Numerical Magnitude Representations and Individual Differences in Children's Arithmetic Strategy Use

Against the background of neuroimaging studies on how the brain processes numbers, there is now converging evidence that numerical magnitude representations are crucial for successful mathematics achievement. One major drawback of this research is that it mainly investigated mathematics performance as measured through general standardized achievement tests. We extended this research by investigating the association between numerical magnitude representations and children's strategy use during single‐digit arithmetic. Our findings reveal that children's symbolic but not nonsymbolic numerical magnitude processing skills are associated with individual differences in arithmetic. Children with better access to magnitude representations from symbolic digits retrieve more facts from their memory and are faster in executing fact retrieval as well as procedural strategies. These associations remain even when intellectual ability, digit naming, and general mathematics achievement are additionally controlled for. All this indicates that particularly the access to numerical meaning from Arabic symbols is key for children's arithmetic strategy development, which suggests that educators and remedial teachers should focus on connecting Arabic symbols to the quantities they represent.     

Pathways to arithmetic: The role of visual-spatial and language skills in written arithmetic,arithmetic word problems,and nonsymbolic arithmetic

This study set out to develop and test a pathway model of the relations between general cognitive skills, specifically visual-spatial and spoken and written language skills, and competence in three forms of arithmetic that vary in modes of number representation. A total of 88 Chinese 4-year-olds participated and were tested first in kindergarten second grade (K2) and then in kindergarten third grade (K3). Language skills, including phonological, morphological, and visual-orthographic skills, and visual-spatial skills were measured at K2, and arithmetic outcomes, including written arithmetic, word problems, and nonsymbolic arithmetic, at K3. The results generally supported our model. Specifically, visual-spatial skills contributed to the prediction of all three types of arithmetic outcomes. Morphological skills predicted word problems, whereas phonological skills predicted written arithmetic. Finally, visual-orthographic skills contributed to both written and nonsymbolic arithmetic. These findings underscore the importance of delineating the specificity of cognitive processes in learning diverse forms of arithmetic.     

无名指和食指的指长比与运动成绩的相关分析

研究人类第二根手指长度（second finger length,2D）与第四根手指长度（fourth fingerlength,4D）的比率（digit ratio of 2D and 4D,2D：4D）与运动能力遗传存在相关性。结果显示,2D：4D在出生前就已经定型,其与母亲子宫睾酮浓度及成年后睾酮浓度存在着负相关。睾酮浓度会影响大脑右半球和空间视觉能力的发育,从而影响运动能力。     

Working memory deficits in children with specific learning disorders

This article examines working memory functioning in children with specific developmental disorders of scholastic skills as defined by ICD-10. Ninety-seven second to fourth graders with a minimum IQ of 80 are compared using a 2 x 2 factorial (dyscalculia vs. no dyscalculia; dyslexia vs. no dyslexia) design. An extensive test battery assesses the three subcomponents of working memory described by Baddeley (1986): phonological loop, visual-spatial sketchpad, and central executive. Children with dyscalculia show deficits in visual-spatial memory; children with dyslexia show deficits in phonological and central executive functioning. When controlling for the influence of the phonological loop on the performance of the central executive, however, the effect is no longer significant. Although children with both reading and arithmetic disorders are consistently outperformed by all other groups, there is no significant interaction between the factors dyscalculia and dyslexia.     

The development of working memory in normally achieving and subtypes of learning disabled children

Working memory has been proposed as an important component of reading and arithmetic skills. The development of working memory was studied in normally achieving and subtypes of learning disabled children. The performance of reading disabled (RD), arithmetic disabled (ARITHD), and attentional deficit disordered (ADD) children, age 7-13, was compared to normal achievers (NA) on 2 working memory tasks, 1 involving sentences and the other involving counting. There was a significant growth of working memory as a function of age. In addition, the RD children had significantly lower scores on both tasks. The ARITHD children had significantly lower scores only on the Working Memory--Counting task, and the ADD group had scores similar to the normally achieving children except at the youngest age level in the Working Memory--Sentences task. Thus, a reading disability appears to involve a generalized deficit in working memory. Children with an arithmetic disability do not have a generalized language deficit but have a specific working memory deficit in relation to processing numerical information. As children with ADD did not have deficits in these tasks, working memory may not have significant attentional components. An important component of the development of reading and computational arithmetic skills appears to be the growth of working memory for language and numerical information.     

