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Most studies of children's attitudes to mathematics have dealt with children in second grade or later, and have suggested that attitudes deteriorate, and anxiety increases with age. The present study investigated attitudes to mathematics in 67 English and 49 Chinese children at the end of their first year of school. The participants were given Thomas and Dowker's (2000) Mathematics Attitude Questionnaire, which uses pictorial rating scales to assess primary school children's mathematics anxiety, liking for mathematics, unhappiness at poor performance in mathematics, and self-rating in mathematics. They were also given the British Abilities Scales Basic Number Skills test. Attitudes were generally positive, though not more so than previously found for older primary school children. The Chinese children performed better in the arithmetic test and also rated themselves higher than the English children, but did not differ in other attitudes. Self-rating in mathematics and lack of unhappiness at poor performance were associated with better performance in the English group. There were no significant relationships between attitudes and performance in the Chinese group. Implications of the findings are discussed. [ABSTRACT FROM AUTHOR]

We investigated derived fact strategy use in RR, an aphasic patient with severely impaired working memory (no phonological loop), and 16 neurologically healthy matched controls. Participants were tested on derived fact strategy use in multi-digit addition, subtraction, multiplication, and division. RR’s accuracy only differed from controls in multiplication. He was as quick as controls in addition and subtraction when able to use the strategies, though significantly slower in addition, division, and multiplication without strategies. Our findings suggest the phonological loop is non-essential for multi-digit arithmetic, and derived fact strategies can help speed up arithmetic in individuals with impaired working memory. [ABSTRACT FROM PUBLISHER]

The surge in noninvasive brain stimulation studies investigating cognitive enhancement has neglected the effect of interindividual differences, such as traits, on stimulation outcomes. Using the case of mathematics anxiety in a sample of healthy human participants in a placebo-controlled, double-blind, crossover experiment, we show that identical transcranial direct current stimulation (tDCS) exerts opposite behavioral and physiological effects depending on individual trait levels. Mathematics anxiety is the negative emotional response elicited by numerical tasks, impairing mathematical achievement. tDCS was applied to the dorsolateral prefrontal cortex, a frequent target for modulating emotional regulation. It improved reaction times on simple arithmetic decisions and decreased Cortisol concentrations (a biomarker of stress) in high mathematics anxiety individuals. In contrast, tDCS impaired reaction times for low mathematics anxiety individuals and prevented a decrease in Cortisol concentration compared with sham stimulation. Both groups showed a tDCS-induced side effect--impaired executive control in a flanker task--a cognitive function subserved by the stimulated region. These behavioral and physiological double dissociations have implications for brain stimulation research by highlighting the role of individual traits in experimental findings. Brain stimulation clearly does not produce uniform benefits, even applied in the same configuration during the same tasks, but may interact with traits to produce markedly opposed outcomes [ABSTRACT FROM AUTHOR]

Many children who would not be identified as having special educational needs are low-attaining in mathematics, which often has a severe impact on their progress at school and their successes in later life. This paper describes Catch Up Numeracy, a non-intensive targeted intervention for children who are low-attaining in mathematics, which is delivered by classroom assistants in only thirty minutes per week. Data for 440 children, including controls, show that children receiving Catch Up Numeracy intervention attained average gains more than twice that expected of typically attaining children, and more than twice that attained by children receiving non-targeted mathematics support. The evidence suggests that Catch Up Numeracy is effective for children who are low-attaining in mathematics. More generally, it supports the view that many children's arithmetical difficulties are highly susceptible to intervention, and that the intervention does not need to be intensive or delivered by highly-trained teachers to be effective. [ABSTRACT FROM AUTHOR]

This article examines the treatment of disabled characters in British and North-American children's classics and in books that are out-of-print or less available to children from the 19th century to early 20th century. One of the main findings of this article is that the treatment of disabled characters is often more complex and varied in the latter than in the former. Moreover, the prevailing view of many 19th century and some early 20th century authors was that one should submit to misfortunes, both as a form of obedience to God's will, and because these seeming misfortunes are ultimately intended for one's own good. Therefore, in many books, disability, where it occurs, and its cure are associated with character. [ABSTRACT FROM AUTHOR]

