Executive function effects and numerical development in children: Behavioural and ERP evidence from a numerical Stroop paradigm

Most research on numerical development in children is behavioural, focusing on accuracy and response time in different problem formats. However, Temple and Posner (1998) used ERPs and the numerical distance task with 5-year-olds to show that the development of numerical representations is difficult to disentangle from the development of the executive components of response organization and execution. Here we use the numerical Stroop paradigm (NSP) and ERPs to study possible executive interference in numerical processing tasks in 6–8-year-old children. In the NSP, the numerical magnitude of the digits is task-relevant and the physical size of the digits is task-irrelevant. We show that younger children are highly susceptible to interference from irrelevant physical information such as digit size, but that access to the numerical representation is almost as fast in young children as in adults. We argue that the developmental trajectories for executive function and numerical processing may act together to determine numerical development in young children.     

儿童非符号数量表征的特点及作用探析

数量表征是人类重要的基础心理能力,包括了符号和非符号两种表征系统。非符号数量表征是个体不需要依赖符号知识对视觉、听觉或跨通道呈现的实物或实物记号的数量刺激进行表达和运算的过程,具有一定的种系进化基础,先于语言发生。在未接受正式数学教育之前,儿童在一定程度上就能在平面空间和三维空间内表征非符号数量,并表现出了在视觉-听觉跨通道条件下的抽象非符号数量表征能力。个体早期即可能拥有两种特点不同的离散量表征系统:对非符号小数量的精确表征和对大数量的近似表征,但对其产生机制还存在不同的理论解释。在符号系统出现后,非符号数量表征和符号数量表征在行为及神经机制既有区别又有联系,并可能通过映射过程在头脑内部相互转换。与符号数量表征相互作用发展成为个体高级数能力的重要基础。     

Numerical Estimation in Deaf and Hearing Adults

Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the Number-to-Position task as a measure of estimation, and completed standardised assessments of arithmetical and mathematical reasoning. Deaf students performed significantly more poorly on all measures, including making less accurate number-line estimates. For deaf students, there was also a strong relationship showing that those more accurate in making number-line estimates achieved higher scores on the math achievement tests. No such relationship was apparent for hearing students. Further insights into the estimation abilities of deaf individuals should be made, including tasks that require symbolic and non-symbolic estimation and which address the quality of estimation strategies being used.     

Early Numerical Competencies in 5- and 6-Year-Old Children With Autism Spectrum Disorder

Research Findings: To date, studies comparing the mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are scarce, and results remain inconclusive. In general, studies on this topic focus on mathematical abilities learned from elementary school onward, with little attention for possible precursors at younger ages. The current exploratory study focused on the important developmental period of preschool age, investigating 5 early numerical competencies in 30 high-functioning children with ASD and 30 age-matched control children: verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Children were examined at 5 or 6 years of age, attending the 3rd and final year of preschool. Overall, rather similar early number processing was found in children with and without ASD, although marginally significant results indicated a weaker performance of children with ASD on verbal subitizing and conceptual counting. Practice or Policy: Given the pervasiveness and impact of ASD on other domains of functioning, it is important to know that no general deficits in early numerical competencies were found in this study. However, some downward trends in mathematics performance were identified in children with ASD, which can serve as the basis for additional research in this field.     

The hands have it: number representations in adult deaf signers

This study examines a wide range of numerical representations (i.e., quantity, knowledge of multiplication facts, and use of parity information) in adult deaf signers. We introduce a modified version of the number bisection task, with sequential stimulus presentation, which allows for a systematic examination of mathematical skills in deaf individuals in different modalities (number signs in streaming video vs. Arabic digit displays). Reaction times and accuracy measures indicated that deaf signers make use of several representations simultaneously when bisecting number triplets, paralleling earlier findings in hearing individuals. Furthermore, some differences were obtained between the 2 display modalities, with effects being less prominent in the Arabic digit mode, suggesting that mathematical abilities in deaf signers should be assessed in their native sign language.     

