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 (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…

Student explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 4th-grade students at-risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of students'…

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…

The three purposes of this study were to (a) describe fraction ordering errors among at-risk fourth 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…

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory,…

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 article is to describe the Taxonomy of Intervention Intensity, which articulates 7 dimensions for evaluating and building intervention intensity. We explain the Taxonomy's dimensions of intensity. In explaining the Taxonomy, we rely on a case study to illustrate how the Taxonomy can systematize the process by which special…

The purpose of the study was to determine whether individual differences in at-risk 4th graders' language comprehension, nonverbal reasoning, concept formation, working memory, and use of decimal labels (i.e., place value, point, incorrect place value, incorrect fraction, or whole number) are related to their decimal magnitude understanding.…

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 6 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

The focus of the present study was enhancing word problem and calculation achievement in ways that support prealgebraic thinking among second-grade students at risk for mathematics difficulty. Intervention relied on a multitier support system (i.e., responsiveness to intervention, or RTI) in which at-risk students participate in general classroom…

This randomized control trial examined the efficacy of a multitiered supplemental tutoring program within a first-grade responsiveness-to-intervention prevention model. Struggling first-grade readers (n = 649) were screened and progress monitored at the start of the school year. Those identified as unresponsive to general education Tier 1 (n =…