Subitizing is the ability to enumerate small quantities efficiently and automatically. Counting is a strategy adopted for larger numerosities resulting in a near linear increase in response time with each increase in quantity. Some developmental studies suggest that being able to subitize efficiently may be a predictor of later arithmetical ability. Being able to enumerate small quantities efficiently may be necessary for at least some aspects of arithmetical skill and understanding to develop. According to this view, arithmetic ability ultimately depends upon subitizing. If this were the case, when acquired brain injury results in impaired performance on subitizing tasks, mathematical performance may also be impaired. The following study tested eleven healthy control participants and nine chronic patients with acquired brain injury on tasks focused on visual enumeration, addition and multiplication to explore a potential relationship between subitizing ability and calculation performance. No overall correlations were found between subitizing and addition or multiplication speed. However, a very clear subitizing impairment was found in two patients who then demonstrated very different levels of preserved addition skills. The dissociations found and the large inter-individual variability supports a more componential view of arithmetical ability. [ABSTRACT FROM AUTHOR]

Abstract: 339 children aged 6 and 7 at Oxford primary schools took part in a study of arithmetic. 204 of the children had been selected by their teachers as having mathematical difficulties and the other 135 children were unselected. They were assigned to an Addition Performance Level on the basis of a calculation pretest, and then given Dowker''s (1998) test of derived fact strategies in addition, involving strategies based on the Identity, Commutativity, Addend+1, Addend−1, and addition/subtraction Inverse principles. The exact arithmetic problems given varied according to the child''s previously assessed calculation level and were selected to be just a little too difficult for the child to solve unaided. The technique was used of giving children the answer to a problem and then asking them to solve another problem that could be solved quickly by using this answer, together with the principle under consideration. The children were also given the WISC Arithmetic subtest and the British Abilities Scales Basic Number Skills Subtest. Performance on the standardized arithmetic tests was independently affected by both Addition Performance Level and group membership (unselected children versus those with mathematical difficulties). Derived fact strategy use was affected by Addition Performance Level, but there was no independent effect of group membership. [Copyright &y& Elsevier]

This study investigated the effect of educational level and of the syntactic representation of numbers in Arabic on the task of transcoding two-digit numbers from dictation. The participants were primary, junior-high, and high school pupils and higher education students. All spoke Arabic as a mother tongue. They performed a transcoding task, namely writing two-digit numbers from dictation. Units first\decades first writing patterns were collected depending on the differential syntactic structures of the two-digit number dictated (decades first: whole tens; units first: teen numbers; identical units and decades, remaining two-digit numbers). The findings reveal that in general, Arabic speakers adopt a decades-first writing pattern for two-digit numbers, especially when it is consistent with the syntactic structure of two-digit numbers, as in whole-tens numbers. This decade-first writing pattern is more evident and consistent in junior-high school, high school, and higher education than in primary school due to the improvement in mathematical skills and second and third languages. However, this pattern is modulated by the syntactic complexity of the unit–decade structure. This complexity is more pronounced in two-digit numbers whose processing is more dependent on numerical syntax. Thus, whole-tens numbers, teen numbers, and identical-decade–unit numbers are less complex than the remaining two-digit numbers. [ABSTRACT FROM AUTHOR]

This study investigated individual differences in different aspects of early number concepts in preschoolers. Eighty 4-year-olds from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; and predicting the results of repeated addition and subtraction by 1 from a set of objects. There were marked individual differences for most tasks. Most children were reasonably proficient at counting and 70% understood the cardinal word principle. Based on the results of a repeated addition and subtraction by 1 task, the children were divided into three approximately equal groups: those who were already able to use an internalized counting sequence for the simplest forms of addition and subtraction; those who relied on a repeated ‘counting-all’ procedure for such tasks; and those who were as yet unable to cope with such tasks. In each group, significant relationships between some, but not all, of the numerical tasks were found. However, for almost any two tasks, it was possible to find individuals who could carry out either one of the tasks but not the other. Thus, even before formal instruction, arithmetical cognition is not unitary but is made up of many components. [ABSTRACT FROM AUTHOR]

