Learning and Individual Differences

This study examined age-related changes in complex executive function (EF) in a large, representative sample (N = 2,036) aged 5 to 17 using the Cognitive Assessment System (CAS; Naglieri & Das, 1997a). Relations between complex EF and academic achievement were examined on a sub-sample (N = 1,395) given the Woodcock-Johnson Tests of Achievement-Revised (Woodcock & Johnson, 1989). Performance on the three complex EF tasks improved until at least age 15, although improvement slowed with increasing age and varied some across tasks. Moreover, the different developmental patterns in the correlations between completion time and accuracy provide clues to developmental processes. Examination of individual achievement subtests clarified the specific aspects of academic performance most related to complex EF. Finally, the correlation between complex EF and academic achievement varied across ages, but the developmental pattern of the strength of these correlations was remarkably similar for overall math and reading achievement, suggesting a domain-general relation between complex EF and academic achievement.

The present study examined the phenotypic and genetic relationship between fluency and non-fluency-based measures of reading and mathematics performance. Participants were drawn from the Western Reserve Reading and Math Project, an ongoing longitudinal twin project of same-sex MZ and DZ twins from Ohio. The present analyses are based on tester-administered measures available from 228 twin pairs (age M=9.86 years). Measurement models suggested that four factors represent the data, namely Decoding, Fluency, Comprehension, and Math. Subsequent quantitative genetic analyses of these latent factors suggested that a single genetic factor accounted for the covariance among these four latent factors. However, there were also unique genetic effects on Fluency and Math, independent from the common genetic factor. Thus, although there is a significant genetic overlap among different reading and math skills, there may be independent genetic sources of variation related to measures of decoding fluency and mathematics.

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.

There is accumulating evidence that genetic influences on achievement are more pronounced among children living in higher socioeconomic status homes, and that these gene-by-environment interactions occur prior to children's entry into formal schooling. We hypothesized that one pathway through which socioeconomic status promotes genetic influences on early achievement is by facilitating the processes by which children select, evoke, and attend to learning experiences that are consistent with genetically influenced individual differences in their motivation to learn. We examined this hypothesis in a nationally representative sample of approximately 650 pairs of four-year old identical and fraternal twins who were administered a measure of math achievement, and rated by their parents on a broad set of items assessing learning motivation. Results indicated a genetic link between learning motivation and math achievement that varied positively with family socioeconomic status: Genetic differences in learning motivation contributed to math achievement more strongly in more advantaged homes. Once this effect of learning motivation was controlled for, gene-by-socioeconomic status interaction on math achievement was reduced from previously significant levels, to nonsignificant levels.

Existing behavior-genetic research implicates substantial influence of heredity and modest influence of shared environment on reading achievement and reading disability. Applying DeFries-Fulker analysis to a combined sample of twins and adoptees (N = 4,886, including 266 reading-disabled probands), the present study replicates prior findings of considerable heritability for both reading achievement and reading disability. A simple biometric model adequately described parent and offspring data (combined N = 9,430 parents and offspring) across differing types of families present in the sample Analyses yielded a high heritability estimate (around 0.70) and a negligible shared-environmentality estimate for both reading achievement and reading disability. No evidence of gene × environment interaction was found for parental reading ability and parental educational attainment, the two moderators analyzed.

A person-centered approach was used to explore the mediating role of self-regulation between learner typology at age 8 and academic achievement at age 14while controlling for domain-specific achievement in a longitudinal sample of 113 children born to adolescent mothers. Children were classified into one of 5 learner typologies at age 8based on interactive patterns of intellectual, achievement, and adaptive abilities. Typology classification explained significant variance in both reading and mathematics achievement at age 14. A bootstrapping approach confirmed that self-regulation mediated the relationship between typology and reading and mathematical achievement for children from all typologies except those classified as Cognitively and Adaptively Challenged. Implications of person-centered approaches for understanding processes involved with achievement are discussed.

Children whose parents have higher education enjoy greater age-linked gains in cognitive abilities and academic achievement. Different researchers have typically focused on different outcomes, and the extent to which parental education relates to multiple child outcomes via a single developmental pathway has received little empirical attention. This issue was examined by applying common factor structural equation models to a large (N = 4,810) nationally representative sample of kindergarten through 12(th) grade children, who were measured on 6 distinct cognitive abilities and 5 distinct forms of knowledge and academic achievement. Results indicated that a single pathway accounted for the relations between parental education and age differences in children's cognitive abilities. However, additional unique pathways were necessary to account for the relations between parental education and age differences in academic knowledge and mathematics. These results suggest that while socioeconomic differences are largely manifest in global aspects of cognitive development, they have incremental relations with some forms of academic achievement.