Fostering Parental Support for Children's Mathematical Development: An Intervention with Head Start Families

The first national education goal, school readiness, recognizes a need for young children to be better prepared for entry into elementary school. Many low-income children exhibit a pattern of underachievement in school mathematics. Research has revealed a developmental gap between low-income preschool children and their middle-class peers with respect to the extent of their numerical knowledge. Research has also found that many low-income children do not receive a broad base of support for mathematical development at home or in preschool. In each of two studies, we conducted a bi-generation (parent and child) mathematics intervention with Head Start families. The intervention was designed to enhance parental support for pre-kindergarten children's mathematical development. It was found that low-income parents were willing and able to support this area of their children's development once they were provided with the training to do so. The support that parents provided to their children through the intervention was clearly effective in enhancing the development of children's informal mathematical knowledge. Intervention children developed more extensive mathematical knowledge than a comparison group of low-income children. Thus, an important step toward achieving the school readiness goal can be taken by fostering low- income parents' support for young children's mathematical development.     

Fostering Parental Support for Children's Mathematical Development: An Intervention with Head Start Families

The first national education goal, school readiness, recognizes a need for young children to be better prepared for entry into elementary school. Many low-income children exhibit a pattern of underachievement in school mathematics. Research has revealed a developmental gap between low-income preschool children and their middle-class peers with respect to the extent of their numerical knowledge. Research has also found that many low-income children do not receive a broad base of support for mathematical development at home or in preschool. In each of two studies, we conducted a bi-generation (parent and child) mathematics intervention with Head Start families. The intervention was designed to enhance parental support for pre-kindergarten children's mathematical development. It was found that low-income parents were willing and able to support this area of their children's development once they were provided with the training to do so. The support that parents provided to their children through the intervention was clearly effective in enhancing the development of children's informal mathematical knowledge. Intervention children developed more extensive mathematical knowledge than a comparison group of low-income children. Thus, an important step toward achieving the school readiness goal can be taken by fostering low- income parents' support for young children's mathematical development.     

Visual spatial representation in mathematical problem solving by deaf and hearing students

This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers.     

The role of numerical and non-numerical ordering abilities in mathematics and reading in middle childhood

This study investigated whether different types of ordering skills were related to mathematics achievement in children (n = 100) in middle childhood, after the effects of age, socio-economic status, IQ, and processing speed were taken into account. The relations between ordering skills and magnitude processing were also investigated, as well as the possibility that some of the shared variance between math and reading is explained by ordering abilities. The ordering tasks included the ordering of familiar numerical and non-numerical sequences, a parental report of children’s everyday ordering skills, and an order working memory task. Three magnitude processing tasks (symbolic and non-symbolic comparison and number line estimation), were also administered, as well as measures of inhibition and spatial working memory. From this set of measures, number ordering, order working memory and number line estimation emerged as the most important predictors of mathematics skills. We found that number ordering mediated the effect of both symbolic and non-symbolic comparison skills on mathematics, further confirming that this task captures some essential skills related to mathematics. Additionally, order working memory mediated the effect of both number comparison and reading skills on math. Finally, whereas non-symbolic comparison and number line estimation are considered important indicators of magnitude processing skills, there was no relationship between these abilities, but there was a correlation between each of these abilities and reading skills, with number line estimation also mediating the effect of reading skills on math. These novel findings could contribute to a better understanding of the basic processes underlying math ability, and why math and reading are strongly related in typical populations and in children with learning difficulties.     

Subitizing, magnitude representation, and magnitude retrieval in deaf and hearing adults

This study examines basic number processing (subitizing, automaticity, and magnitude representation) as the possible underpinning of mathematical difficulties often evidenced in deaf adults. Hearing and deaf participants completed tasks to assess the automaticity with which magnitude information was activated and retrieved from long-term memory (using a Stroop-like paradigm to assess congruity effects), the representational format of magnitude information (by analysis of distance and Spatial Numerical Association of Response Codes effects), and the ability to rapidly enumerate small sets (subitizing). Both groups showed distance effects taken to indicate the use of a visual-spatial analog number line representing approximate quantity. Furthermore, both groups showed similar patterns of performance on the subitizing tasks and showed similar amounts of interference in an analysis of congruity effects. This is taken as evidence against the notion that idiosyncratic differences in basic number processing account for mathematical difficulties experienced by deaf individuals.     

Manipulatives and number sentences in computer aided arithmetic word problem solving

In this study we investigated the relative contribution of two main components often used in the instruction of arithmetic word problem solving to first-grade children and children with learning problems, external representation with manipulatives and formal mathematical representation with number sentences. Four computer aided treatments were developed along these dimensions. Furthermore, an assessment control group was formed.It was shown that performance improved significantly after treatment in comparison to the performance of the assessment control group. Comparison of the different training conditions showed that a number sentence treatment was the most effective training component. However, this effect was only present with the relatively high competent children and not with the relatively low performing children.     

