Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Bolema: Boletim de Educação Matemática |
Texto Completo: | https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/7831 |
Resumo: | This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties. Key words: Mathematical Abstraction. Activity-effect Reflection. Reflective Abstraction. Formation of Mathematical Objects. Participatory and Anticipatory Stages. |
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Bolema: Boletim de Educação Matemática |
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Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical ConceptionsThis study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties. Key words: Mathematical Abstraction. Activity-effect Reflection. Reflective Abstraction. Formation of Mathematical Objects. Participatory and Anticipatory Stages.UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas2013-08-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/7831Bolema: Boletim de Educação Matemática; v. 26 n. 44 (2012); 1345-13661980-44150103-636Xreponame:Bolema: Boletim de Educação Matemáticainstname:Universidade Estadual Paulista (UNESP)instacron:UNESPporhttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/7831/5488Roig, Ana-IsabelLlinares, SalvadorPenalva, Maria del Carmeninfo:eu-repo/semantics/openAccess2015-10-14T00:00:02Zoai:periodicos.rc.biblioteca.unesp.br:article/7831Revistahttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/PUBhttps://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/oaibolema.contato@gmail.com||romiarka@gmail.com1980-44150103-636Xopendoar:2015-10-14T00:00:02Bolema: Boletim de Educação Matemática - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
title |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
spellingShingle |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions Roig, Ana-Isabel |
title_short |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
title_full |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
title_fullStr |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
title_full_unstemmed |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
title_sort |
Different Moments in the Participatory Stage of the Secondary Students’ Abstraction of Mathematical Conceptions |
author |
Roig, Ana-Isabel |
author_facet |
Roig, Ana-Isabel Llinares, Salvador Penalva, Maria del Carmen |
author_role |
author |
author2 |
Llinares, Salvador Penalva, Maria del Carmen |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Roig, Ana-Isabel Llinares, Salvador Penalva, Maria del Carmen |
description |
This study provides support to the characteristics of participatory and anticipatory stages in secondary school pupils’ abstraction of mathematical conceptions. We carried out clinical task-based interviews with 71 secondary-school pupils to obtain evidence of the different constructed mathematical conceptions (Participatory Stage) and how they were used (Anticipatory Stage). We distinguish two moments in the Participatory Stage based on the coordination of information from particular cases by activity-effect reflection which, in some cases, lead to a change of focus enabling secondary-school pupils to achieve a reorganization of their knowledge. We argue that (a) the capacity of perceiving regularities in sets of particular cases is a characteristic of activity-effect reflection in the abstraction of mathematical conceptions in secondary school, and (b) the coordination of information by pupils provides opportunities for changing the attention-focus from the particular results to the structure of properties. Key words: Mathematical Abstraction. Activity-effect Reflection. Reflective Abstraction. Formation of Mathematical Objects. Participatory and Anticipatory Stages. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-08-10 |
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://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/7831 |
url |
https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/7831 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/7831/5488 |
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 |
UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas |
publisher.none.fl_str_mv |
UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas |
dc.source.none.fl_str_mv |
Bolema: Boletim de Educação Matemática; v. 26 n. 44 (2012); 1345-1366 1980-4415 0103-636X reponame:Bolema: Boletim de Educação Matemática instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Bolema: Boletim de Educação Matemática |
collection |
Bolema: Boletim de Educação Matemática |
repository.name.fl_str_mv |
Bolema: Boletim de Educação Matemática - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
bolema.contato@gmail.com||romiarka@gmail.com |
_version_ |
1800215874784722945 |