Longitudinal contributions of executive functioning and visual-spatial skills to mathematics learning in young Chinese children

One hundred sixty-five Hong Kong Chinese children were administered measures of early mathematics, visual-spatial skills, and executive functioning (working memory, inhibition, shifting, updating) once in kindergarten (mean age?=?62.80 months, SD?=?3.74) and again in first grade (mean age?=?77.25 months, SD?=?4.60). In kindergarten, visual-spatial skills, inhibition, shifting, and working memory were all uniquely associated with concurrent mathematics performance; in first grade, only working memory and visual-spatial skills were significantly related to concurrent mathematics abilities. Furthermore, working memory and visual-spatial skills in kindergarten predicted 19% of the variance in children’s mathematics performance in first grade, beyond the autoregressive effects of mathematics performance in kindergarten as well as demographic variables. Findings highlight the importance of working memory and visual-spatial skills for young Chinese children in mastering mathematics.     

Gender Differences in Social Mastery Motivation and Its Relationships to Vocabulary Knowledge,Behavioral Self-Regulation,and Socioemotional Skills

The present study investigated gender differences in social mastery motivation, vocabulary knowledge, behavioral self-regulation, and socioemotional skills and examined the relationships among this knowledge and these skills by gender. Participants were 134 Chinese children (68 boys, M age = 3.80; 66 girls, M age = 3.89) and their parents recruited through local kindergartens’ parent groups. The children were administered measures of social mastery motivation, vocabulary knowledge, behavioral self-regulation, and nonverbal intelligence. Parents reported their education level and children’s socioemotional skills. Research Findings: Results revealed that boys exhibited more social mastery interactions than girls, and girls showed better behavioral self-regulation and socioemotional skills than boys. Girls with higher social mastery interaction frequency demonstrated better vocabulary knowledge and socioemotional skills, whereas boys with higher social mastery interaction frequency showed lower behavioral self-regulation. Boys, who showed more positive affect during social mastery interactions, tended to have better expressive vocabulary, which facilitated their behavioral self-regulation. Practice or Policy: Findings highlight social mastery motivation as a potential factor that facilitates children’s early development, but it may contribute to boys and girls in different ways.     

Sex-related differences in response to practice on a visual-spatial test and generalization to a related test

93 first graders (mean age 6.5 years) were given a pretest and posttest on half of the items from the Children's Embedded Figures Test. Half of the children were randomly assigned to a training condition and received a brief training procedure on visual-spatial disembedding prior to the administration of the posttest. Children in the control condition received no training. The performance of girls improved significantly more from pretest to posttest than the performance of boys. Boys and girls showed similar beneficial effects of training in addition to the benefit of direct practice. The tendency that was observed for boys to perform higher than girls on the pretest, p less than .10, was not evident on the posttest. Scores on the pretest predicted scores on a different measure of visual-spatial ability only for children in the control group. The results are interpreted in terms of current theories of sex differences in visual-spatial perception.     

Mathematics learning disabilities in girls with fragile X or Turner syndrome during late elementary school

The present study focuses on math and related skills among 32 girls with fragile X (n = 14) or Turner (n = 18) syndrome during late elementary school. Performance in each syndrome group was assessed relative to Full Scale IQ-matched comparison groups of girls from the general population (n = 32 and n = 89 for fragile X syndrome and Turner syndrome, respectively). Differences between girls with fragile X and their comparison group emerged on untimed arithmetic calculations, mastery of counting skills, and arithmetic problem verification accuracy. Relative to girls in the comparison group, girls with Turner syndrome did not differ on untimed arithmetic calculations or problem verification accuracy, but they had limited mastery of counting skills and longer response times to complete the problem verification task. Girls with fragile X or Turner syndrome also differed from their respective comparison groups on math-related abilities, including visual-spatial, working memory, and reading skills, and the associations between math and those related skills. Together, these findings support the notion that difficulty with math and related skills among girls with fragile X or Turner syndrome continues into late elementary school and that the profile of math and related skill difficulty distinguishes the two syndrome groups from each other.     

Gender Differences in Arithmetic Strategy Use: A Function of Skill and Preference

This study was designed to examine whether first-grade boys' use of retrieval and first-grade girls' use of manipulatives reflected gender differences in their abilities to use these strategies or gender differences in preferences for strategy use. Eighty-four first-grade students, 42 boys and 42 girls, from two suburban elementary schools participated in this study. The children solved basic arithmetic problems under two conditions: a free-choice condition in which they were allowed to solve the problems any way they preferred and a game condition in which the children's strategy use was constrained so that all children used the same strategies on the same arithmetic problems. Strategy use during the free-choice session replicated the findings of earlier research indicating that girls tend to use strategies utilizing manipulatives and boys tend to use retrieval. During the game condition, when we controlled the types of strategies children used on different problems we found that boys were as able as girls to calculate solutions using manipulatives. Girls, however, were not as capable as boys in their retrieval of answers to arithmetic problems from memory. No differences were found in error rates or speed of retrieval. Gender differences were found in the variability of correct retrieval, with boys being significantly more variable than girls.     

