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

Motor activities to improve maths performance in pre-school children with typical development

Poor maths skills are associated with negative outcomes throughout life, such as lower academic qualifications, decreased professional success and socio-economic results. Mathematical skills emerge continuously throughout childhood and those that children acquire in pre-school are crucial for activities that support analytical thinking, problem-solving and reasoning and argumentation skills. Many of these activities are related to motor skills, since certain cognitive and motor areas of the brain are activated simultaneously when solving maths problems. Of all motor skills, visuomotor integration skills have been documented as those that are most consistently positively and significantly associated with maths performance in pre-school children. These skills are influenced by visual perception (spatial and attention skills), fine motor coordination and gross motor skills. Early intervention can improve visuomotor integration skills in pre-school children. Of all skills that make up visuomotor integration, spatial skills, in addition to being the first skills to influence numerical knowledge and the recognition of geometric shapes, are also those skills that form part of the majority of programs and activities to be worked on with pre-school children for the development of mathematical concepts. However, most intervention programs or activities to develop spatial skills are carried out in the classroom, usually through activities involving handling small objects. In this sense and given the significant association between visuomotor integration skills and gross motor skills, the main objective of this study was to list a set of activities to develop spatial skills, with a strong involvement of gross motor skills, in a classroom, playground or home context.

Numerosity comparison, cognitive strategies, and general cognitive functioning in older people

Introduction

Studies have shown age-related differences in numerical cognition, for example, in the level of numerosity comparison ability. Moreover, some studies point out individual differences in the cognitive strategies employed during the performance of numerosity comparison tasks and reveal that they are related to the aging process. One probable cause of these differences is the level of cognitive functioning. The aim of our study was to determine the relationships among numerosity comparison ability, the cognitive strategies utilized in the performance of numerosity comparison tasks and the general cognitive functioning in older people.

Methods

Forty-seven elderly people participated in the study. The participants were examined using overall cognitive functioning scales and computerized numerosity comparison task.

Results

The results showed many correlations between the participants' level of cognitive functioning and the percent of correct responses (PCR) and response time (RT) during numerosity comparison, as well as with the cognitive strategies applied by the participants. Task correctness was positively related to the level of performance in the attention and executive function tasks. In contrast, the long-term memory resources index and visuospatial skills level were negatively correlated with RT regarding numerosity comparison task performance. The level of long-term memory resources was also positively associated with the frequency of use of more complex cognitive strategies. Series of regression analyses showed that both the level of general cognitive functioning and the cognitive strategies employed by participants in numerosity comparison can explain 9-21 percent of the variance in the obtained results.

Discussion

In summary, these results showed significant relationships between the level of cognitive functioning and proficiency in numerosity comparison measured in older people. Moreover, it has been shown that cognitive resources level is related to the strategies utilized by older people, which indicates the potential application for cognitive strategy examinations in the development of new diagnostic tools.

The importance of spatial language for early numerical development in preschool: Going beyond verbal number skills

Recent evidence suggests that spatial language in preschool positively affects the development of verbal number skills, as indexed by aggregated performances on counting and number naming tasks. We firstly aimed to specify whether spatial language (the knowledge of locative prepositions) significantly relates to both of these measures. In addition, we assessed whether the predictive value of spatial language extends beyond verbal number skills to numerical subdomains without explicit verbal component, such as number writing, symbolic magnitude classifications, ordinal judgments and numerosity comparisons. To determine the unique contributions of spatial language to these numerical skills, we controlled in our regression analyses for intrinsic and extrinsic spatial abilities, phonological awareness as well as age, socioeconomic status and home language. With respect to verbal number skills, it appeared that spatial language uniquely predicted forward and backward counting but not number naming, which was significantly affected only by phonological awareness. Regarding numerical tasks that do not contain explicit verbal components, spatial language did not relate to number writing or numerosity comparisons. Conversely, it explained unique variance in symbolic magnitude classifications and was the only predictor of ordinal judgments. These findings thus highlight the importance of spatial language for early numerical development beyond verbal number skills and suggest that the knowledge of spatial terms is especially relevant for processing cardinal and ordinal relations between symbolic numbers. Promoting spatial language in preschool might thus be an interesting avenue for fostering the acquisition of these symbolic numerical skills prior to formal schooling.

Is Nonsymbolic Arithmetic Truly "Arithmetic"? Examining the Computational Capacity of the Approximate Number System in Young Children

Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like structure, like symbolic arithmetic. Children (n = 74 4- to -8-year-olds in Experiment 1; n = 52 7- to 8-year-olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and asked children which of the two derived solutions should be added to the smaller of the two sets to make them "about the same." We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge.

