Students' Whole Number Multiplicative Concepts: A Critical Constructive Resource for Fraction Composition Schemes

Autor/inn/en	Hackenberg, Amy J.; Tillema, Erik S.
Titel	Students' Whole Number Multiplicative Concepts: A Critical Constructive Resource for Fraction Composition Schemes
Quelle	In: Journal of Mathematical Behavior, 28 (2009) 1, S.1-18 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0732-3123
DOI	10.1016/j.jmathb.2009.04.004
Schlagwörter	Numbers; Concept Formation; Grade 6; Mathematics Instruction; Number Concepts; Multiplication; Arithmetic; Teaching Methods; Mathematics Skills + Suchen Sie Ihr Suchwort? Zahlenraum; Concept learning; Begriffsbildung; School year 06; 6. Schuljahr; Schuljahr 06; Mathematics lessons; Mathematikunterricht; Number concept; Zahlbegriff; Multiplikation; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Teaching method; Lehrmethode; Unterrichtsmethode; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz
Abstract	This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students' construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in relation to the whole. Students' whole number multiplicative concepts were found to be critical constructive resources for students' fraction composition schemes. Specifically, the "interiorization of two levels of units," a particular multiplicative concept, was found to be necessary for the construction of a "unit fraction composition scheme," while the "interiorization of three levels of units" was necessary for the construction of a "general fraction composition scheme." These findings contribute to previous research on students' construction of fraction multiplication that has emphasized partitioning and conceptualizing quantitative units. Implications of the findings for teaching are considered. (Contains 5 figures.) (As Provided).
Anmerkungen	Elsevier. 6277 Sea Harbor Drive, Orlando, FL 32887-4800. Tel: 877-839-7126; Tel: 407-345-4020; Fax: 407-363-1354; e-mail: usjcs@elsevier.com; Web site: http://www.elsevier.com
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10