Wales uses languages with both regular (Welsh) and irregular (English) counting systems. Three groups of 6- and 8-year-old Welsh children with varying degrees of exposure to the Welsh language—those who spoke Welsh at both home and school; those who spoke Welsh only at home; and those who spoke only English—were given standardized tests of arithmetic and a test of understanding representations of two-digit numbers. Groups did not differ on the arithmetic tests, but both groups of Welsh speakers read and compared 2-digit numbers more accurately than monolingual English children. A similar study was carried out with Tamil/English bilingual children in England. The Tamil counting system is more transparent than English but less so than Welsh or Chinese. Tamil-speaking children performed better than monolingual English-speaking children on one of the standardized arithmetic tests but did not differ in their comparison of two-digit numbers. Reasons for the findings are discussed. [ABSTRACT FROM AUTHOR]

One experiment investigated the effects of distortion and multiple prime repetition (super-repetition) on repetition priming using divided-visual-field word identification at test and mixed-case words (e.g., goAT). The experiment measured form-specificity (the effect of matching lettercase at study and test) for two non-conceptual study tasks. For an ideal typeface, super-repetition increased form-independent priming leaving form-specificity constant. The opposite pattern was found for a distorted typeface; super-repetition increased form-specificity, leaving form-independent priming constant. These priming effects did not depend on the study task or test hemifield for either typeface. An additional finding was that only the ideal typeface showed the usual advantage of right hemifield presentation. These results demonstrate that super-repetition produced abstraction for the ideal typeface and perceptual individuation for the distorted typeface; abstraction and perceptual individuation dissociated. We suggest that there is a fundamental duality between perceptual individuation and abstraction consistent with Tulving's (1984) distinction between episodic and semantic memory. This could reflect a duality of system or process. [ABSTRACT FROM AUTHOR]

Abstract: Functional brain imaging has been largely reserved for adults. However, in recent years there have been increasing attempts to use functional brain imaging to inform our understanding of child development. These have taken three main forms: [(1)] Children with known or suspected neurological disorders may undergo brain imaging for medical diagnostic purposes and/or for the purpose of research into the nature of the disorders. [(2)] There have been a few studies where children, usually over the age of 8, have undergone functional brain imaging. [(3)] Results from brain imaging studies of adults have influenced theories about children’s development. This chapter discusses the impact of brain imaging studies on our understanding of working memory; reading; and arithmetic. The different forms of brain imaging converge in demonstrating that different brain regions show differential activation for different domains and for different components within the domains: e.g. different reading strategies and different components of arithmetic. They show important similarities between children and adults, though it must be remembered that very few studies have involved young children. They also indicate that experience influences brain function, as well as the other way around. [Copyright &y& Elsevier]

This article presents a commentary on the article by Russell Gersten, Nancy C. Jordan, and Jonathan R. Flojo about mathematics difficulties (MD), published in this issue. According to the author of this commentary, the most important conclusion of the said article by Gersten and his coauthors is that it is important to identify early signs and predictors of MD to ameliorate and perhaps prevent later MD. This commentary discusses three issues related to MD research: first, the research on the nature and heterogeneity of MD; second, the research on early screening and intervention; and third, some ongoing research on early predictors of specific mathematical strengths and weaknesses. According to the author, it is important to use the existing research on MD to develop screening techniques and interventions for children who are developing or are likely to develop problems in mathematics. It is also, suggestively, desirable to investigate the possibility of preventive interventions for preschoolers and school beginners who have not yet begun to fail in school.

Investigates the role of nonlogical cues in transitive inference. Relationship between taught premise and relational information; Problems with appropriate controls; Difficulty in tasks involving pretend information.

