Cognitive Predictors of Calculations and Number Line Estimation with Whole Numbers and Fractions among At-Risk Students.

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 7 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and incoming calculation skill at the start of 4th grade. Then, they were assessed on whole-number and fraction calculation and number line estimation measures at the end of 4th grade. Structural equation modeling and path analysis indicated that processing speed, attentive behavior, and incoming calculation skill were significant predictors of whole-number calculations whereas language, in addition to processing speed and attentive behavior, significantly predicted fraction calculations. In terms of number line estimation, nonverbal reasoning significantly predicted both whole-number and fraction outcome, with numerical working memory predicting whole-number number line estimation and language predicting fraction number line estimation. Findings are discussed in terms of distinctions between whole-number and fraction development and between calculations and number line learning.