Spontaneous Meta-Arithmetic as a First Step toward School Algebra

Autor/inn/en	Caspi, Shai; Sfard, Anna
Titel	Spontaneous Meta-Arithmetic as a First Step toward School Algebra
Quelle	In: International Journal of Educational Research, 51-52 (2012) 3, S.45-65 (21 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0883-0355
DOI	10.1016/j.ijer.2011.12.006
Schlagwörter	Grade 7; Grade 5; Arithmetic; Algebra; Mathematics; Young Children; Data Collection; Elementary School Students; Middle School Students + Suchen Sie Ihr Suchwort? School year 07; 7. Schuljahr; Schuljahr 07; School year 05; 5. Schuljahr; Schuljahr 05; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematik; Frühe Kindheit; Data capture; Datensammlung; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin
Abstract	Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that occur along time in the discourse produced by the students when they deal with specific types of algebraic problems. In this paper we take a look at the earliest stage in this process. Our 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. This finding prompted us to extend the study and take a look at spontaneous meta-arithmetic of younger children. Our data collected among 5th graders have confirmed that informal algebraic discourse emerges early, and they shed light on the development of meta-arithmetic in the span of two years prior to the formal introduction of algebra in school. (Contains 11 tables and 5 figures.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10