The Numeracy Recovery scheme described here involves working with children who have been identified by their teachers as having problems with arithmetic. These children are assessed on eight components of early numeracy: (1) principles and procedures related to counting; (2) use of written arithmetical symbolism; (3) use of place value in arithmetic; (4) understanding and solution of word problems; (5) translation between concrete, verbal and numerical formats; (6) use of derived fact strategies for calculation; (7) arithmetical estimation and (8) memory for number facts. The children received weekly individual intervention in the particular components with which they were found to have difficulty. For the first 62 children in the project, Wilcoxon tests showed a significant improvement in standardised scores in both tests following intervention. [ABSTRACT FROM AUTHOR]

Two hundred and fifteen children aged between 5 and 9 years were asked to estimate the answers to addition sums. Their competence at addition was first assessed, and they were accordingly divided into five groups. Children of each level were given a set of estimation problems involving sums a little too difficult for them to calculate (termed their ''base correspondence"). Of the 215 children, 108 were then given sets of estimation problems corresponding to levels higher than their own. In the base correspondence, children of higher levels tended to produce more reasonable estimates than did children of lower levels. As difficulty increased beyond the base correspondence, the reasonableness of the estimates declined. The existence and nature of a zone of partial knowledge and understanding are discussed. [ABSTRACT FROM AUTHOR]

Selected groups of 44 academic ''pure'' mathematicians, 44 accountants, 44 psychology students, and 44 English students were given Levine's (1982) computational estimation task, which involved mentally estimating the products and quotients of 20 multiplication and division problems and describing their strategies. The mathematicians were the most accurate estimators, and the English students the least accurate, with psychology students and accountants obtaining similar scores intermediate between the other groups. All groups demonstrated an impressively versatile use of appropriate strategies. The mathematicians and accountants used significantly larger numbers of appropriate strategies than the other groups and strongly resembled one another in this respect, despite the significantly greater accuracy of the mathematicians. All the non-mathematician groups used significantly larger numbers of inappropriate strategies than did the mathematicians. We discuss (1) the implications for cognitive psychology of the great variability of strategy use in an apparently simple task; and (2) the relationship between people's mathematical knowledge and experience and their estimation accuracy and strategy variability. [ABSTRACT FROM AUTHOR]

Presents a study which examined young children's understanding of the order-irrelevance principle. Information on the task used to estimate knowledge of order-irrelevance; Features which may affect orientation to principles; Indepth look at the experiments performed; Results of these experiments.

This paper reviews and discusses research on arithmetical strengths and weaknesses in children with specific developmental cognitive disabilities. It focusses on children with dyslexia, developmental language disorder, attention deficit hyperactivity disorder and autism. In general, studies show that arithmetical weaknesses are commoner in children with any of these disorders than in controls. Autism is sometimes associated with specific strengths in arithmetic; but even in autism, it is commoner for arithmetic to be a relative weakness than a relative strength. There may be some genetic reasons why there is an overlap between mathematical difficulties and other developmental learning difficulties; but much of the reason seems to be that specific aspects of arithmetic are often influenced by other factors, including language comprehension, phonological awareness, verbal and spatial working memory and long-term memory, and executive functions. The findings discussed here will be discussed in relation to Pennington's (2006) Multiple Deficit Model. [ABSTRACT FROM AUTHOR]

The study focuses on the effect of the lexical-syntactic structure on the patterns of errors by Arab first graders in tasks involving reading two-digit number and writing two-digit numbers to dictation. Children made few change or omission errors, indicating that they had little problem with the lexical aspects of the counting system. However, they made frequent substitution errors (e.g., 23 for 32), especially in the number reading task, and especially for numbers that depended strongly on the numerical syntactic structure. Such errors were less common for decade numbers and for the 11–19 number range than for other two-digit numbers. The results suggest particular difficulty with the syntactic rather than lexical aspects of the counting system. The syntactic aspects may be particularly difficult for Arabic-speaking children, due to the inversion feature of the Arabic counting system. [ABSTRACT FROM AUTHOR]

The article presents an introduction to a series of articles on mathematical development. They include the investigation of the earliest stages of number representation, the individual differences in numerical abilities in early school years, the development of number representation at a later stage in childhood, the individual differences in four-year-olds' performance on various types of numerical task, and the environmental effects on numerical magnitude estimation in preschool children.

Opinion. Examines the significance of gender differences in spatial ability to gender differences in mathematics. Argument on the central role of spatial ability in mathematical ability; Impact of spatial ability on the issue of single-minded concentration.