Numerical competence in young children and in children with mathematics learning disabilities

A longitudinal study was conducted on 82 children to investigate, firstly the numerical competence of young children and the predictive value of (pre)-numerical tests in kindergarten, and, secondly, whether children's knowledge of the numerical system and representation of the number size is related to their computation and logical knowledge and to their counting skills. In an additional cross-sectional study on 30 children with a clinical diagnosis of mathematical learning disability (MLD) of 8,5 years, age- and ability-matched with 2 × 30 children the same parameters of numerical competence were assessed. The longitudinal data showed individual differences in numerosity, as well as the relationship between a delay in arithmetics in grade l and problems on numerosity in kindergarten. In the cross-sectional results some evidence was found for the independence of numerical abilities in MLD-children. About 13% of them had still severe pre-numerical processing deficits (in number sequence production, cardinality skills and logical knowledge) in grade 3. About 67% had severe difficulties in executing calculation procedures and a lack of conceptual knowledge. A feature of 87% of the MLD-children was severe translation deficits, with a significantly worse knowledge of number words compared with the knowledge of Arab numerals. Finally a severe deficit in subitizing was found to be present in 33% of the MLD children. On a group level the processing deficits were linked to understanding numerosity, since the ability-matched younger children and the MLD-children had the same pre-numerical and numerical profile. Implications for the assessment of mathematical disabilities and the value of TEDI-MATH® as an instrument in this process are discussed.     

Effects of skill training on working memory capacity

In this study we examined the effects of skill training, in particular mental abacus and music training, on working memory. Two groups of participants—children who had received mental abacus training and their controls—participated in Experiment 1. All participants performed the following span tasks: forward digit span, backward digit span, non-word span, operation span, simple spatial span, and complex spatial span tasks. Children (mean age: 12 years) who had received training exhibited greater simple spatial spans, but not other spans. In Experiment 2, the same span tests were given to groups of children (mean age: 12 years) and adults (mean age: 22 years) who had received music training and to their controls. For adults, the experimental group performed better than the control group with respect to both the digit span and non-word span tests. For children, the experimental group performed better than did the control group in all of the span tests. We discuss our results in terms of the domain-specific effects of skill training on working memory.     

Loneliness and Peer Relations in Young Children

Recent studies indicate that feelings of loneliness and social dissatisfaction can be reliably assessed with third- through sixth-grade children, and that children who are sociometrically rejected by their peers are significantly more lonely than other children. The present research was designed (a) to examine whether loneliness could be reliably assessed in a population younger than previously studied, (b) to learn whether young children who are poorly accepted by peers report elevated levels of loneliness and social dissatisfaction, (c) to assess whether young children understand the concept of loneliness, and (d) to examine the behavioral characteristics of lonely young children. Kindergarten and first-grade children (N = 440) responded to a questionnaire about feelings of loneliness and social dissatisfaction in school. A subset of children (N = 46) were individually interviewed to assess their understanding of loneliness. To assess sociometric status and behavior, peers were asked to respond to various sociometric measures and behavioral assessment items. Teachers also provided behavioral information about children using a newly developed instrument. Results indicated that nearly all children understood loneliness, that loneliness was reliably assessed in young children, and that poorly accepted children were more lonely than other children. In addition, children who reported the most loneliness were found to differ from others on several behavioral dimensions.     

Nonsocial Play Patterns of Young Children With Communication Disorders: Implications for Behavioral Adaptation

It has been well established that young children with communication disorders (CD) have considerable difficulties interacting socially with peers in free-play settings. The central purpose of this study was to determine whether behavioral adaptations of children with CD could contribute to their peer interaction problems. To accomplish this, the behavioral patterns of reticent, solitary-passive, and solitary-active subtypes of nonsocial play of children with CD were observed in unstructured playgroup settings and compared to the nonsocial play of matched groups of typically developing children. Also examined was whether the associations with peer social interaction measures and child and family characteristics differed among the reticent, solitary-passive, and solitary-active subtypes and whether the context factors of the developmental status and familiarity of peers influenced these patterns. Results revealed that preschool children with CD do not exhibit distinct patterns of nonsocial play and provide no evidence for situation-specific (i.e., with peers) behavioral adaptations despite difficulties interacting with peers. The developmental characteristics of or familiarity with one's peers did not influence these results. Moreover, the peer social interaction patterns corresponding to each subtype, as well as child and family characteristics associated with each subtype, were also similar for both groups of children. Recommendations for preventive intervention programs to minimize future peer interaction problems emphasizing social-information and emotional regulation processes were presented.     

