Natural Number Bias on Evaluations of the Effect of Multiplication and Division: The Role of the Type of Numbers

Autor/inn/en	Christou, Konstantinos P.; Vamvakoussi, Xenia
Titel	Natural Number Bias on Evaluations of the Effect of Multiplication and Division: The Role of the Type of Numbers
Quelle	In: Mathematics Education Research Journal, 35 (2023) 3, S.427-443 (17 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Christou, Konstantinos P.) ORCID (Vamvakoussi, Xenia)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1033-2170
DOI	10.1007/s13394-021-00398-3
Schlagwörter	Number Concepts; Bias; Multiplication; Division; Prior Learning; Expectation; Middle School Students; Arithmetic; Misconceptions; Mathematical Applications + Suchen Sie Ihr Suchwort? Number concept; Zahlbegriff; Multiplikation; Vorkenntnisse; Expectancy; Erwartung; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Missverständnis; Angewandte Mathematik; Innermathematische Anwendung
Abstract	Over the last years, there is a growing interest in studying students' difficulties with rational numbers from a cognitive/developmental perspective, focusing on the role of prior knowledge in students' understanding of rational numbers. The present study tests the effect of the "whole" or "natural number bias" (i.e., the tendency to count on natural number knowledge to interpret information about rational numbers and deal with rational number tasks), on students' expectations about the "size" (i.e., bigger or smaller) and the "type" (i.e., natural number or decimal) of the results of multiplication and division. Items that were congruent and incongruent with students' assumed expectations were administered to 91 seventh and eighth graders, asking them to evaluate equalities presenting multiplication and division between given and missing numbers. The results showed that besides the already well-documented effect of the size of results (i.e., "multiplication makes bigger" and "division makes smaller"), students tended to think that the numbers involved in multiplication and division should be of the same type (i.e., natural or non-natural, e.g., decimals). Both size and type of the numbers involved in the operations were significant factors affecting students' evaluations, with size being stronger than type. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01