Gender differences in intelligence, language, visual-motor abilities, and academic achievement in students with learning disabilities: a review of the literature

A substantial body of research confirms higher verbal ability in normally achieving females and higher visual-spatial and mathematical abilities in normally achieving males. However, the specific nature of these differences varies by age, specific measure, magnitude, and variability within the groups. Re-analysis of earlier research showed that, although differences in visual-spatial ability were larger than verbal ability differences, gender differences did not account for more than 1% to 5% of the group variance. In the population with learning disabilities (LD), research must be interpreted cautiously because LD samples were drawn mainly from the system-identified population and may reflect selection bias. Findings indicate that system-identified females with LD are lower in IQ, have more severe academic achievement deficits in some aspects of reading and math, and are somewhat better in visual-motor abilities, spelling, and written language mechanics than males with LD. In mathematics, however, it is difficult to document consistent differences in computational skills in the elementary school ages. More consistent findings, however, indicate superiority in mathematical reasoning in males with LD. A limited number of studies on research-identified samples indicate that findings from studies of school-identified LD samples must be interpreted cautiously because females with LD identified in the schools may not be representative of females with LD in general.     

大班幼儿加减运算能力的发展特点——以武汉市8所幼儿园为例

选取武汉市8所幼儿园112名大班幼儿作为被试,对幼儿加减运算能力进行测试。结果发现:(1)幼儿笔算、口算、解答应用题和自编应用题四种能力之间均显著相关,解答应用题和自编应用题的能力低于笔算和口算能力。(2)幼儿解答应用题能力的发展有显著的性别差异,男孩的能力优于女孩。(3)省示范园和市示范园幼儿的加减运算能力发展优于私立园幼儿。     

Using collaborative technology to enhance pre-service teachers’ pedagogical content knowledge in Science

Groups of 11‐year‐olds in their first term at secondary school were given three cognitive tests. Girls and boys were found to be approximately equal in science knowledge. Boys did slightly better on tests of physical science, especially when these were in multiple choice form, but otherwise there were few sex differences. Neither the style of the question (multiple choice or structured) nor the content (feminine or masculine) had any great effect on sex differences in performance. However, boys performed markedly better than girls on tests of spatial ability and mechanical reasoning. These skills may be important for later success in technical studies at school.     

Explaining common variance shared by early numeracy and literacy

How can be explained that early literacy and numeracy share variance? We specifically tested whether the correlation between four early literacy skills (rhyming, letter knowledge, emergent writing, and orthographic knowledge) and simple sums (non-symbolic and story condition) reduced after taking into account preschool attention control, short-term memory, speed of processing, visual-spatial skills, vocabulary, and shared book reading. 228 Dutch native preschoolers (mean age 54.25; SD = 2.12 months) participated. The results revealed that 1) all literacy skills were related to sums (non-symbolic and story condition), 2) rhyming was the strongest predictor of non-symbolic sums, and letter knowledge of sums in story context, 3) visual-spatial skills explained part of the shared variance in the non-symbolic condition and visualspatial skills, vocabulary and short-term memory explained part of the shared variance in sums in story context. Implications for the preschool curriculum and early interventions are discussed.     

Undergraduate students' ability to revise text effectively: relationships with topic knowledge and working memory

In order to communicate understanding, students are often required to produce texts which present an explicit, coherent argument. This study examined the extent to which individual differences in undergraduates' topic knowledge and working memory skills were related to their ability to revise texts to better fulfil these goals. Forty-seven students revised texts containing three types of error: language, structure and argument. Topic knowledge was indexed by multiple choice test performance. Verbal short-term and working memory were measured using forward and backward digit recall and reading span. Rates of identification, diagnosis and correction of errors were generally poor. Contrary to expectations neither topic knowledge nor verbal working memory was associated with text revision although significant associations were identified with verbal short-term memory. When revising texts students may focus on the surface features of the text rather than addressing issues of structure and argument. Possible accounts of this tendency are considered.     

