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	(2018), (46 Seiten) PDF als Volltext (1); PDF als Volltext kostenfreie Datei (2) Verfügbarkeit
Zusatzinformation	Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
DOI	10.1037/xlm0000546
Schlagwörter	Correlation; Fractions; Arithmetic; Mathematics Instruction; Mathematical Concepts; Grade 6; Grade 8; Middle School Students; Foreign Countries; Textbooks; Prediction; Addition; Subtraction; Multiplication; Hypothesis Testing; Pennsylvania (Pittsburgh); China (Beijing) + Suchen Sie Ihr Suchwort? Korrelation; Bruchrechnung; Addition; Arithmetik; Arithmetikunterricht; Rechnen; Mathematics lessons; Mathematikunterricht; School year 06; 6. Schuljahr; Schuljahr 06; School year 08; 8. Schuljahr; Schuljahr 08; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; Ausland; Textbook; Text book; Schulbuch; Lehrbuch; Vorhersage; Subtraktion; Multiplikation; Hypothesenprüfung; Hypothesentest
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 US (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 US and Chinese children's fraction arithmetic performance are discussed, as are implications of these differences for educational practice. [This paper was published in "Journal of Experimental Psychology: Learning, Memory, and Cognition" v44 n11 p1765-1777 Nov 2018.] (As Provided).
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01