The assistance of John Holahan, who bore responsibility for maintaining and updating the database, is gratefully acknowledged. Thanks are also due to Lois Dreyer, who supervised the testing of the children. In addition, we acknowledge many others at the Yale University Center for the Study of Learning and Attention Disorders and at Haskins Laboratories, whose help was essential to the completion of the project. Finally, we thank Linda Kimbrough for her work on preparation of this article.

Individual growth curves were used to test whether the development of children with reading disabilities is best characterized by models of developmental lag or developmental deficit. Developmental changes in reading ability were modeled by using 9 yearly longitudinal assessments of a sample of 403 children classified into three groups representing (a) deficient reading achievement relative to IQ expectations (RD-D), (b) deficient reading achievement consistent with IQ expectations (LA), and (c) no reading deficiency (NRI). Using a model of quadratic growth to a plateau, the age and level at which reading scores plateaued were estimated for each child. Reading-disabled children differed on average from nondisabled children in the level but not in the age at which reading skills plateaued. The RD-D and LA groups did not differ in reading plateau or age at plateau. The subgroup of RD-D children scoring below the 25th percentile in reading differed from LA children only in reading plateau. Results suggest that the developmental course of reading skills in children with reading disability is best characterized by deficit as opposed to lag models. In addition, no support for the validity of classifications of reading disability based on IQ discrepancies was apparent.Despite 30 years of research, it remains unclear whether children who vary in reading abilities are best characterized by models involving developmental lags or deficits (Fletcher, 1981;Stanovich, Nathan, & Vala-Rossi, 1986). The deficit model assumes that children fail to read proficiently because of the absence of a skill that never develops

This meta-analysis synthesizes the literature on interventions for struggling readers in Grades 4 through 12 published between 1980 and 2011. It updates Scammacca et al.’s analysis of studies published between 1980 and 2004. The combined corpus of 82 study-wise effect sizes was meta-analyzed to determine (a) the overall effectiveness of reading interventions studied over the past 30 years, (b) how the magnitude of the effect varies based on student, intervention, and research design characteristics, and (c) what differences in effectiveness exist between more recent interventions and older ones. The analysis yielded a mean effect of 0.49, considerably smaller than the 0.95 mean effect reported in 2007. The mean effect for standardized measures was 0.21, also much smaller than the 0.42 mean effect reported in 2007. The mean effects for reading comprehension measures were similarly diminished. Results indicated that the mean effects for the 1980–2004 and 2005–2011 groups of studies were different to a statistically significant degree. The decline in effect sizes over time is attributed at least in part to increased use of standardized measures, more rigorous and complex research designs, differences in participant characteristics, and improvements in the school’s “business-as-usual” instruction that often serves as the comparison condition in intervention studies.

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...

Eight measures of cognitive and language functions in 232 children were subjected to multiple methods of cluster analysis in an effort to identify subtypes of reading disability. Clustering yielded 9 reliable subtypes representing 90% of the sample, including 2 nondisabled subtypes, and 7 reading-disabled subtypes. Of the reading-disabled subtypes, 2 were globally deficient in language skills, whereas 4 of the 5 specific reading-disabled subtypes displayed a relative weakness in phonological awareness and variations in rapid serial naming and verbal short-term memory. The remaining disabled subtype was impaired on verbal and nonverbal measures associated with rate of processing, including rate and accuracy of oral reading. Studies showed evidence for discriminative validity among the 7 reading-disabled subtypes. Results support the view that children with reading disability usually display impairments on phonological awareness measures, with discriminative variability on other measures involving phonological processing, language, and cognitive skills.