Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N=435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

This study investigated the accuracy of three fraction measures (i.e., fraction number line estimation accuracy, general fraction concepts, and fraction arithmetic) for screening fourth graders who might be at risk for mathematics difficulties. Receiver operating characteristic (ROC) curve analyses assessed diagnostic accuracy of the fraction…

The importance of fraction knowledge to later mathematics achievement, along with U.S. students' poor knowledge of fraction concepts and procedures, has prompted research on the development of fraction learning. In the present study, participants' (N = 536) development of fraction magnitude understanding and fraction arithmetic skills was assessed…

The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention. At-risk fourth graders (n = 213) were randomly assigned to the school's business-as-usual program, or one of two…

The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention delivered as part of the larger program. At-risk 4th graders (n = 213) were randomly assigned at the individual…

This chapter situates fraction learning within the integrated theory of numerical development. We argue that the understanding of numerical magnitudes for whole numbers as well as for fractions is critical to fraction learning in particular and mathematics achievement more generally. Results from the Delaware Longitudinal Study, which examined…

The goal of the present article is to synthesize findings to date from the Delaware Longitudinal Study of Fraction Learning. The study followed a large cohort of children (N = 536) between Grades 3 and 6. The findings showed that many students, especially those with diagnosed learning disabilities, made minimal growth in fraction knowledge and…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multicomponent fraction…