Children's Understanding of the Inverse Relation between Multiplication and Division

Autor/inn/en	Robinson, Katherine M.; Dube, Adam K.
Titel	Children's Understanding of the Inverse Relation between Multiplication and Division
Quelle	In: Cognitive Development, 24 (2009) 3, S.310-321 (12 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0885-2014
DOI	10.1016/j.cogdev.2008.11.001
Schlagwörter	Problem Solving; Knowledge Level; Early Adolescents; Preadolescents; Elementary School Students; Middle School Students; Mathematical Concepts; Multiplication; Arithmetic; Computation; Mathematics Skills; Comprehension + Suchen Sie Ihr Suchwort? Problemlösen; Wissensbasis; Pre-adolescence; Präadoleszenz; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Multiplikation; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Verstehen; Verständnis
Abstract	Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple multiplication and division. Application of the inversion concept in the problem-solving task was low and constant across grades. Most participants approved of the inversion-based shortcut but only a slight majority preferred it. Three clusters of children were identified based on their performance on the three tasks. The inversion cluster used and approved of the inversion shortcut the most and had high factual knowledge. The negation cluster used the negation strategy, had lower approval of the inversion shortcut, and had medium factual knowledge. The computation cluster used computation and had the lowest approval and the weakest factual knowledge. The findings highlight the importance of addressing the multiplication and division inversion concept in theories of children's mathematical competence. (Contains 3 tables.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10