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We examined the role of visuo-spatial working memory in different types of arithmetic ability in children. Previous research had suggested that arithmetic is not a single entity (Dowker, 2005, 2015), and also that visuo-spatial working memory is specifically involved in mathematical cognition (McKenzie et al., 2003) There has, however, been little research on the relationships between visuo-spatial working memory and different types of arithmetic. We tested 39 children in Year 2 (6 to 7 years) and Year 4 (8 to 9 years), taking measures of written arithmetic, mental oral arithmetic, and derived fact strategy use (the ability to derive unknown arithmetical facts from known facts, by using arithmetical principles). We also measured visuospatial working memory, verbal comprehension, and spelling ability. We investigated the relationships between visuo-spatial working memory and our three arithmetic measures, as well as spelling and verbal comprehension, to test whether these effects were specific to mathematical abilities. We found that visuo-spatial working memory was specifically associated with both verbal oral and mental written arithmetic, and but not with spelling or derived fact strategy use.

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.

Developmental cognitive neuroscience highlights the importance of interactions between children and their environment. As young children spend increasing time in childcare, it is key to investigate the impact of "maths-talk" and maths provisions in preschools. Qualitative insights from early educators indicate a greater bias toward counting activities than would be expected given the Early Years curriculum. In addition, we quantified the observed breadth of preschool practitioners' maths language (e.g., place-value language), setting-based maths provisions (e.g., quality of maths-related activities), and their relation with children's early numeracy skills. In settings with greater practitioners' breadth of maths language, children display greater cardinality skills although our data call for the further investigation of parental socioeconomic status and education. We conclude with a discussion on the need to operationalize children's maths learning environments as diversely as possible. Enriching practitioners' skill sets may be an effective and needed way of improving early maths outcomes.

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.

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.

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.

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. (Contains 3 tables.)

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.