Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment

Detalhes bibliográficos
Autor(a) principal: Karrer, Monica
Data de Publicação: 2018
Outros Autores: Santos, Renata Caroline Mota
Tipo de documento: Artigo
Idioma: por
Título da fonte: Research, Society and Development
Texto Completo: https://rsdjournal.org/index.php/rsd/article/view/405
Resumo: The purpose of this article is to present a teaching experiment on the content of linear transformations in the plane and the results of its application in a pair of students of Mechanical Engineering course. Difficulties of the students in Linear Algebra discipline concerning its formal aspect are pointed by Aydin, Hannah, et al. and Isik, furthermore, new pedagogical practices which considers this problematic are required. In this context, elaborating and applying a teaching approach to geometrical linear transformations is aimed at bringing innovative learning and teaching perspectives. This experiment essentially regards the concepts of composition, nucleus and image and also integrates the GeoGebra software to explore the relations among representations of different registers such as graphic, algebraic, figural and of natural language. The study is grounded on the registers of semiotic representations provided by Duval's theory and on a technology according to the views of Drijvers, Baki, Hoyles and Noss and Borba and Penteado, in order to allow different developments from those reached by paper and pencil environment. For the experiment preparation and conduction, it is used some aspects of the Design Experiment by Cobb et al., a specific method to build an innovative approach to the mathematics education. This research has a qualitative character and the results revealed that providing a favorable environment to the students to coordinate representations of different registers, there was progress in understanding the concepts related to linear transformations, mainly, nucleus and image. The autonomy in building concepts is privileged by the GeoGebra software utilization, regarding its dynamic character, the students could test their conjectures in its environment.
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spelling Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviromentNúcleo, Imagen y Composición de Transformaciones Lineales: un enfoque gráfico desarrollado en ambiente computacionalNúcleo, Imagem e Composição de Transformações Lineares: uma abordagem gráfica desenvolvida em ambiente computacionalÁlgebra LinealTransformaciones linealesGeoGebraRepresentaciones SemióticasDiseño Experiment.Álgebra LinearTransformações LinearesGeoGebraRepresentações SemióticasDesign Experiment.The purpose of this article is to present a teaching experiment on the content of linear transformations in the plane and the results of its application in a pair of students of Mechanical Engineering course. Difficulties of the students in Linear Algebra discipline concerning its formal aspect are pointed by Aydin, Hannah, et al. and Isik, furthermore, new pedagogical practices which considers this problematic are required. In this context, elaborating and applying a teaching approach to geometrical linear transformations is aimed at bringing innovative learning and teaching perspectives. This experiment essentially regards the concepts of composition, nucleus and image and also integrates the GeoGebra software to explore the relations among representations of different registers such as graphic, algebraic, figural and of natural language. The study is grounded on the registers of semiotic representations provided by Duval's theory and on a technology according to the views of Drijvers, Baki, Hoyles and Noss and Borba and Penteado, in order to allow different developments from those reached by paper and pencil environment. For the experiment preparation and conduction, it is used some aspects of the Design Experiment by Cobb et al., a specific method to build an innovative approach to the mathematics education. This research has a qualitative character and the results revealed that providing a favorable environment to the students to coordinate representations of different registers, there was progress in understanding the concepts related to linear transformations, mainly, nucleus and image. The autonomy in building concepts is privileged by the GeoGebra software utilization, regarding its dynamic character, the students could test their conjectures in its environment.El objetivo del presente artículo consiste en presentar un nuevo enfoque de enseñanza relativa a las transformaciones lineales planas y las implicaciones de su aplicación en