Achievement in Fundamental Movement Skills, Spatial Abilities, and Mathematics among Lower Key Stage 2 Children

Research has demonstrated links between sport and mathematics learning, and their relationship with spatial abilities in children. This study explored the association between the development of fundamental movement skills (FMS) and mathematics achievement, and whether the understanding of specific spatial concepts mediated these relationships. Overall, 154 Year 3 children (69 males, 85 females, aged 7-8 years) from four schools in England completed an FMS assessment involving six skills; four spatial tasks assessing intrinsic-static, intrinsic-dynamic, extrinsic-static, and extrinsic-dynamic spatial abilities; and a mathematics test assessing numerical, geometrical, and arithmetical abilities. Overall FMS ability (a combined score across the six skills) was significantly positively correlated to overall mathematics achievement. This relationship was mediated by children's performance on the intrinsic-static spatial ability test. These findings suggest that children who have more mature FMS perform better in mathematics tasks, and this could be due to more developed intrinsic-static spatial ability. However, further research is necessary to determine the mediation effects of intrinsic-dynamic and extrinsic-static spatial ability.

Academic Challenges in Developmental Coordination Disorder: A Systematic Review and Meta-Analysis

AIMS

Developmental Coordination Disorder (DCD) is a chronic condition affecting motor coordination in daily activities. While motor difficulties are well documented in this population, it is unclear how frequent and to what extent academic activities are affected. This systematic review aims to comprehensively summarize the knowledge regarding the prevalence and extent of academic difficulties in reading, writing and mathematics in school-aged children with DCD.

METHODS

Two independent reviewers analyzed original studies on academic difficulties in school-aged children with DCD. A binary random-effects model was used to calculate the pooled prevalence by academic difficulty. A random-effects model using standardized mean differences (g statistic) was calculated to estimate the extent of the academic difficulties.

RESULTS

Twenty-four studies were included. A pooled prevalence of 84% of handwriting difficulties and 89.5% of mathematical difficulties was reported. No pooled prevalence of difficulties could be calculated for the other academic outcomes. Children with DCD present with poorer performance in handwriting legibility (g = -1.312) and speed (g = -0.931), writing (g = -0.859), mathematics (g = -1.199) and reading (g = -1.193).

CONCLUSIONS

This review highlights the high frequency and severity of academic difficulties in children with DCD, specifically in mathematics, which stresses the importance of evaluating academic performance to target interventions to support optimal functioning in daily life.

Mediating process between fine motor skills, finger gnosis, and calculation abilities in preschool children

Previous studies have found a relationship between fine motor skills, finger gnosis, and calculation skill. However, what mediates this association remains unclear. Therefore, this study investigated whether fine motor skills and finger gnosis are selectively associated with counting and symbolic comparison, and whether fine motor skills and finger gnosis are associated with calculation skills through numerical concepts to which they are selectively associated. We measured the counting, symbolic comparison, fine motor skills, finger gnosis, and working memory in preschool children (N = 48). The hierarchical multiple regression analysis results demonstrated that fine motor skills were selectively associated with counting, and finger gnosis with symbolic comparison. Moreover, based on the results of the mediation analysis, counting mediated the relationship between fine motor and calculation skills. However, the direct effects of fine motor skills and finger gnosis on calculation skills were also maintained. The findings were that fine motor skills and finger gnosis were related to numerical abilities, including counting, symbolic comparison, and calculations. Therefore, the findings were discussed in terms of the functional view and redeployment views, suggesting that the two views were complementary rather than exclusive.

Walking another pathway: The inclusion of patterning in the pathways to mathematics model

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753-1767], children's cognitive skills in three domains-linguistic, attentional, and quantitative-predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a non-numeric repeating patterning task. Chilean children who attended schools of low or high socioeconomic status (N = 98; 54% girls) completed cognitive measures in kindergarten (M_age = 71 months) and numeracy and mathematics outcomes 1 year later in Grade 1. Patterning and the original three pathways were correlated with the outcomes. Using Bayesian regressions, after including the original pathways and mother's education, we found that patterning skills predicted additional variability in applied problem solving and arithmetic fluency, but not number ordering, in Grade 1. Similarly, patterning skills were included in the best model for applied problem solving and arithmetic fluency, but not for number ordering, in Grade 1. In accord with the hypotheses of the original Pathways to Mathematics model, patterning varied in its unique and relative contributions to later mathematical performance, depending on the demands of the tasks. We conclude that patterning is a useful addition to the Pathways to Mathematics model, providing further insights into the range of cognitive precursors that are related to children's mathematical development.

