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The purpose of this study was to examine the cognitive correlates of 3rd-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N ϭ 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word efficiency as well as on arithmetic, algorithmic computation, and arithmetic word problems. Teacher ratings of inattentive behavior also were collected. Path analysis indicated that arithmetic was linked to algorithmic computation and to arithmetic word problems and that inattentive behavior independently predicted all 3 aspects of mathematics performance. Other independent predictors of arithmetic were phonological decoding and processing speed. Other independent predictors of arithmetic word problems were nonverbal problem solving, concept formation, sight word efficiency, and language.

This study examined the efficacy of preventive 1st-grade tutoring in mathematics, estimated the prevalence and severity of mathematics disability, and explored pretreatment cognitive characteristics associated with mathematics development. Participants were 564 first graders, 127 of whom were designated at risk (AR) for mathematics difficulty and randomly assigned to tutoring or control conditions. Before treatment, all participants were assessed on cognitive and academic measures. Tutoring occurred 3 times weekly for 16 weeks; treatment fidelity was documented; and math outcomes were assessed. Tutoring efficacy was supported on computation and concepts/applications, but not on fact fluency. Tutoring decreased the prevalence of math disability, with prevalence and severity varying as a function of identification method and math domain. Attention accounted for unique variance in predicting each aspect of end-of-year math performance. Other predictors, depending on the aspect of math performance, were nonverbal problem solving, working memory, and phonological processing.

This review examines the efficacy of curriculum-based measurement (CBM) as an assessment methodology for enhancing student achievement. We describe experimental-contrast studies in reading and mathematics in which teachers used CBM to monitor student progress and to make instructional decisions. Overall, teachers' use of CBM produced significant gains in student achievement; however, several critical variables appeared to be associated with enhanced achievement for students with disabilities: teachers' use of systematic data-based decision rules, skills analysis feedback, and instructional recommendations for making program modifications. In general education, positive effects for CBM were associated with use of class profiles and implementation of peer-assisted learning strategies. Implications for instructional practice and future applications of CBM are described. © 2005 Wiley Periodicals, Inc.An increasingly popular form of alternative assessment, known as curriculum-based measurement (CBM), is used by teachers and school psychologists for monitoring student progress. The roots of CBM lay with the University of Minnesota's Institute for Research on Learning Disabilities (IRLD) in the mid-to late 1970s during the time of the original passage and implementation of the Individuals with Disabilities Education Act (IDEA), known then as Public Law 94-142. Stan Deno and colleagues sought to develop a simple and efficient, but technically adequate, measurement system for assisting special educators in tracking student growth in basic skills (for review, see Deno, 1985). Deno and colleagues designed a program of research to determine the technical features of CBM and to examine the utility of CBM for enhancing teachers' instructional planning and student learning. Consequently, the initial purpose for developing CBM was to assist special educators in using progress-monitoring data to make meaningful decisions about student progress and to improve the quality of instructional programs. Over the past 25 years, numerous investigations have emerged that utilized CBM in a variety of ways including, but not limited to: (a) establishing norms for screening and identifying students in need of special education services (Shinn, 1989b), (b) evaluating the effectiveness of educational programs (Tindal, 1992), (c) reintegrating students with disabilities into general education classrooms (D. Fuchs, Fernstrom, Reeder, Bowers, & Gilman, 1992), (d) monitoring progress and planning instruction within general education classrooms (L.S. Fuchs, Fuchs, Hamlett, Phillips, & Bentz, 1994), and (e) identifying potential candidates for special education evaluation using a dual-discrepancy model of low level of performance and inadequate rate of improvement (L.S. Fuchs, Fuchs, & Speece, 2002).Despite the various ways in which CBM has been applied, the original intent was for teachers to use technically sound, but simple, data in a meaningful fashion to document student growth and determine the necessity for modifying instructional programs. Th...

In this introduction to the special issue, a response-to-instruction approach to learning disabilities (LD) identification is discussed. Then, an overview of the promise and the potential pitfalls of such an approach is provided. The potential benefits include identification of students based on risk rather than deficit, early identification and instruction, reduction of identification bias, and linkage of identification assessment with instructional planning. Questions concern the integrity of the LD concept, the need for validated interventions and assessment methods, the adequacy of response to instruction as the endpoint in identification, the appropriate instruction intensity, the need for adequately trained personnel, and due process. Finally, an overview of the articles constituting the special issue is provided.

