Development of Fraction Comparison Strategies: A Latent Transition Analysis

Autor/inn/en	Rinne, Luke F.; Ye, Ai; Jordan, Nancy C.
Titel	Development of Fraction Comparison Strategies: A Latent Transition Analysis
Quelle	In: Developmental Psychology, 53 (2017) 4, S.713-730 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	Weitere Informationen
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0012-1649
DOI	10.1037/dev0000275
Schlagwörter	Elementary School Mathematics; Elementary School Students; Intermediate Grades; Fractions; Longitudinal Studies; Mathematics Skills; Multivariate Analysis; Number Concepts; Bias; Learning Strategies; Accuracy; Predictor Variables; Probability; Factor Analysis; Learning Processes; Task Analysis + Suchen Sie Ihr Suchwort? Elementare Mathematik; Schulmathematik; Mittelstufe; Bruchrechnung; Longitudinal study; Longitudinal method; Longitudinal methods; Längsschnittuntersuchung; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Multivariate Analyse; Number concept; Zahlbegriff; Learning methode; Learning techniques; Lernmethode; Lernstrategie; Prädiktor; Wahrscheinlichkeitsrechnung; Wahrscheinlichkeitstheorie; Faktorenanalyse; Learning process; Lernprozess; Aufgabenanalyse
Abstract	The present study investigated the development of fraction comparison strategies through a longitudinal analysis of children's responses to a fraction comparison task in 4th through 6th grades (N = 394). Participants were asked to choose the larger value for 24 fraction pairs blocked by fraction type. Latent class analysis of performance over item blocks showed that most children initially exhibited a "whole number bias," indicating that larger numbers in numerators and denominators produce larger fraction values. However, some children instead chose fractions with "smaller" numerators and denominators, demonstrating a partial understanding that smaller numbers can yield larger fractions. Latent transition analysis showed that most children eventually adopted normative comparison strategies. Children who exhibited a partial understanding by choosing fractions with smaller numbers were more likely to adopt normative comparison strategies earlier than those with larger number biases. Controlling for general math achievement and other cognitive abilities, whole number line estimation accuracy predicted the probability of transitioning to normative comparison strategies. Exploratory factor analyses showed that over time, children appeared to increasingly represent fractions as discrete magnitudes when simpler strategies were unavailable. These results support the integrated theory of numerical development, which posits that an understanding of numbers as magnitudes unifies the process of learning whole numbers and fractions. The findings contrast with conceptual change theories, which propose that children must move from a view of numbers as counting units to a new view that accommodates fractions to overcome whole number bias. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01