Children's use of egocentric reference frames in spatial language is related to their numerical magnitude understanding

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position (e.g., in front of, behind, to the right/left) have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old's spatial language skills in tasks that allow responses in egocentric and allocentric frames of reference, as well as their relative understanding of numerical magnitude (assessed by a number word comparison task). In addition, we evaluated influences of children's absolute understanding of numerical magnitude assessed by their number word comprehension (montring different numbers using their fingers) and of their knowledge on numerical sequences (determining predecessors and successors as well as identifying missing dice patterns of a series). Results indicated that when considering responses that corresponded to the egocentric perspective, children's spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children's SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers' relative understanding of numerical magnitude.

Spatial skills and number skills in preschool children: The moderating role of spatial anxiety

Spatial ability is a strong and stable predictor of mathematical performance. However, of the three key components of spatial ability, spatial perception and spatial visualization have received less attention than mental rotation in relation to specific mathematical competencies of young children. Even less is known about the role of spatial anxiety in this relationship. This study examined the longitudinal relations of spatial perception and spatial visualization to three number skills (i.e., number line estimation, subitizing, and word problem-solving) among 190 preschool children, and whether these relations varied as a function of spatial anxiety. The results showed that children's spatial perception and spatial visualization skills, measured in the third preschool year (Time 1 [T1]), were positively associated with their word problem-solving six months later (Time 2 [T2]). Children's T1 spatial perception was also positively associated with their T2 subitizing and number line skills. In addition, T1 spatial anxiety moderated the relation between T1 spatial perception and T2 subitizing: the relation between the two was stronger for children with low levels of spatial anxiety than it was for those with moderate or high levels. The findings offer valuable insights into how spatial cognition and affect jointly relate to children's early number skills.

Bidirectional relationship between visual perception and mathematics performance in Chinese kindergartners

In this longitudinal study, 64 kindergartners (mean age at T1 = 4.69 ± 0.33 years; 34 girls) were tested on visual perception skills (T2 and T3) and mathematics performance (T1 to T3) with 6-month intervals between the three testing waves. Cross-lagged path analysis showed a bidirectional relationship between visual perception and mathematics performance from T2 to T3. Specifically, children's visual perception at T2 significantly predicted their mathematics performance at T3 (B = 0.30, SE = 0.14, p = 0.03, β = 0.19). Children's mathematics performance at T1 accounted for unique variance in visual perception at T2 (B = 0.79, SE = 0.11, p < 0.001, β = 0.68) and visual perception at T3 (B = 0.27, SE = 0.12, p = 0.02, β = 0.32). Their mathematics performance at T2 also significantly predicted visual perception at T3 (B = 0.21, SE = 0.10, p = 0.04, β = 0.28). Totally, they explained 61% of the variance in mathematics performance and 39% of the variance in visual perception at T3. The results highlight the developmental courses as well as the reciprocal facilitations between visual perception and mathematics performance in the kindergarten period.

Longitudinal relations between the approximate number system and symbolic number skills in preschool children

This study examined the longitudinal relation between the approximate number system (ANS) and two symbolic number skills, namely word problem-solving skill and number line skill, in a sample of 138 Chinese 4- to 6-year-old children. The ANS and symbolic number skills were measured first in the second year of preschool (Time 1 [T1], mean age = 4.98 years; SD = 0.33) and then in the third year of preschool (Time 2 [T2]). Cross-lagged analyses indicated that word problem-solving skill at T1 predicted ANS acuity at T2 but not vice versa. In addition, there were bidirectional relations between children's word problem-solving skill and number line estimation skill. The observed longitudinal relations were robust to the control of child's sex, age, maternal education, receptive vocabulary, spatial visualization, and working memory except for the relation between T1 word problem-solving skill and T2 number line estimation skill, which was explained by child's age.

Home activities and cognitive skills in relation to early literacy and numeracy: testing a multifactorial model in preschoolers

The aim of the present study was to test environmental and cognitive variables as possible cross-domain predictors of early literacy and numeracy skills. One hundred forty-eight preschool children (mean age = 64.36 months ± 3.33) were enrolled in the study. The battery included a home literacy and home numeracy questionnaire, measures and phonological and visuo-spatial working memory, tasks tapping response inhibition, and predictors of literacy (vocabulary, phonological awareness, letter knowledge) and numeracy (magnitude comparison, number knowledge) skills. The structural equation model indicated that verbal working memory and, to a lesser extent, inhibition represented cross-domain predictors, whereas home numeracy activities and visuo-spatial working memory explained additional variance only for early numeracy skills. Implications for parents and educators are discussed.