una pareja de estudiantes del curso de Ingeniería Mecánica. Aydin, Hannah et al. y Isik revelaron las dificultades de los estudiantes con el formalismo del álgebra lineal, apuntando la necesidad de elaboración de alternativas pedagógicas que consideren esa problemática. En este contexto, se intentó elaborar y aplicar un enfoque de enseñanza sobre las transformaciones lineales geométricas, enfocando los conceptos de composición, núcleo e imagen e integrando el software GeoGebra para explorar las relaciones entre los registros gráfico, algebraico, figural y de la lengua natural. El estudio fue fundamentado en la teoría de los registros de representaciones semióticas de Duval y se utilizó de recursos computacionales según las indicaciones de Drijvers, Baki, Noss y Hoyles y Borba y Peinado, para permitir exploraciones diferenciadas de las obtenidas en ambientes del tipo papel y lápiz. Para orientar la construcción del experimento, se utilizaron aspectos de la metodología de Diseño Experiment de Cobb et al., La cual baliza la construcción de innovaciones en el área de Educación Matemática. La investigación tuvo carácter cualitativo, siendo constatado que, al proporcionar a los sujetos un ambiente favorable para coordinar representaciones de diferentes registros, hubo progresos en la comprensión de los conceptos. La utilización del software GeoGebra favoreció la autonomía en la construcción del concepto, ya que, utilizando su dinamismo, los alumnos pudieron, de forma independiente, elaborar y probar sus conjeturas en el propio ambiente.O objetivo do presente artigo consiste em apresentar uma nova abordagem de ensino relativa às transformações lineares planas e as implicações de sua aplicação em uma dupla de estudantes do curso de Engenharia Mecânica. Aydin, Hannah et al. e Isik revelaram as dificuldades dos estudantes com o formalismo da Álgebra Linear, apontando a necessidade de elaboração de alternativas pedagógicas que considerem essa problemática. Nesse contexto, procurou-se elaborar e aplicar uma abordagem de ensino sobre as transformações lineares geométricas, focando os conceitos de composição, núcleo e imagem e integrando o software GeoGebra para explorar as relações entre os registros gráfico, algébrico, figural e da língua natural. O estudo foi fundamentado na teoria dos registros de representações semióticas de Duval e se utilizou de recursos computacionais segundo as indicações de Drijvers, Baki, Noss e Hoyles e Borba e Penteado, de modo a permitir explorações diferenciadas das obtidas em ambientes do tipo papel&lápis. Para nortear a construção do experimento, foram utilizados aspectos da metodologia de Design Experiment de Cobb et al., a qual baliza a construção de inovações na área de Educação Matemática. A pesquisa teve caráter qualitativo, sendo constatado que, ao proporcionar aos sujeitos um ambiente favorável para coordenar representações de diferentes registros, houve progressos na compreensão dos conceitos. A utilização do software GeoGebra favoreceu a autonomia na construção do conceito, visto que, utilizando o seu dinamismo, os alunos puderam, de forma independente, elaborar e testar suas conjecturas no próprio ambiente.Research, Society and Development2018-05-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://rsdjournal.org/index.php/rsd/article/view/40510.17648/rsd-v7i10.405Research, Society and Development; Vol. 7 No. 10; e9710405Research, Society and Development; Vol. 7 Núm. 10; e9710405Research, Society and Development; v. 7 n. 10; e97104052525-3409reponame:Research, Society and Developmentinstname:Universidade Federal de Itajubá (UNIFEI)instacron:UNIFEIporhttps://rsdjournal.org/index.php/rsd/article/view/405/324Copyright (c) 2018 Monica Karrer, Renata Caroline Mota Santosinfo:eu-repo/semantics/openAccessKarrer, MonicaSantos, Renata Caroline Mota2019-01-22T01:15:00Zoai:ojs.pkp.sfu.ca:article/405Revistahttps://rsdjournal.org/index.php/rsd/indexPUBhttps://rsdjournal.org/index.php/rsd/oairsd.articles@gmail.com2525-34092525-3409opendoar:2024-01-17T09:25:56.124401Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)false
dc.title.none.fl_str_mv Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
Núcleo, Imagen y Composición de Transformaciones Lineales: un enfoque gráfico desarrollado en ambiente computacional
Núcleo, Imagem e Composição de Transformações Lineares: uma abordagem gráfica desenvolvida em ambiente computacional
title Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
spellingShingle Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
Karrer, Monica
Álgebra Lineal
Transformaciones lineales
GeoGebra
Representaciones Semióticas
Diseño Experiment.
