Sources of individual differences in children's understanding of fractions.

Longitudinal associations of domain-general and numerical competencies with individual differences in children's understanding of fractions were investigated. Children (n = 163) were assessed at 6 years of age on domain-general (nonverbal reasoning, language, attentive behavior, executive control, visual-spatial memory) and numerical (number knowledge) competencies; at 7 years on whole-number arithmetic computations and number line estimation; and at 10 years on fraction concepts. Mediation analyses controlling for general mathematics ability and general academic ability revealed that numerical and mathematical competencies were direct predictors of fraction concepts, whereas domain-general competencies supported the acquisition of fraction concepts via whole-number arithmetic computations or number line estimation. Results indicate multiple pathways to fraction competence.

The language of mathematics: investigating the ways language counts for children's mathematical development.

This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations.

Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge.

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across Grades 2-3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems.

Components and context: exploring sources of reading difficulties for language minority learners and native English speakers in urban schools.

Drawing on the cognitive and ecological domains within the componential model of reading, this longitudinal study explores heterogeneity in the sources of reading difficulties for language minority learners and native English speakers in urban schools. Students (N = 150) were followed from first through third grade and assessed annually on standardized English language and reading measures. Structural equation modeling was used to investigate the relative contributions of code-related and linguistic comprehension skills in first and second grade to third grade reading comprehension. Linguistic comprehension and the interaction between linguistic comprehension and code-related skills each explained substantial variation in reading comprehension. Among students with low reading comprehension, more than 80% demonstrated weaknesses in linguistic comprehension alone, whereas approximately 15% demonstrated weaknesses in both linguistic comprehension and code-related skills. Results were remarkably similar for the language minority learners and native English speakers, suggesting the importance of their shared socioeconomic backgrounds and schooling contexts.

The double-deficit hypothesis: a comprehensive analysis of the evidence.

The double-deficit hypothesis of developmental dyslexia proposes that deficits in phonological processing and naming speed represent independent sources of dysfunction in dyslexia. The present article is a review of the evidence for the double-deficit hypothesis, including a discussion of recent findings related to the hypothesis. Studies in this area have been characterized by variability in methodology--how dyslexia is defined and identified, and how dyslexia subtypes are classified. Such variability sets limitations on the extent to which conclusions may be drawn with respect to the double-deficit hypothesis. Furthermore, the literature is complicated by the persistent finding that measures of phonological processing and naming speed are significantly correlated, resulting in a statistical artifact that makes it difficult to disentangle the influence of naming speed from that of phonological processing. Longitudinal and intervention studies of the double-deficit hypothesis are needed to accumulate evidence that investigates a naming speed deficit that is independent of a phonological deficit for readers with dyslexia. The existing evidence does not support a persistent core deficit in naming speed for readers with dyslexia.

Naming speed deficits in adults with reading disabilities: a test of the double-deficit hypothesis.

The present study investigated the persistent nature of naming speed deficits within the context of the double-deficit hypothesis in a university sample of adults with reading disabilities (RD). Twenty-five university students with RD were compared to 28 typically achieving readers on measures of reading skill, phonological processing, and naming speed. The results indicated that both naming speed and phonological processing deficits characterized the RD group. In a regression analysis, neither naming speed nor phonological processing were important variables in explaining comprehension when reading rate was in the model. The results of the present study are mixed at best and are consistent with earlier conclusions that support for the double-deficit hypothesis of dyslexia remains limited.