Developing flexible-adaptive reasoning and computing
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.26/22222 |
Resumo: | The project ‘Numerical thinking and flexible calculation: critical issues’ aims to study students’ conceptual knowledge associated with the understanding of the different levels of learning numbers and operations. We follow the idea proposed by several authors that flexibility refers to the ability to manipulate numbers as mathematical objects which can be decomposed and recomposed in multiple ways using different symbolisms for the same objet (Gravemeijer, 2004; Gray &Tall, 1994;). The project plan is based on a qualitative and interpretative methodology (Denzin & Lincoln, 2005) with a design research approach (Gravemeijer & Cobb, 2006). This article focus the preparation of a teaching experience centered in the flexible learning of multiplication. It describes the analysis of a clinical interview where Pedro (9 years) solves the task 'Prawn skewers'. It illustrates how we identify and describe Pedro’s conceptual knowledge associated with the different levels of understanding of numbers and multiplication/division and analyzes if and how this knowledge facilitates adaptive thinking and flexible calculation. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Developing flexible-adaptive reasoning and computingPedro's understanding of the task "Prawn Skewers"Multiplicative reasoningFlexible calculationMathematical tasksThe project ‘Numerical thinking and flexible calculation: critical issues’ aims to study students’ conceptual knowledge associated with the understanding of the different levels of learning numbers and operations. We follow the idea proposed by several authors that flexibility refers to the ability to manipulate numbers as mathematical objects which can be decomposed and recomposed in multiple ways using different symbolisms for the same objet (Gravemeijer, 2004; Gray &Tall, 1994;). The project plan is based on a qualitative and interpretative methodology (Denzin & Lincoln, 2005) with a design research approach (Gravemeijer & Cobb, 2006). This article focus the preparation of a teaching experience centered in the flexible learning of multiplication. It describes the analysis of a clinical interview where Pedro (9 years) solves the task 'Prawn skewers'. It illustrates how we identify and describe Pedro’s conceptual knowledge associated with the different levels of understanding of numbers and multiplication/division and analyzes if and how this knowledge facilitates adaptive thinking and flexible calculation.Instituto Politécnico de Viana do Castelo, Escola Superior de EducaçãoRepositório ComumBrocardo, JoanaKraemer, Jean-MarieMendes, FátimaDelgado, Catarina2018-04-09T13:51:41Z20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.26/22222eng2183-2234info: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:RCAAP2023-11-21T09:53:42Zoai:comum.rcaap.pt:10400.26/22222Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:09:37.173285Repositório 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 |
Developing flexible-adaptive reasoning and computing Pedro's understanding of the task "Prawn Skewers" |
title |
Developing flexible-adaptive reasoning and computing |
spellingShingle |
Developing flexible-adaptive reasoning and computing Brocardo, Joana Multiplicative reasoning Flexible calculation Mathematical tasks |
title_short |
Developing flexible-adaptive reasoning and computing |
title_full |
Developing flexible-adaptive reasoning and computing |
title_fullStr |
Developing flexible-adaptive reasoning and computing |
title_full_unstemmed |
Developing flexible-adaptive reasoning and computing |
title_sort |
Developing flexible-adaptive reasoning and computing |
author |
Brocardo, Joana |
author_facet |
Brocardo, Joana Kraemer, Jean-Marie Mendes, Fátima Delgado, Catarina |
author_role |
author |
author2 |
Kraemer, Jean-Marie Mendes, Fátima Delgado, Catarina |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Repositório Comum |
dc.contributor.author.fl_str_mv |
Brocardo, Joana Kraemer, Jean-Marie Mendes, Fátima Delgado, Catarina |
dc.subject.por.fl_str_mv |
Multiplicative reasoning Flexible calculation Mathematical tasks |
topic |
Multiplicative reasoning Flexible calculation Mathematical tasks |
description |
The project ‘Numerical thinking and flexible calculation: critical issues’ aims to study students’ conceptual knowledge associated with the understanding of the different levels of learning numbers and operations. We follow the idea proposed by several authors that flexibility refers to the ability to manipulate numbers as mathematical objects which can be decomposed and recomposed in multiple ways using different symbolisms for the same objet (Gravemeijer, 2004; Gray &Tall, 1994;). The project plan is based on a qualitative and interpretative methodology (Denzin & Lincoln, 2005) with a design research approach (Gravemeijer & Cobb, 2006). This article focus the preparation of a teaching experience centered in the flexible learning of multiplication. It describes the analysis of a clinical interview where Pedro (9 years) solves the task 'Prawn skewers'. It illustrates how we identify and describe Pedro’s conceptual knowledge associated with the different levels of understanding of numbers and multiplication/division and analyzes if and how this knowledge facilitates adaptive thinking and flexible calculation. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 2015-01-01T00:00:00Z 2018-04-09T13:51:41Z |
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 |
http://hdl.handle.net/10400.26/22222 |
url |
http://hdl.handle.net/10400.26/22222 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2183-2234 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Instituto Politécnico de Viana do Castelo, Escola Superior de Educação |
publisher.none.fl_str_mv |
Instituto Politécnico de Viana do Castelo, Escola Superior de Educação |
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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1799135358892376064 |