions. But, with analyzes and studies made on materials already obtained, both on interactions between gears and on gear changes made of LEGO® pieces, we could carry out the construction of the proposed gear. We use gears reductions, which, in sequence, form a geometric progression, which, in turn, was associated with the exponential type function. Thus, this exchange is used as an object of study of a didactic sequence and content, both with regard to its construction and its functioning. And as a result of this work, first it is possible to glimpse the great mathematical collection existing in the interactions between gears, which, when associated with Educational Robotics, allows us to fully work on the integral development of students, and second, a didactic sequence for teaching exponential function, which starts from the concrete construction of something, for mathematical abstraction. O tema central deste trabalho é a função exponencial e a do tipo exponencial através de interações entre engrenagens do Kit LEGO® Mindstorms NXT. Para isso, utilizamos a construção de um carrinho com peças do kit, composto por um câmbio de quatro marchas, que funcionam sob uma taxa de variação exponencial. A motivação deste trabalho foi descobrir se seria possível ou não abstrair essa função, a partir de interações entre engrenagens, que, em sua grande maioria, são associadas apenas às questões de proporcionalidade e, consequentemente, a funções lineares. Mas, com análises e estudos feitos em materiais já produzidos, tanto sobre interações entre engrenagens, como sobre câmbios de marchas feitos de peças LEGO®, conseguimos efetuar a construção do câmbio proposto. Utilizamo-nos de reduções de giros nas engrenagens, que, em sequência, formaram uma progressão geométrica, a qual, por sua vez, foi associada à função do tipo exponencial. Assim, esse câmbio é utilizado como objeto de estudo de uma sequência didática e de conteúdos, tanto no que diz respeito a sua construção como quanto a seu funcionamento. Como resultados deste trabalho, primeiro é possível vislumbrar o grande acervo matemático existente nas interações entre engrenagens, o que, quando associado à Robótica Educacional, permite trabalhar de forma plena o desenvolvimento integral dos alunos, e segundo, uma sequência didática para o ensino da função exponencial, que parte da construção concreta de algo, para a abstração matemática.Universidade Federal de Minas Gerais2020-08-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/ziphttps://periodicos.ufmg.br/index.php/textolivre/article/view/2489010.35699/1983-3652.2020.24890Texto Livre; Vol. 13 No. 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270Texto Livre; Vol. 13 Núm. 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270Texto Livre; Vol. 13 No 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270Texto Livre; v. 13 n. 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-2701983-3652reponame:Texto livreinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGporhttps://periodicos.ufmg.br/index.php/textolivre/article/view/24890/19663https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/27705https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/27706https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/27707https://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessSilva, Fernando Kennedy daCosta, Cristhian Pires da2021-07-07T23:33:27Zoai:periodicos.ufmg.br:article/24890Revistahttp://www.periodicos.letras.ufmg.br/index.php/textolivrePUBhttps://periodicos.ufmg.br/index.php/textolivre/oairevistatextolivre@letras.ufmg.br1983-36521983-3652opendoar:2021-07-07T23:33:27Texto livre - Universidade Federal de Minas Gerais (UFMG)false |
dc.title.none.fl_str_mv |
Teaching exponential functions through robotics gears O ensino de funções exponenciais por engrenagens robóticas |
title |
Teaching exponential functions through robotics gears |
spellingShingle |
Teaching exponential functions through robotics gears Silva, Fernando Kennedy da Engrenagens Função exponencial LEGO® Sequência didática Robótica educacional Gears Exponential function LEGO® Didactic sequence Educational robotics |
title_short |
Teaching exponential functions through robotics gears |
title_full |
Teaching exponential functions through robotics gears |
title_fullStr |
Teaching exponential functions through robotics gears |
title_full_unstemmed |
Teaching exponential functions through robotics gears |
title_sort |
Teaching exponential functions through robotics gears |
author |
Silva, Fernando Kennedy da |
author_facet |
Silva, Fernando Kennedy da Costa, Cristhian Pires da |
author_role |
author |
author2 |
Costa, Cristhian Pires da |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Silva, Fernando Kennedy da Costa, Cristhian Pires da |
dc.subject.por.fl_str_mv |
Engrenagens Função exponencial LEGO® Sequência didática Robótica educacional Gears Exponential function LEGO® Didactic sequence Educational robotics |
topic |
Engrenagens Função exponencial LEGO® Sequência didática Robótica educacional Gears Exponential function LEGO® Didactic sequence Educational robotics |
description |
The central theme of this work is the exponential function and the exponential type through interactions between gears of the LEGO® Mindstorms NXT Kit. For this, we used the construction of a cart with parts from the kit, composed of a 4-speed gearbox, which works under an exponential rate of change. The motivation of this work was to discover if it would be possible or not to abstract this function, from interactions between gears that, in the great majority, are only associated with the proportionality issues and, consequently, with linear functions. But, with analyzes and studies made on materials already obtained, both on interactions between gears and on gear changes made of LEGO® pieces, we could carry out the construction of the proposed gear. We use gears reductions, which, in sequence, form a geometric progression, which, in turn, was associated with the exponential type function. Thus, this exchange is used as an object of study of a didactic sequence and content, both with regard to its construction and its functioning. And as a result of this work, first it is possible to glimpse the great mathematical collection existing in the interactions between gears, which, when associated with Educational Robotics, allows us to fully work on the integral development of students, and second, a didactic sequence for teaching exponential function, which starts from the concrete construction of something, for mathematical abstraction. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-08-24 |
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://periodicos.ufmg.br/index.php/textolivre/article/view/24890 10.35699/1983-3652.2020.24890 |
url |
https://periodicos.ufmg.br/index.php/textolivre/article/view/24890 |
identifier_str_mv |
10.35699/1983-3652.2020.24890 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/19663 https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/27705 https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/27706 https://periodicos.ufmg.br/index.php/textolivre/article/view/24890/27707 |
dc.rights.driver.fl_str_mv |
https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf application/zip |
dc.publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
publisher.none.fl_str_mv |
Universidade Federal de Minas Gerais |
dc.source.none.fl_str_mv |
Texto Livre; Vol. 13 No. 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270 Texto Livre; Vol. 13 Núm. 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270 Texto Livre; Vol. 13 No 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270 Texto Livre; v. 13 n. 2 (2020): Texto Livre: Linguagem e Tecnologia; 238-270 1983-3652 reponame:Texto livre instname:Universidade Federal de Minas Gerais (UFMG) instacron:UFMG |
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Universidade Federal de Minas Gerais (UFMG) |
instacron_str |
UFMG |
institution |
UFMG |
reponame_str |
Texto livre |
collection |
Texto livre |
repository.name.fl_str_mv |
Texto livre - Universidade Federal de Minas Gerais (UFMG) |
repository.mail.fl_str_mv |
revistatextolivre@letras.ufmg.br |
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1799711142968295424 |