The purpose of this study was to assess the relative contribution of teacher and tutor ratings of inattentive behavior in two different instructional settings in predicting students' performance on fraction concepts and whole-number calculations. Classroom teachers rated each student's attentive behavior in a whole-class setting and tutors rated…

The purpose of this study was to assess whether intervention with an integrated focus on fraction and decimal magnitude provides added value in improving rational number performance over intervention focused exclusively on fractions. We randomly assigned 4th graders with poor whole-number performance to 3 conditions: a business-as-usual control…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

In 2010, the Institute of Education Sciences commissioned a much-needed national evaluation of response to intervention (RTI). The evaluators defined their task very narrowly, asking "Does the use of universal screening, including a cut-point for designating students for more intensive Tier 2 and Tier 3 interventions, increase children's…

This article describes the Taxonomy of Intervention Intensity, which articulates seven principles for evaluating and building intervention intensity based upon research. The Taxonomy's seven dimensions of intensity are strength, dosage, alignment, attention to transfer, comprehensiveness, behavioral support, and individualization (see Table 1). In…

Development of fraction number line estimation was assessed longitudinally over 5 time points between 4th and 6th grades. Although students showed positive linear growth overall, latent class growth analyses revealed 3 distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n = 154);…

Development of fraction number line estimation was assessed longitudinally over five time points between fourth and sixth grades. Although students showed positive linear growth overall, latent class growth analyses revealed three distinct growth trajectory classes: Students who were highly accurate from the start and became even more accurate (n…

The purposes of this study were to investigate the effects of an intervention designed to improve at-risk 4th graders' understanding of fractions and to examine the processes by which effects occurred. The intervention focused more on the measurement interpretation of fractions; the control condition focused more on the part-whole interpretation…

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…

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on…

The 3 purposes of this study were to: (a) describe fraction ordering errors among at-risk 4th-grade students; (b) assess the effect of part-whole understanding and accuracy of fraction magnitude estimation on the probability of committing errors; and (c) examine the effect of students' ability to explain comparing problems on the probability of…

This study investigated contributions of general cognitive abilities and foundational mathematical competencies to numeration understanding (i.e., base-10 structure) versus multidigit calculation skill. Children (n = 394, M = 6.5 years) were assessed on general cognitive abilities and foundational numerical competencies at start of 1st grade; on…

The purpose of this study was to examine the extent to which teacher ratings of behavioral attention predicted responsiveness to word reading instruction in first-grade and third-grade reading comprehension performance. Participants were 110 first-grade students identified as at risk for reading difficulties who received 20 weeks of intensive…

The Common Core State Standards provide teachers with a framework of necessary mathematics skills across grades K-12, which vary considerably from previous mathematics standards. In this article, we discuss concerns about the implications of the Common Core for students with mathematics difficulties (MD), given that students with MD, by…