Children Learn Spurious Associations in Their Math Textbooks: Examples from Fraction Arithmetic

Autor/inn/en	Braithwaite, David W.; Siegler, Robert S.
Titel	Children Learn Spurious Associations in Their Math Textbooks: Examples from Fraction Arithmetic
Quelle	In: Journal of Experimental Psychology: Learning, Memory, and Cognition, 44 (2018) 11, S.1765-1777 (13 Seiten) PDF als Volltext Verfügbarkeit
Zusatzinformation	Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0278-7393
DOI	10.1037/xlm0000546
Schlagwörter	Addition; Arithmetic; Correlation; Foreign Countries; Fractions; Grade 6; Grade 8; Hypothesis Testing; Mathematical Concepts; Mathematics Instruction; Middle School Students; Multiplication; Prediction; Subtraction; Textbooks; China (Beijing); Pennsylvania (Pittsburgh) + Suchen Sie Ihr Suchwort? Addition; Arithmetik; Arithmetikunterricht; Rechnen; Korrelation; Ausland; Bruchrechnung; School year 06; 6. Schuljahr; Schuljahr 06; School year 08; 8. Schuljahr; Schuljahr 08; Hypothesenprüfung; Hypothesentest; Mathematics lessons; Mathematikunterricht; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Multiplikation; Vorhersage; Subtraktion; Textbook; Text book; Schulbuch; Lehrbuch
Abstract	Fraction arithmetic is among the most important and difficult topics children encounter in elementary and middle school mathematics. Braithwaite, Pyke, and Siegler (2017) hypothesized that difficulties learning fraction arithmetic often reflect reliance on associative knowledge--rather than understanding of mathematical concepts and procedures--to guide choices of solution strategies. They further proposed that this associative knowledge reflects distributional characteristics of the fraction arithmetic problems children encounter. To test these hypotheses, we examined textbooks and middle school children in the United States (Experiments 1 and 2) and China (Experiment 3). We asked the children to predict which arithmetic operation would accompany a specified pair of operands, to generate operands to accompany a specified arithmetic operation, and to match operands and operations. In both countries, children's responses indicated that they associated operand pairs having equal denominators with addition and subtraction, and operand pairs having a whole number and a fraction with multiplication and division. The children's associations paralleled the textbook input in both countries, which was consistent with the hypothesis that children learned the associations from the practice problems. Differences in the effects of such associative knowledge on U.S. and Chinese children's fraction arithmetic performance are discussed, as are implications of these differences for educational practice. [For the corresponding grantee submission, see ED580430.] (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01