Álgebra Linear
Transformações Lineares
GeoGebra
Representações Semióticas
Design Experiment.
title_short Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
title_full Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
title_fullStr Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
title_full_unstemmed Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
title_sort Nucleus, Image and Composition of Linear Transformations: a graphical approach in computational enviroment
author Karrer, Monica
author_facet Karrer, Monica
Santos, Renata Caroline Mota
author_role author
author2 Santos, Renata Caroline Mota
author2_role author
dc.contributor.author.fl_str_mv Karrer, Monica
Santos, Renata Caroline Mota
dc.subject.por.fl_str_mv Álgebra Lineal
Transformaciones lineales
GeoGebra
Representaciones Semióticas
Diseño Experiment.
Álgebra Linear
Transformações Lineares
GeoGebra
Representações Semióticas
Design Experiment.
topic Álgebra Lineal
Transformaciones lineales
GeoGebra
Representaciones Semióticas
Diseño Experiment.
Álgebra Linear
Transformações Lineares
GeoGebra
Representações Semióticas
Design Experiment.
description The purpose of this article is to present a teaching experiment on the content of linear transformations in the plane and the results of its application in a pair of students of Mechanical Engineering course. Difficulties of the students in Linear Algebra discipline concerning its formal aspect are pointed by Aydin, Hannah, et al. and Isik, furthermore, new pedagogical practices which considers this problematic are required. In this context, elaborating and applying a teaching approach to geometrical linear transformations is aimed at bringing innovative learning and teaching perspectives. This experiment essentially regards the concepts of composition, nucleus and image and also integrates the GeoGebra software to explore the relations among representations of different registers such as graphic, algebraic, figural and of natural language. The study is grounded on the registers of semiotic representations provided by Duval's theory and on a technology according to the views of Drijvers, Baki, Hoyles and Noss and Borba and Penteado, in order to allow different developments from those reached by paper and pencil environment. For the experiment preparation and conduction, it is used some aspects of the Design Experiment by Cobb et al., a specific method to build an innovative approach to the mathematics education. This research has a qualitative character and the results revealed that providing a favorable environment to the students to coordinate representations of different registers, there was progress in understanding the concepts related to linear transformations, mainly, nucleus and image. The autonomy in building concepts is privileged by the GeoGebra software utilization, regarding its dynamic character, the students could test their conjectures in its environment.
publishDate 2018
dc.date.none.fl_str_mv 2018-05-28
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://rsdjournal.org/index.php/rsd/article/view/405
10.17648/rsd-v7i10.405
url https://rsdjournal.org/index.php/rsd/article/view/405
identifier_str_mv 10.17648/rsd-v7i10.405
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://rsdjournal.org/index.php/rsd/article/view/405/324
dc.rights.driver.fl_str_mv Copyright (c) 2018 Monica Karrer, Renata Caroline Mota Santos
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2018 Monica Karrer, Renata Caroline Mota Santos
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Research, Society and Development
publisher.none.fl_str_mv Research, Society and Development
dc.source.none.fl_str_mv Research, Society and Development; Vol. 7 No. 10; e9710405
Research, Society and Development; Vol. 7 Núm. 10; e9710405
Research, Society and Development; v. 7 n. 10; e9710405
2525-3409
reponame:Research, Society and Development
instname:Universidade Federal de Itajubá (UNIFEI)
instacron:UNIFEI
instname_str Universidade Federal de Itajubá (UNIFEI)
instacron_str UNIFEI
institution UNIFEI
reponame_str Research, Society and Development
collection Research, Society and Development
repository.name.fl_str_mv Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)
repository.mail.fl_str_mv rsd.articles@gmail.com
_version_ 1797052828749922304

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