Using the biological and adoptive families in the Minnesota-based Sibling Interaction and Behavior Study, we investigated the associations among genetic and environmental influences on IQ, parenting, parental expectations for offspring educational attainment, engagement in school, and school grades. All variables showed substantial genetic influence, and very modest shared environmental influence. No gender differences were evident. There were significant genetic influences common to IQ and parental expectations of educational attainment, parenting and engagement in school, school grades and engagement in school, parental expectations for offspring educational attainment and school grades, and IQ and school grades. A possible interpretation of the common genetic influences involving parenting is that parents use their own experience with school in shaping the ways in which they parent their offspring.

In order to better understand the extent to which operationalizations of response to intervention (RTI) overlap and agree in identifying adequate and inadequate responders, an existing database of 399 first grade students was evaluated in relation to cut-points, measures, and methods frequently cited for the identification of inadequate responders to instruction. A series of 543 2x2 measures of association (808 total comparisons) were computed to address the agreement of different operationalizations of RTI. The results indicate that agreement is generally poor and that different methods tend to identify different students as inadequate responders, although agreement for identifying adequate responders is higher. Approaches to the assessment of responder status must use multiple criteria and avoid formulaic decision making.

Previous research shows that children's ability to estimate numbers of items using their Approximate Number System (ANS) predicts later math ability. To more closely examine the predictive role of early ANS acuity on later abilities, we assessed the ANS acuity, math ability, and expressive vocabulary of preschoolers twice, six months apart. We also administered attention and memory span tasks to ask whether the previously reported association between ANS acuity and math ability is ANS-specific or attributable to domain-general cognitive skills. We found that early ANS acuity predicted math ability six months later, even when controlling for individual differences in age, expressive vocabulary, and math ability at the initial testing. In addition, ANS acuity was a unique concurrent predictor of math ability above and beyond expressive vocabulary, attention, and memory span. These findings of a predictive relationship between early ANS acuity and later math ability add to the growing evidence for the importance of early numerical estimation skills.

A core assumption of response to instruction or intervention (RTI) models is the importance of measuring growth in achievement over time in response to effective instruction or intervention. Many RTI models actively monitor growth for identifying individuals who need different levels of intervention. A large-scale (N=23,438), two-year longitudinal study of first grade children was carried out to compare the predictive validity of measures of achievement status, growth in achievement, and their combination for predicting future reading achievement. The results indicate that under typical conditions, measures of growth do not make a contribution to prediction that is independent of measures of achievement status. These results question the validity of a core assumption of RTI models.

Genetic and environmental influences on early reading and spelling at the end of kindergarten and Grade 1 were compared across three twin samples tested in the United States, Australia, and Scandinavia. Proportions of variance due to genetic influences on kindergarten reading were estimated at .84 in Australia, .68 in the U.S., and .33 in Scandinavia. The effects of shared environment on kindergarten reading were estimated at .09 in Australia, .25 in the U.S., and .52 in Scandinavia. A similar pattern of genetic and environmental influences was obtained for kindergarten spelling. One year later when twins in all three samples had received formal literacy instruction for at least one full school year, heritability was similarly high across country, with estimated genetic influences varying between .79 and .83 for reading and between .62 and .79 for spelling. These findings indicate that the pattern of genetic and environmental influences on early reading and spelling development varies according to educational context, with genetic influence increasing as a function of increasing intensity of early instruction. Longitudinal analyses revealed genetic continuity for both reading and spelling between kindergarten and Grade 1 across country. However, a new genetic factor comes into play accounting for independent variance in reading at Grade 1 in the U.S. and Scandinavia, suggesting a change in genetic influences on reading. Implications for response-to-instruction are discussed.

