Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions
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Título: | Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions |
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Título alternativo: | Diferentes momentos na abstração de conceitos matemáticos de estudantes secundários |
Autor/es: | Roig Albiol, Ana Isabel | Llinares, Salvador | Penalva Martínez, María del Carmen |
Grupo/s de investigación o GITE: | Investigación y Formación Didáctica |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Innovación y Formación Didáctica |
Palabras clave: | Mathematical abstraction | Activity-effect reflection | Reflective abstraction | Formation of mathematical objects | Participatory and anticipatory stages |
Área/s de conocimiento: | Didáctica de la Matemática |
Fecha de publicación: | dic-2012 |
Editor: | Universidade Estadual Paulista. Pró-Reitoria de Pesquisa Programa de Pós-Graduação em Educação Matemática |
Cita bibliográfica: | ROIG, Ana-Isabel; LLINARES, Salvador; PENALVA, Maria del Carmen. “Different moments in the participatory stage of the secondary students’ abstraction of mathematical conceptions”. Bolema: Boletim de Educação Matemática. Vol. 26, N. 44 (Dez. 2012). ISSN 0103-636X, pp. 1345-1366 |
Resumen: | 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. |
Patrocinador/es: | The research reported here has been financed by the University of Alicante, Spain, under grant no. GRE08-P03 and a grant from Gil-Albert Foundation. |
URI: | http://hdl.handle.net/10045/33459 |
ISSN: | 0103-636X | 1980-4415 (Online) |
DOI: | 10.1590/S0103-636X2012000400011 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | Licencia Creative Commons Reconocimiento-NoComercial-SinObraDerivada 3.0 |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1590/S0103-636X2012000400011 |
Aparece en las colecciones: | INV - IFD-DM - Artículos de Revistas |
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