The purpose of this article is to revisit the issue of treatment validity as a framework for identifying learning disabilities. In 1995, an eligibility assessment process, rooted within a treatment validity model, was proposed that (a) examines the level of a student's performance as well as his/her responsiveness to instruction, (b) reserves judgment about the need for special education until the effects of individual student adaptations in the regular classroom have been explored, and (c) prior to placement, verifies that a special education program enhances learning. We review the components of this model and reconsider the advantages and disadvantages of verifying a special education program's effectiveness prior to placement.

The purpose of this study was to examine the interplay between basic numerical cognition and domain-general abilities (such as working memory) in explaining school mathematics learning. First graders (n=280; 5.77 years) were assessed on 2 types of basic numerical cognition, 8 domain-general abilities, procedural calculations (PCs), and word problems (WPs) in fall and then reassessed on PCs and WPs in spring. Development was indexed via latent change scores, and the interplay between numerical and domain-general abilities was analyzed via multiple regression. Results suggest that the development of different types of formal school mathematics depends on different constellations of numerical versus general cognitive abilities. When controlling for 8 domain-general abilities, both aspects of basic numerical cognition were uniquely predictive of PC and WP development. Yet, for PC development, the additional amount of variance explained by the set of domain-general abilities was not significant, and only counting span was uniquely predictive. By contrast, for WP development, the set of domain-general abilities did provide additional explanatory value, accounting for about the same amount of variance as the basic numerical cognition variables.Inquiries should be sent to Lynn S. Fuchs, 228 Peabody, Vanderbilt University, Nashville, TN 37203. Publisher's Disclaimer: The following manuscript is the final accepted manuscript. It has not been subjected to the final copyediting, fact-checking, and proofreading required for formal publication. It is not the definitive, publisher-authenticated version. The American Psychological Association and its Council of Editors disclaim any responsibility or liabilities for errors or omissions of this manuscript version, any version derived from this manuscript by NIH, or other third parties. The published version is available at www.apa.org/pubs/journals/dev NIH Public Access Author ManuscriptDev Psychol. Author manuscript; available in PMC 2011 November 1. Published in final edited form as:Dev Psychol. 2010 November ; 46(6): 1731-1746. doi:10.1037/a0020662. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptLanguage, attentive behavior, nonverbal problem solving, and listening span were uniquely predictive.Keywords mathematics development; procedural calculations; word problems; basic numerical cognition; domain-general abilitiesAchieving mathematics competence in its many forms during the elementary school years provides the foundation for learning algebra and other higher forms of mathematics and eventually for success in the labor market and a society that increasingly depends on quantitative skills (National Mathematics Advisory Panel, 2008). Yet, the cognitive mechanisms that support learning of formal mathematics during elementary school are not well understood: specifically, the relative contributions of children's basic numerical cognition that emerges without formal schooling (e.g., competence in number, counting, and simple arithmetic) as contra...

The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed. Keywordscalculations; word problems; cognitive predictors; mathematics Mathematics, which involves the study of quantities as expressed in numbers or symbols, comprises a variety of related branches. In elementary school, for example, mathematics is conceptualized in strands such as concepts, numeration, measurement, arithmetic, algorithmic computation, and problem solving. In high school, curriculum offerings include algebra, geometry, trigonometry, and calculus. Little is understood, however, about how different aspects of mathematical cognition relate to one another (i.e., which aspects of performance are shared or distinct, or how difficulty in one domain corresponds with difficulty in another). SuchCorrespondence concerning this article should be addressed to Lynn S. Fuchs, Peabody College, Box 228, Vanderbilt University, Nashville, TN 37203. lynn.fuchs@vanderbilt.edu. NIH Public AccessAuthor Manuscript J Educ Psychol. Author manuscript; available in PMC 2010 January 6. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript understanding would provide theoretical insight into the nature of mathematics competence and practical guidance about the identification and treatment of mathematics difficulties.The purpose of the present study was to explore the overlap of difficulty with two aspects of primary-grade mathematical cognition and to examine how characteristics differ among subgroups with difficulty in one, the other, both, or neither. The first aspect of performance was computation, including skill with number combinations (e.g., 2 + 5; 8 − 3) and procedural computation (e.g., 25 + 38; 74 − 22). The second aspect of performance was problem solving, including one-step, contextually straightforward word problems (e.g., John had 9 pennies. He spent 3 pennies at the store. How many pennies did he have left?) and multistep, contextually more complex problems (e.g., Fred went to the ballgame with 2 friends. He left his house with $42. While at the game, he bought 5 h...