In this study, the relationship between latent constructs of phonological awareness (PA) and rapid automatized naming (RAN) were investigated and related to later measures of reading and spelling in children learning to read in different alphabetic writing systems (i.e., Norwegian/Swedish vs. English). 750 U.S./Australian children and 230 Scandinavian children were followed longitudinally between kindergarten and 2nd grade. PA and RAN were measured in kindergarten and Grade 1, while word recognition, phonological decoding, and spelling were measured in kindergarten, Grade 1, and Grade 2. In general, high stability was observed for the various reading and spelling measures, such that little additional variance was left open for PA and RAN. However, results demonstrated that RAN was more related to reading than spelling across orthographies, with the opposite pattern shown for PA. In addition, tests of measurement invariance show that the factor loadings of each observed indicator on the latent PA factor was the same across U.S./Australia and Scandinavia. Similar findings were obtained for RAN. In general, tests of structural invariance show that models of early literacy development are highly transferable across languages.

Little is known about individual differences in integrating numeric base-rates and qualitative text in making probability judgments. Fuzzy-Trace Theory predicts a preference for fuzzy processing. We conducted six studies to develop the FPPI, a reliable and valid instrument assessing individual differences in this fuzzy processing preference. It consists of 19 probability estimation items plus 4 "M-Scale" items that distinguish simple pattern matching from "base rate respect." Cronbach's Alpha was consistently above 0.90. Validity is suggested by significant correlations between FPPI scores and three other measurers: "Rule Based" Process Dissociation Procedure scores; the number of conjunction fallacies in joint probability estimation; and logic index scores on syllogistic reasoning. Replicating norms collected in a university study with a web-based study produced negligible differences in FPPI scores, indicating robustness. The predicted relationships between individual differences in base rate respect and both conjunction fallacies and syllogistic reasoning were partially replicated in two web-based studies.

The present study examined the components of end of kindergarten writing, using data from 242 kindergartners. Specifically of interest was the importance of spelling, letter writing fluency, reading, and word- and syntax-level oral language skills in writing. The results from structural equation modeling revealed that oral language, spelling, and letter writing fluency were positively and uniquely related to writing skill after accounting for reading skills. Reading skill was not uniquely related to writing once oral language, spelling, and letter writing fluency were taken into account. These findings are discussed from a developmental perspective.

Examined how aspects of social-emotional learning (SEL)-specifically, emotion knowledge, emotional and social behaviors, social problem-solving, and self-regulation-clustered to typify groups of children who differ in terms of their motivation to learn, participation in the classroom, and other indices of early school adjustment and academic success. 275 four-year-old children from private day schools and Head Start were directly assessed and observed in these areas, and preschool and kindergarten teachers provided information on social and academic aspects of their school success. Three groups of children were identified: SEL Risk, SEL Competent-Social/Expressive, and SEL Competent-Restrained. Group members differed on demographic dimensions of gender and center type, and groups differed in meaningful ways on school success indices, pointing to needed prevention/intervention programming. In particular, the SEL Risk group could benefit from emotion-focused programming, and the long-term developmental trajectory of the SEL Competent-Restrained group requires study.

Chaos in the home is a key environment in cognitive and behavioral development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modeling to explore the genetic and environmental etiology of children's perceptions of chaos. We found that these perceptions are significantly heritable (22%), with the remainder explained by environmental influences. Finding that genes influence children's experience of chaotic environments has far-reaching implications for how we conceptualize the family home and its impact on cognitive and behavioral development.

To better understand early predictors of weak language and academic abilities, we identified children with and without weak abilities at age 8. We then looked back at age 2 vocabulary and word combining, and evaluated these measures as predictors of age 8 outcomes. More than 60% of children with weak oral language abilities at 8 were not late talkers at 2. However, no word combining at 2 was a significant risk factor for poor oral language, reading comprehension, and math outcomes at 8. The association of no word combining with age 8 reading comprehension and math ability was mediated by age 8 oral language ability. The findings indicate that children take different developmental pathways to weak language abilities in middle childhood. One begins with a delayed onset of language. A second begins with language measures in the typical range, but ends with language ability falling well below typical peers.

In an effort to understand the role of interhemispheric transfer in numerical development, we investigated the relationship between children's developing knowledge of numbers and the integrity of their white matter connections between the cerebral hemispheres (the corpus callosum). We used diffusion tensor imaging (DTI) tractography analyses to test the link between the development of the corpus callosum and performance on symbolic and non-symbolic numerical judgment tasks. We were especially interested in the interhemispheric connections of parietal cortex in 6-year-old children, because regions of parietal cortex have been implicated in the development of numerical skills by several prior studies. Our results revealed significant structural differences between children and adults in the fibers of the corpus callosum connecting the left and right parietal lobes. Importantly, these structural differences were predictive of individual differences among children in performance on numerical judgment tasks: children with poor numerical performance relative to their peers exhibited reduced white matter coherence in the fibers passing through the isthmus of the corpus callosum, which connects the parietal hemispheres.