男童血清瘦素水平与肥胖及性发育的关系

目的探讨男童血清瘦素水平与肥胖及性发育的关系。方法选择9—14岁符合单纯性肥胖标准的男性患儿34例为肥胖组,健康男性儿童32例为对照组,分别计算体重指数（BMI）、应用放射性免疫法测定血清瘦素（Leptin）水平、化学发光法测定血清雌二醇（E2）及睾酮（T）水平,用游标卡尺测量并计算睾丸体积,应用SPSS16．0软件进行组间t检验比较两组间差异,线性相关分析肥胖男童血清瘦素水平与BMI,E2及T之间的相关性。结果肥胖男童血清瘦素、雌二醇水平及BMI均较对照组儿童高,且差异有统计学意义（P〈0．01）;肥胖男童血清睾酮水平及睾丸体积均较对照组儿童低,且差异有统计学意义（P〈0．01）。肥胖男童血清瘦素水平与BMI呈正相关（r=0．69,P〈0.01）,与雌二醇呈正相关（r=0．381,P〈0.05）,与睾酮呈负相关（r=-0.347,P〈0.05）。结论肥胖男童存在瘦素抵抗现象,且有性发育不良的趋势。     

The Cognitive Correlates of Computational Estimation Skill Among Third‐Grade Students

The purpose of this study was to examine the relations of various cognitive abilities and aspects of math performance with computational estimation skill among third graders. Students (n= 315) were assessed on language, nonverbal reasoning, concept formation, processing speed, long‐term memory, working memory, inattentive behavior, basic reading skill, arithmetic number combination skill, double‐digit computation skill, and computational estimation ability. One‐way analysis of variance indicated significant differences in estimation skill among students of low, average, and high math computation performance. The unique predictors of estimation skill were arithmetic number combination skill, nonverbal reasoning, concept formation, working memory, and inattentive behavior.     

Executive Function Skills,Early Mathematics,and Vocabulary in Head Start Preschool Children

Research Findings: The contribution of 3 executive function skills (shifting, inhibitory control, and working memory) and their relation to early mathematical skills was investigated with preschoolers attending 6 Head Start centers. Ninety-two children ranging in age from 3 years, 1 month, to 4 years, 11 months, who were native English or Spanish speakers were assessed for these executive function skills as well as their receptive vocabulary skills and early mathematical abilities using the Child Math Assessment (Starkey, Klein, & Wakeley, 2004), which captures an array of skills across 4 domains. Hierarchal regression analyses revealed that inhibitory control and working memory made unique contributions to children’s early mathematical abilities in the domains of numeracy, arithmetic, spatial/geometric reasoning, and patterning/logical relations after we controlled for age, receptive vocabulary, and previous Head Start experience. Furthermore, receptive vocabulary also accounted for significant variance in children’s early mathematical abilities above and beyond executive function skills. No group differences emerged between English-only and dual language learners on the fit of the regression models. Practice or Policy: These findings extend previous research highlighting the interface of executive function skills and mathematical learning in early childhood with further evidence to support this relationship beyond early numeracy and counting using a broad measure of critical early math skills. In addition, the intricate role of language in the development of early mathematical competence is considered. Implications of these findings for scaffolding executive function skills and vocabulary within prekindergarten math curricula are discussed, with particular consideration for children from low socioeconomic backgrounds.     

Risk factors in early child development: Is prenatal cocaine/poly-drug exposure a key variable?

In order to explore the possible confounding effects of age, race, sex, and socioeconomic status on developmental outcomes of prenatal cocaine exposure, two matched samples of preschoolers (20 children with cocaine/polydrug in utero exposure and 20 children with no prenatal drug exposure) were compared on the Stanford-Binet: 4th ed. (S-B: 4th ed.), Social Skills Rating System, Vineland Adaptive Behavior Scale—Survey Form, Preschool Language Scale: 3rd ed. (PLS: 3rd ed.), and the Child Behavior Checklist. None of the 40 children had attended or were currently enrolled in preschool programs. Both groups had scores approximately one standard deviation below the expected mean in social skills, auditory comprehension, and expressive language. Likewise, externalizing behavior difficulties were approximately one standard deviation above the mean for both groups. Results suggest in utero drug exposure had no independent impact on cognitive, social, language, and behavioral developmental outcomes when the confounding variables of age, ethnicity, gender, and SES were controlled. © 1997 John Wiley & Sons, Inc.     

Working memory in Dutch children with reading- and arithmetic-related LD

The aim of the two studies presented in this article was to examine working memory performance in Dutch children with various subtypes of learning disabilities. The performance of children with reading disabilities (RD) was compared to that of children with arithmetic disabilities (AD), children with both reading and arithmetic disabilities (RAD), and chronological age-matched controls (CA). Measures covered the phonological loop, the visuospatial sketchpad, and the central executive. In both studies, the children with RD showed no working memory deficits whatsoever. Children with AD showed a single impairment on the task tapping working memory for dynamic visual information. Children with RAD performed lower only on the digit span backward task. The failure to replicate the expected working memory deficits in children with reading-related disabilities is discussed.