Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic
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.23878 |
Resumo: | This paper focuses on the role of combinatorics as a modelling tool to inquire about different situations involving counting and simulation with real objects. Based on the Anthropological Theory of the Didactic, our research presents the design and implementation of a Study and Research Path (SRP) for compulsory secondary education in the area of combinatorics. The SRP starts from a generating question about discovering which padlock (among several) is safer. The empirical results correspond to a second implementation of the SRP with grade 10 students in a Catalan school with a long experience in educational innovation. We distinguish two modelling phases. First, we look at the role of combinatorics in the modelling process that emerged from the initial padlocks’ problem situation. We consider students’ construction of models to represent their explorations through the interaction with the padlocks, highlighting the importance of naming and defining the variables and the relationships used to characterise the types of padlocks. Second, we analyse how students simulate and validate these elementary combinatorial models before generalising them to explore other systems beyond padlocks. |
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Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the DidacticEnsino e aprendizagem de combinatória no ensino secundário: uma abordagem de modelação baseada na Teoria Antropológica do DidáticoArtigosThis paper focuses on the role of combinatorics as a modelling tool to inquire about different situations involving counting and simulation with real objects. Based on the Anthropological Theory of the Didactic, our research presents the design and implementation of a Study and Research Path (SRP) for compulsory secondary education in the area of combinatorics. The SRP starts from a generating question about discovering which padlock (among several) is safer. The empirical results correspond to a second implementation of the SRP with grade 10 students in a Catalan school with a long experience in educational innovation. We distinguish two modelling phases. First, we look at the role of combinatorics in the modelling process that emerged from the initial padlocks’ problem situation. We consider students’ construction of models to represent their explorations through the interaction with the padlocks, highlighting the importance of naming and defining the variables and the relationships used to characterise the types of padlocks. Second, we analyse how students simulate and validate these elementary combinatorial models before generalising them to explore other systems beyond padlocks.Este artigo centra-se no papel da combinatória como ferramenta de modelação para investigar e estudar diferentes situações que envolvem contagem e simulação com objetos reais. Com base na Teoria Antropológica do Didático, a nossa investigação apresenta a conceção e implementação de um Percurso de Estudo e Pesquisa (PEP) para o ensino secundário obrigatório na área da combinatória. O PEP parte de uma questão geradora sobre a descoberta do cadeado (entre vários) que é mais seguro. Os resultados empíricos correspondem à segunda implementação do PEP com estudantes do 10.º ano de uma escola catalã com uma longa experiência de inovação educacional. Distinguimos duas fases de modelação. Primeiro, analisamos o papel da combinatória no processo de modelação que emergiu da situação problemática inicial dos cadeados. Consideramos a construção de modelos pelos alunos para representar as suas explorações através da interação com os cadeados e a importância de nomear e definir as variáveis e as relações utilizadas para caracterizar os tipos de cadeados. Em segundo lugar, analisamos a simulação e validação destes modelos combinatórios elementares utilizados pelos estudantes e a sua generalização para explorar outros sistemas para além dos cadeados.APM - Associação de Professores de Matemática2021-12-31T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttps://doi.org/10.48489/quadrante.23878eng2183-28380872-3915Vásquez, SusanaBarquero, BertaBosch, Mariannainfo: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/23878Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:01:32.631206Repositório 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 |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic Ensino e aprendizagem de combinatória no ensino secundário: uma abordagem de modelação baseada na Teoria Antropológica do Didático |
title |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic |
spellingShingle |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic Vásquez, Susana Artigos |
title_short |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic |
title_full |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic |
title_fullStr |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic |
title_full_unstemmed |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic |
title_sort |
Teaching and learning combinatorics in secondary school: a modelling approach based on the Anthropological Theory of the Didactic |
author |
Vásquez, Susana |
author_facet |
Vásquez, Susana Barquero, Berta Bosch, Marianna |
author_role |
author |
author2 |
Barquero, Berta Bosch, Marianna |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Vásquez, Susana Barquero, Berta Bosch, Marianna |
dc.subject.por.fl_str_mv |
Artigos |
topic |
Artigos |
description |
This paper focuses on the role of combinatorics as a modelling tool to inquire about different situations involving counting and simulation with real objects. Based on the Anthropological Theory of the Didactic, our research presents the design and implementation of a Study and Research Path (SRP) for compulsory secondary education in the area of combinatorics. The SRP starts from a generating question about discovering which padlock (among several) is safer. The empirical results correspond to a second implementation of the SRP with grade 10 students in a Catalan school with a long experience in educational innovation. We distinguish two modelling phases. First, we look at the role of combinatorics in the modelling process that emerged from the initial padlocks’ problem situation. We consider students’ construction of models to represent their explorations through the interaction with the padlocks, highlighting the importance of naming and defining the variables and the relationships used to characterise the types of padlocks. Second, we analyse how students simulate and validate these elementary combinatorial models before generalising them to explore other systems beyond padlocks. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-12-31T00:00:00Z |
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.23878 |
url |
https://doi.org/10.48489/quadrante.23878 |
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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1799130480539336704 |