The purposes of this study were to assess the efficacy of remedial tutoring for 3rd graders with mathematics difficulty, to investigate whether tutoring is differentially efficacious depending on students' math difficulty status (mathematics difficulty alone vs. mathematics plus reading difficulty), to explore transfer from number combination (NC) remediation, and to examine the transportability of the tutoring protocols. At 2 sites, 133 students were stratified on mathematics difficulty status and site and then randomly assigned to 3 conditions: control (no tutoring), tutoring on automatic retrieval of NCs (i.e., Math Flash), or tutoring on word problems with attention to the foundational skills of NCs, procedural calculations, and algebra (i.e., Pirate Math). Tutoring occurred for 16 weeks, 3 sessions per week and 20-30 min per session. Math Flash enhanced fluency with NCs with transfer to procedural computation but without transfer to algebra or word problems. Pirate Math enhanced word problem skill as well as fluency with NCs, procedural computation, and algebra. Tutoring was not differentially efficacious as a function of students' mathematics difficulty status. The tutoring protocols proved transportable across sites. Keywords mathematics disability; validated mathematics tutoring; word problems; number combinationsMathematics competence accounts for variance in employment, income, and work productivity even after intelligence and reading have been explained (Rivera-Batiz, 1992). So it is unfortunate that mathematics disability is widespread, affecting 5%-9% of the school-age population (e.g., Badian, 1983;Gross-Tsur, Manor, & Shalev, 1996). Together, the lifelong challenges associated with mathematics disability and the high prevalence of the disorder make mathematics disability a critical public health problem. For this reason, it is essential to prevent mathematics difficulties.Research shows that early prevention activities can substantially improve math performance (e.g., Clements & Sarama, 2007;Fuchs, Fuchs, Yazdian, & Powell, 2002;Griffin, Case, & Siegler, 1994). Yet there are no interventions that are effective for all students. In Fuchs et al. (2005), for example, a first-grade prevention program reduced the prevalence of mathematics disability at the end of first grade, with effects maintaining 1 year after tutoring ended Correspondence concerning this article should be addressed to Lynn S. Fuchs, Department of Special Education, Vanderbilt University, 228 Peabody, Nashville, TN 37203. lynn.fuchs@vanderbilt.edu. (Compton, Fuchs, & Fuchs, 2007). Even so, a subset of tutored students, approximately 3%-6% of the school population, continued to manifest severe mathematics deficits. Because we cannot expect prevention activities to be universally effective, the need for intensive remedial intervention persists even when strong prevention services are available. NIH Public AccessIn the present study, we focused on the remediation of mathematics delays at third grade, when serious mathematics d...

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students' word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students' emerging algebraic reasoning.When solving word problems, students are faced with novel problems that require transfer. This can be difficult to effect in the primary grades (Durnin, Perrone, & MacKay, 1997; Foxman, Ruddock, McCallum, & Schagen, 1991, cited in Boaler, 1993Larkin, 1989). Some psychologists view such transfer in terms of the development of schemas, by which students conceptualize word problems within categories or problem types that share structural, defining features and require similar solution methods (Chi, Feltovich, & Glaser, 1981; Gick & Holyoake, 1983;Mayer, 1992;Quilici & Mayer, 1996). The broader the schema or problem type, the greater the probability students will recognize connections between novel problems and those used for instruction and will understand when to apply the solution methods they have learned.In a series of studies, we have relied on this conceptualization of transfer to design instruction for helping students build schemas for word-problem types and for broadening those schemas. Prior work (e.g., Fuchs et al., 2003;Fuchs, Fuchs, Prentice, et al., 2004) illustrates the efficacy of this approach, which we refer to as schema-broadening instruction (SBI), for third-grade students on problem types relevant to the third-grade curriculum. More recently, Fuchs, Powell et al. (2009) demonstrated the efficacy of SBI tutoring for a subset of third graders who experience severe mathematics difficulty. With this population, we taught simpler word-problem types, while introducing algebraic equations to represent the defining, structural features of those problem types.Inquiries should be sent to Lynn S. Fuchs, Box 328 Peabody, Vanderbilt University, Nashville,; lynn.fuchs@vanderbilt.edu). NIH Public Access Author ManuscriptElem Sch J. Author manuscript; available in PMC 2010 June 9. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptWe extend this line of work in the present study, applying SBI to problem types appropriate to the second-grade curriculum. We focused on typically developing second-grade students while relying on a whole-class format to deliver instruction, again ...

This study examined several aspects of Passage Reading Fluency (PRF) including performance variability across passages alternative designs for measuring PRF gain, and effects on PRF level from retesting with the same passages. Participants were 33 students from grades 2 to 10 attending a school for students with learning disabilities. PRF was measured at three test points. Time-2 tests occurred 10 weeks after time-1 tests, and time-3 tests occurred 5 weeks after the time-2 tests. At Test points 2 and 3, students read old passages (same-passage design) and new passages (different-passage design). Results showed substantial individual variation on concurrent PRF measures, smaller variation in gains measured with the same-passage design, and no passage memory effects (i.e., from retested passages). Results are discussed in relation to measuring reading gains in Response to Intervention models.

This study assessed the effects of sampling breadth on technical features of word identification fluency (WIF), a tool for screening and monitoring the reading development of first graders. From a potential pool of 704 first-grade students, the authors measured both a representative sample (n = 284) and 2 other subgroups: those with low reading achievement (n = 202) and those with high/average achievement (n = 213). Data were collected weekly on broadly and narrowly sampled WIF lists for 15 weeks and on criterion measures in the fall and spring. Broad lists were developed by sampling words from 500 high-frequency words, whereas narrow lists were created by sampling from the 133 words from Dolch preprimer, primer, and first-grade word lists. Overall, predictive validity for performance level, predictive validity for growth, and commonality analysis showed narrow sampling was better for screening the representative group and the high/average subgroup. Broad sampling was superior for screening the low-achieving subgroup and for progress monitoring across groups.

Progress monitoring is an important component of effective instructional practice. Curriculum-based measurement (CBM) is a form of progress monitoring that has been the focus of rigorous research. Two approaches for formulating CBM systems exist. The first is to assess performance regularly on a task that serves as a global indicator of competence at the relevant grade level. The second approach is to systematically sample the year-long curriculum so that each skill is represented and receives the same emphasis on each alternate form. In this article, the systematic curriculum sampling approach is illustrated for monitoring progress in mathematics concepts and applications systems. A description of the system's components, background, and technical properties is provided. Then, a sample case explains how the CBM system can be used in a special education setting to monitor progress, plan instruction, and enhance communication.