Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://doi.org/10.48489/quadrante.23721 |
Resumo: | Mathematical modelling is a significant and productive context for teaching linear algebra, favoring students’ learning of concepts and modelling competencies, often neglected in undergraduate mathematics. This study aims to characterize the modelling routes performed and the competencies put into practice by Costa Rican undergraduate students in a linear algebra course, when solving a mathematical modelling task involving the concepts of spanning set and basis of a vector subspace, using the Excel spreadsheet. Data collection included participant observation of the students’ discussions, their written work on the task, and the Excel files produced. The analysis reveals incomplete and complete modelling routes performed by the students, in which they used the concepts of linear combination, span, standard and non-standard basis to build models. The use of technology influenced the way students obtained mathematical and/or real results from their mathematical model. In complete modelling routes, the computer model has driven several transitions within the modelling cycle, namely between computational, mathematical, and real results, enhancing the modelling processes. In addition, the spreadsheet performed two main functions, calculating and simulating, allowing the groups who used it to assess the effectiveness of their mathematical and computer models and validate them against the real situation. |
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Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate studentsRotas de modelação matemática apoiadas pela tecnologia na aprendizagem da álgebra linear: um estudo com estudantes universitários da Costa RicaArtigosMathematical modelling is a significant and productive context for teaching linear algebra, favoring students’ learning of concepts and modelling competencies, often neglected in undergraduate mathematics. This study aims to characterize the modelling routes performed and the competencies put into practice by Costa Rican undergraduate students in a linear algebra course, when solving a mathematical modelling task involving the concepts of spanning set and basis of a vector subspace, using the Excel spreadsheet. Data collection included participant observation of the students’ discussions, their written work on the task, and the Excel files produced. The analysis reveals incomplete and complete modelling routes performed by the students, in which they used the concepts of linear combination, span, standard and non-standard basis to build models. The use of technology influenced the way students obtained mathematical and/or real results from their mathematical model. In complete modelling routes, the computer model has driven several transitions within the modelling cycle, namely between computational, mathematical, and real results, enhancing the modelling processes. In addition, the spreadsheet performed two main functions, calculating and simulating, allowing the groups who used it to assess the effectiveness of their mathematical and computer models and validate them against the real situation.A modelação matemática é um contexto relevante e produtivo para o ensino da álgebra linear, favorecendo a aprendizagem de conceitos e competências de modelação dos estudantes, comumente negligenciadas na matemática universitária. Este estudo visa caracterizar rotas de modelação realizadas e competências postas em prática por estudantes universitários da Costa Rica, numa disciplina de álgebra linear, ao resolverem uma tarefa de modelação matemática envolvendo conceitos de conjunto gerador e base de um subespaço vetorial, usando uma folha de cálculo. A recolha de dados incluiu observação participante das discussões dos estudantes e suas resoluções escritas, bem como os ficheiros Excel produzidos. A análise revelou rotas de modelação dos estudantes incompletas e completas, nas quais utilizaram conceitos de combinação linear, subespaço gerado, base canónica e não canónica para construir modelos. O uso da tecnologia influenciou o modo como os alunos obtiveram resultados matemáticos e reais extraídos do seu modelo matemático. Nas rotas completas, o modelo computacional impulsionou transições no ciclo de modelação entre resultados computacionais, matemáticos e reais, melhorando os processos de modelação. Complementarmente, o Excel desempenhou duas funções principais, calcular e simular, permitindo aos grupos que o utilizaram avaliarem a eficácia dos seus modelos matemáticos e computacionais e validá-los no confronto com a situação real.APM - Associação de Professores de Matemática2021-06-30T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttps://doi.org/10.48489/quadrante.23721eng2183-28380872-3915, Guillermo Ramírez-Montes, Susana CarreiraHenriques, Anainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2022-09-22T17:07:08Zoai:ojs.revistas.rcaap.pt:article/23721Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:01:32.445096Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students Rotas de modelação matemática apoiadas pela tecnologia na aprendizagem da álgebra linear: um estudo com estudantes universitários da Costa Rica |
title |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students |
spellingShingle |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students , Guillermo Ramírez-Montes Artigos |
title_short |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students |
title_full |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students |
title_fullStr |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students |
title_full_unstemmed |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students |
title_sort |
Mathematical modelling routes supported by technology in the learning of linear algebra: a study with Costa Rican undergraduate students |
author |
, Guillermo Ramírez-Montes |
author_facet |
, Guillermo Ramírez-Montes , Susana Carreira Henriques, Ana |
author_role |
author |
author2 |
, Susana Carreira Henriques, Ana |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
, Guillermo Ramírez-Montes , Susana Carreira Henriques, Ana |
dc.subject.por.fl_str_mv |
Artigos |
topic |
Artigos |
description |
Mathematical modelling is a significant and productive context for teaching linear algebra, favoring students’ learning of concepts and modelling competencies, often neglected in undergraduate mathematics. This study aims to characterize the modelling routes performed and the competencies put into practice by Costa Rican undergraduate students in a linear algebra course, when solving a mathematical modelling task involving the concepts of spanning set and basis of a vector subspace, using the Excel spreadsheet. Data collection included participant observation of the students’ discussions, their written work on the task, and the Excel files produced. The analysis reveals incomplete and complete modelling routes performed by the students, in which they used the concepts of linear combination, span, standard and non-standard basis to build models. The use of technology influenced the way students obtained mathematical and/or real results from their mathematical model. In complete modelling routes, the computer model has driven several transitions within the modelling cycle, namely between computational, mathematical, and real results, enhancing the modelling processes. In addition, the spreadsheet performed two main functions, calculating and simulating, allowing the groups who used it to assess the effectiveness of their mathematical and computer models and validate them against the real situation. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-30T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://doi.org/10.48489/quadrante.23721 |
url |
https://doi.org/10.48489/quadrante.23721 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2183-2838 0872-3915 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
APM - Associação de Professores de Matemática |
publisher.none.fl_str_mv |
APM - Associação de Professores de Matemática |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799130480531996672 |