An integrated theory of whole number and fractions development

• Published in: Cognitive psychology Vol. 62; no. 4; pp. 273 - 296
• Main Authors: Siegler, Robert S., Thompson, Clarissa A., Schneider, Michael
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.06.2011; Elsevier; Academic Press
• Subjects: Accuracy; Achievement; Achievement Tests; Adolescent; Arithmetic; Biological and medical sciences; Child; Child development; Children; Children & youth; Cognitive psychology; Comprehension; Concept Formation; Developmental psychology; Fractions; Fundamental and applied biological sciences. Psychology; Humans; Knowledge; Magnitude; Magnitude representations; Mathematics; Mathematics Achievement; Numbers; Problem Solving; Proficiency; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Scores; Strategy choice; Test scores; Mathematics achievement; Fractions; Magnitude representations; Arithmetic; Strategy choice; Human; Choice; Arithmetics; Theory; Cognition; Mathematics; Experimental study; Magnitude; Preadolescent; Number; Strategy; Cognitive development
• ISSN: 0010-0285; 1095-5623
• DOI: 10.1016/j.cogpsych.2011.03.001

► We propose an integrated theory of knowledge of whole numbers and fractions. ► Accurate magnitude representations are crucial to whole number and fraction learning. ► Fraction magnitude representations correlate highly with fractions arithmetic. ► Fraction magnitude representations correlate highly with math achievement test scores. This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds indicate that, as with whole numbers, accuracy of fraction magnitude representations is closely related to both fractions arithmetic proficiency and overall mathematics achievement test scores, that fraction magnitude representations account for substantial variance in mathematics achievement test scores beyond that explained by fraction arithmetic proficiency, and that developing effective strategies plays a key role in improved knowledge of fractions. Theoretical and instructional implications are discussed.