In this paper, we discuss several largely undisputed claims about mathematics anxiety (MA) and propose where MA research should focus, including theoretical clarifications on what MA is and what constitutes its opposite pole; discussion of construct validity, specifically relations between self‐descriptive, neurophysiological, and cognitive measures; exploration of the discrepancy between state and trait MA and theoretical and practical consequences; discussion of the prevalence of MA and the need for establishing external criteria for estimating prevalence and a proposal for such criteria; exploration of the effects of MA in different groups, such as highly anxious and high math–performing individuals; classroom and policy applications of MA knowledge; the effects of MA outside educational settings; and the consequences of MA on mental health and well‐being. [ABSTRACT FROM AUTHOR]

Developmental Dyscalculia (DD) signifies a failure in representing quantities, which impairs the performance of basic math operations and schooling achievement during childhood. The lack of specificity in assessment measures and respective cut-offs are the most challenging factors to identify children with DD, particularly in disadvantaged educational contexts. This research is focused on a numerical cognition battery for children, designed to diagnose DD through 12 subtests. The aims of the present study were twofold: to examine the prevalence of DD in a country with generally low educational attainment, by comparing z-scores and percentiles, and to test three neurodevelopmental models of numerical cognition based on performance in this battery. Participants were 304 Brazilian school children aged 7–12 years of both sexes (143 girls), assessed by the Zareki-R. Performances on subtests and the total score increase with age without gender differences. The prevalence of DD was 4.6% using the fifth percentile and increased to 7.4% via z-score (in total 22 out of 304 children were diagnosed with DD). We suggest that a minus 1.5 standard deviation in the total score of the Zareki-R is a useful criterion in the clinical or educational context. Nevertheless, a percentile ≤ 5 seems more suitable for research purposes, especially in developing countries because the socioeconomic environment or/and educational background are strong confounder factors to diagnosis. The four-factor structure, based on von Aster and Shalev's model of numerical cognition (Number Sense, Number Comprehension, Number Production and Calculation), was the best model, with significant correlations ranging from 0.89 to 0.97 at the 0.001 level. [ABSTRACT FROM AUTHOR]

Background Children have been found to report and demonstrate math anxiety as early as the first grade. However, previous results concerning the relationship between math anxiety and performance are contradictory, with some studies establishing a correlation between them while others do not. These contradictory results might be related to varying operationalizations of math anxiety. Aims In this study, we aimed to examine the prevalence of math anxiety and its relationship with basic arithmetic skills in primary school children, with explicit focus on two aspects of math anxiety: anxiety about failure in mathematics and anxiety in math-related situations. Sample The participants comprised 1,327 children at grades 2-5. Methods Math anxiety was assessed using six items, and basic arithmetic skills were assessed using three assessment tasks. Results Around one-third of the participants reported anxiety about being unable to do math, one-fifth about having to answer teachers' questions, and one tenth about having to do math. Confirmatory factor analysis indicated that anxiety about math-related situations and anxiety about failure in mathematics are separable aspects of math anxiety. Structural equation modelling suggested that anxiety about math-related situations was more strongly associated with arithmetic fluency than anxiety about failure. Anxiety about math-related situations was most common among second graders and least common among fifth graders. Conclusions As math anxiety, particularly about math-related situations, was related to arithmetic fluency even as early as the second grade, children's negative feelings and math anxiety should be identified and addressed from the early primary school years. [ABSTRACT FROM AUTHOR]

Background: Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys' mathematics performance is more negatively affected by MA than girls' performance is. The aim of the current study was to measure girls' and boys' mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Methods: Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. Results: No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Conclusions: Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on 'online' mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance. [ABSTRACT FROM AUTHOR]

The present study compared the relative effects of 2 educational programs on kindergarten children. The experimental group took part in a numeracy-specific program, which focused on conceptual knowledge. Children were taught basic numerical skills such as understanding and handling numbers and their relations as well as counting principles. The control group participated in a more general program which involved training in procedural skills. Results revealed significant learning effects in the children who participated in the numeracy program particularly for counting sequences and mental calculation. Since neither group was explicitly trained in mental calculation, our findings suggest that a learning transfer took place in the experimental group. [ABSTRACT FROM AUTHOR]