We report on a longitudinal study designed to assess possible sex differences in math achievement, math ability, and math-related tasks during the primary school age years. Participants included over 200 children from one public school district. Annual assessments included measures of math ability, math calculation achievement scores, rapid naming and decoding tasks, visual perception tests, visual motor tasks, and reading skills. During select years of the study we also administered tests of counting and math facts skills. We examined whether girls or boys were overrepresented among the bottom or top performers on any of these tasks, relative to their peers, and whether growth rates or predictors of math-related skills differed for boys and girls. Our findings support the notion that sex differences in math are minimal or nonexistent on standardized psychometric tests routinely given in assessments of primary school age children. There was no persistent finding suggesting a male or female advantage in math performance overall, during any single year of the study, or in any one area of math or spatial skills. Growth rates for all skills, and early correlates of later math performance, were comparable for boys and girls. The findings fail to support either persistent or emerging sex differences on non-specialized math ability measures during the primary school age years.

The collection of articles in this special issue and related studies over the past decade provides a fine example of the substantial progress that has been made in our understanding and remediation of mathematical learning disabilities and difficulties since 1993 (Geary, 1993). The originally proposed procedural and retrieval deficits have been supported and a number sense deficit has been identified. There is evidence for visuospatial contributions to some aspects of mathematical learning, but identification of a core visuospatial deficit underlying some forms of mathematics learning disabilities and difficulties has been elusive. The contributions of working memory to the development and expression of these deficits is more nuanced than I originally proposed as are the brain systems supporting mathematical learning. Although much has been learned about children's difficulties in learning mathematics, but there is just as much and likely more than remains to be discovered.

The purpose of the present study was to explore the 3(rd)-grade cognitive predictors of 5th-grade computational skill with rational numbers and how those are similar to and different from the cognitive predictors of whole-number computational skill. Students (n = 688) were assessed on incoming whole-number calculation skill, language, nonverbal reasoning, concept formation, processing speed, and working memory in the fall of 3(rd) grade. Students were followed longitudinally and assessed on calculation skill with whole numbers and with rational numbers in the spring of 5(th) grade. The unique predictors of skill with whole-number computation were incoming whole-number calculation skill, nonverbal reasoning, concept formation, and working memory (numerical executive control). In addition to these cognitive abilities, language emerged as a unique predictor of rational-number computational skill.

Self-regulated learning (SRL) is a multi-dimensional construct that has been difficult to operationalize using traditional, variable-centered methodologies. The current paper takes a person-centered approach to the study of SRL in a sample of 205 high-school students. Using latent profile analysis on self-reports of seven aspects of SRL, three groups were identified: high SRL, low SRL, and average SRL. Student self-reports of goal orientation were used as validation for the profile solution, with the high academic self- regulation group reporting the highest levels of mastery orientation while the low self-regulation group reported highest levels of avoidant orientation. Profiles were also compared on independently collected, behavioral measures of study behaviors, with the highly self-regulated group tending to study more material and for a longer time than less self-regulated individuals.

The primary purpose of this study was to assess the effects of strategic counting instruction, with and without deliberate practice with those counting strategies, on number combination (NC) skill among students with mathematics difficulties (MD). Students (n = 150) were stratified on MD status (i.e., MD alone vs. MD with reading difficulty) and site (proximal vs. distal to the intervention developer) and then randomly assigned to control (no tutoring) or 1 of 2 variants of NC remediation. Both remediations were embedded in the same validated word-problem tutoring protocol (i.e., Pirate Math). In 1 variant, the focus on NCs was limited to a single lesson that taught strategic counting. In the other variant, 4-6 min of practice per session was added to the other variant. Tutoring occurred for 16 weeks, 3 sessions per week for 20-30 min per session. Strategic counting without deliberate practice produced superior NC fluency compared to control; however, strategic counting with deliberate practice effected superior NC fluency and transfer to procedural calculations compared with both competing conditions. Also, the efficacy of Pirate Math word-problem tutoring was replicated.