Title

An integrated theory of whole number and fractions development.

Date of Original Version

6-1-2011

Type

Article

PubMed ID

21569877

Abstract or Description

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.

DOI

10.1016/j.cogpsych.2011.03.001

 

Published In

Cognitive Psychology, 62, 4, 273-296.