Classroom behavior of children and adolescents with learning disabilities: a meta-analysis

Meta-analysis was used to review the results of 25 studies that compared the classroom behavior of children and adolescents with learning disabilities (LD) to children without learning disabilities. The data were analyzed from several different methodological perspectives. Results showed that both methodologically strong and weak studies demonstrated significant behavioral deficits of children with learning disabilities compared to their nondisabled peers in each of five overall areas: on-task behavior, off-task behavior, conduct disorders, distractibility, and shy/withdrawn behavior. Both observational and teacher rating data demonstrated these differences. Effect sizes for both groups of studies seemed to cluster around 1 standard deviation, suggesting noticeable and educationally significant impairment in the behavior of children with disabilities. Analysis of grade-level effect sizes suggests some explanation for the large number of referrals often witnessed during the elementary school years. Educational implications of these behavioral differences in terms of implications for mainstreaming are discussed.     

Psychophysiological and behavioral evidence for varying forms and functions of nonsocial behavior in preschoolers

Four-year-old children showing low levels of social behavior in a laboratory play session with unfamiliar peers were classified as reticent (unoccupied or onlooking behaviors) or solitary-passive (solitary constructive or exploratory play). Compared with a group of more social children, the children in both low-social groups were rated high on maternal reports of shyness and displayed a pattern of right frontal EEG asymmetry. However, only the reticent group was elevated on measures indicative of a fearful temperament, both concurrently and retrospectively. A subset of children in the solitary-passive group showed increasing levels of reticent behavior over the course of the visit, suggesting that for some children solitary-passive behaviors provide a means for coping with feelings of unease.     

Cattell‐Horn‐Carroll broad cognitive ability profiles of low math achievers

This study extends previous research examining the relations between Cattell‐Horn‐Carroll cognitive abilities and math achievement. The cognitive profiles of children with normative weaknesses in Math Calculation Skills or Math Reasoning were compared to those of their average‐achieving peers. The cognitive profile of the low Math Calculation Skills group (n = 68) was similar to that of their average‐achieving peers. The low Math Reasoning group (n = 52) scored lower than their average‐achieving peers on the cognitive abilities as a set and on Fluid Reasoning and Comprehension–Knowledge. When individual profiles were considered, approximately half of the children with normative math weaknesses demonstrated commensurate weaknesses in one or more cognitive abilities, which may inform diagnostic models of learning disabilities. © 2005 Wiley Periodicals, Inc. Psychol Schs 42: 1–12, 2005.     

English Language Proficiency and Early School Attainment Among Children Learning English as an Additional Language

Children learning English as an additional language (EAL) often experience lower academic attainment than monolingual peers. In this study, teachers provided ratings of English language proficiency and social, emotional, and behavioral functioning for 782 children with EAL and 6,485 monolingual children in reception year (ages 4–5). Academic attainment was assessed in reception and Year 2 (ages 6–7). Relative to monolingual peers with comparable English language proficiency, children with EAL displayed fewer social, emotional, and behavioral difficulties in reception, were equally likely to meet curriculum targets in reception, and were more likely to meet targets in Year 2. Academic attainment and social, emotional, and behavioral functioning in children with EAL are associated with English language proficiency at school entry.     

Gender differences in both tails of the distribution of numerical competencies in preschool children

Gender differences in mathematical achievement have been examined in a wide range of age groups but only a few studies addressed this issue in preschool children. We compared preschool girls (n?=?570) and boys (n?=?524) from Germany with regard to numerical competencies. Differences in overall group means and the frequency of representation at low, middle, or high levels of performance were explored for girls and boys. Analysis of overall group means revealed that boys showed a better performance than girls (d?=?.32). The analysis of frequencies showed differences in both tails but not in the middle of the distribution of numerical competencies. While boys were more often found at higher levels of performance, girls were found to be overrepresented in the low-ability end of the distribution. These findings demonstrate that gender differences in mathematical achievement can emerge before school entry and stress the importance of further research looking for gender divides in mathematical achievement in preschool children from different countries as well as possible underlying factors.