Spontaneous Meta-Arithmetic as the First Step Toward School Algebra (La meta-aritmética espontánea como el primer paso hacia el álgebra escolar)

dc.creator	Shai Caspi
dc.creator	Anna Sfard
dc.date	2012-01-01T00:00:00Z
dc.date.accessioned	2015-08-12T11:21:52Z
dc.date.available	2015-08-12T11:21:52Z
dc.identifier	1886-1350
dc.identifier	1887-3987
dc.identifier	https://doaj.org/article/8dc618af3439413c8432bf9265656e47
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/29197
dc.description	Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the “official” algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses.</p><p>Tomando como punto de partida la visión del álgebra escolar como un meta-discurso formalizado de la aritmética, hemos estado siguiendo a seis pares de estudiantes de 7º curso (12-13 años) cuando modifican gradualmente su meta-aritmética espontánea hacia la forma algebraica “oficial” de hablar. En este artículo miramos el principio de este proceso. Los análisis preliminares de los datos han mostrado, como era de esperar, que mientras reflexionaban sobre los procesos y relaciones aritméticas, los alumnos no iniciados emplearon medios coloquiales que no evitaban las ambigüedades ocasionales. Más inesperadamente, esta meta-aritmética espontánea, a pesar de no apoyarse en ninguna enseñanza algebraica previa, desplegó algunas características similares al álgebra que no se encuentran normalmente en los discursos diarios.
dc.language	Spanish
dc.language	English
dc.publisher	Pensamiento Numérico
dc.relation	http://www.pna.es/Numeros2/pdf/Caspi2012Spontaneous_PNA6(2).pdf
dc.relation	https://doaj.org/toc/1886-1350
dc.relation	https://doaj.org/toc/1887-3987
dc.rights	CC BY-NC-ND
dc.source	PNA, Vol 6, Iss 2, Pp 61-71 (2012)
dc.subject	Algebra
dc.subject	Discourse
dc.subject	Formalization
dc.subject	Generalization
dc.subject	Meta-arithmetic
dc.subject	Álgebra
dc.subject	Discurso
dc.subject	Formalización
dc.subject	Generalización
dc.subject	Metaaritmética
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Education (General)
dc.subject	L7-991
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.title	Spontaneous Meta-Arithmetic as the First Step Toward School Algebra (La meta-aritmética espontánea como el primer paso hacia el álgebra escolar)
dc.type	article