Relational Reasoning about Numbers and Operations--Foundation for Calculation Strategy Use in Multi-Digit Multiplication and Division

Autor/in	Schulz, Andreas
Titel	Relational Reasoning about Numbers and Operations--Foundation for Calculation Strategy Use in Multi-Digit Multiplication and Division
Quelle	In: Mathematical Thinking and Learning: An International Journal, 20 (2018) 2, S.108-141 (34 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Schulz, Andreas)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1098-6065
DOI	10.1080/10986065.2018.1442641
Schlagwörter	Computation; Mathematics Instruction; Multiplication; Arithmetic; Logical Thinking; Thinking Skills; Numbers; Number Concepts; Structural Equation Models; Foreign Countries; Grade 4; Factor Analysis; Student Surveys; Statistical Analysis; Maximum Likelihood Statistics; Multivariate Analysis; Regression (Statistics); Germany + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Multiplikation; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Denkfähigkeit; Zahlenraum; Number concept; Zahlbegriff; Ausland; School year 04; 4. Schuljahr; Schuljahr 04; Faktorenanalyse; Schülerbefragung; Statistische Analyse; Multivariate Analyse; Regression; Regressionsanalyse; Deutschland
Abstract	Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary reasoning processes. In a sample of 221 German fourth graders, both kinds of relational reasoning were operationalized, as well as the use of strategies and algorithms in multiplication and division. The multi-dimensionality of the constructs and their discriminant validity were confirmed by a confirmatory factor analysis. The theoretically proposed, unidirectional relations between the constructs were investigated using a structural equation model: Abilities in reasoning about relations between numbers had a significant positive impact on strategy use in multiplication and division. Abilities in reasoning about relations between operations influenced strategy use in multiplication only. The use of algorithms in multiplication and division was exclusively affected by abilities in reasoning about relations between numbers, and not by abilities about relations between operations. Moreover, a negative effect of the use of digit-based algorithms on the use of whole number-based strategies was identified. Finally, the results of the theoretical and empirical analysis were integrated into a synthesis of existing models about calculation strategy use and development. (As Provided).
Anmerkungen	Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01