Visual-spatial skills contribute to Chinese reading and arithmetic for different reasons: A three-wave longitudinal study

Previous literature has revealed that visual-spatial processing is associated with both reading and arithmetic. Yet the strength of their relations and the reasons why visual-spatial processing contributes to reading and arithmetic remain ambiguous. The current study focused on two types of visual-spatial skills that recent evidence has suggested are crucial in children's early reading and arithmetic development: visual-perceptual and spatial visualization skills. With an interval of 6 months, we assessed 104 Hong Kong kindergarten children's visual-spatial skills, word reading, arithmetic performance, and vocabulary knowledge at Wave 1; orthographic awareness, basic number knowledge, and number line estimation at Wave 2; and Chinese word reading and arithmetic performance at Wave 3. Correlational analysis showed that both visual-perceptual and spatial visualization skills were associated with later Chinese word reading and arithmetic performance. Further mediation analyses revealed that spatial visualization skills, rather than visual-perceptual skills, contributed to Chinese word reading via orthographic awareness and also predicted arithmetic performance through basic number knowledge. However, number line estimation failed to mediate any relations of visual-spatial skills with children's arithmetic abilities. The results suggest the importance of visual-spatial processing in Chinese word reading and mathematics, with spatial visualization contributing to reading and mathematics for different reasons.

The Relationship of Reading Abilities With the Underlying Cognitive Skills of Math: A Dimensional Approach

Math and reading are related, and math problems are often accompanied by problems in reading. In the present study, we used a dimensional approach and we aimed to assess the relationship of reading and math with the cognitive skills assumed to underlie the development of math. The sample included 97 children from 4th and 5th grades of a primary school. Children were administered measures of reading and math, non-verbal IQ, and various underlying cognitive abilities of math (counting, number sense, and number system knowledge). We also included measures of phonological awareness and working memory (WM). Two approaches were undertaken to elucidate the relations of the cognitive skills with math and reading. In the first approach, we examined the unique contributions of math and reading ability, as well as their interaction, to each cognitive ability. In the second approach, the cognitive abilities were taken to predict math and reading. Results from the first set of analyses showed specific effects of math on number sense and number system knowledge, whereas counting was affected by both math and reading. No math-by-reading interactions were observed. In contrast, for phonological awareness, an interaction of math and reading was found. Lower performing children on both math and reading performed disproportionately lower. Results with respect to the second approach confirmed the specific relation of counting, number sense, and number system knowledge to math and the relation of counting to reading but added that each math-related marker contributed independently to math. Following this approach, no unique effects of phonological awareness on math and reading were found. In all, the results show that math is specifically related to counting, number sense, and number system knowledge. The results also highlight what each approach can contribute to an understanding of the relations of the various cognitive correlates with reading and math.

The relationship between mental rotation and arithmetic: do number line estimation, working memory, or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.

Predictors of Children's Early Numeracy: Environmental Variables, Intergenerational Pathways, and Children's Cognitive, Linguistic, and Non-symbolic Number Skills

Early numeracy skills in preschool years have been found to be related to a variety of different factors, including Approximate Number System (ANS) skills, children's cognitive and linguistic skills, and environmental variables such as home numeracy activities. The present study aimed to analyze the differential role of environmental variables, intergenerational patterns, children's cognitive and linguistic skills, and their ANS in supporting early math skills. The sample included 64 children in their last year of kindergarten and one parent of each child. Children were administered a battery of cognitive and linguistic tasks, and a non-symbolic comparison task as a measure of ANS. Parents were administered similar tasks assessing cognitive skills, math skills, and ANS skills (estimation and non-symbolic comparison), together with a questionnaire on home numeracy. Results showed that home numeracy predicted children's early math skills better than a number of parent and child variables. Considering children's skills, their ability in the non-symbolic magnitude comparison task was the strongest predictor of early math skills. Results reinforce the importance of the role of home numeracy activities and children's ANS skills above that of parents' math skills.

The importance of visuospatial abilities for verbal number skills in preschool: Adding spatial language to the equation

Children's verbal number skills set the foundation for mathematical development. Therefore, it is central to understand their cognitive origins. Evidence suggests that preschool children rely on visuospatial abilities when solving counting and number naming tasks despite their predominantly verbal nature. We aimed to replicate these findings when controlling for verbal abilities and sociodemographic factors. Moreover, we further characterized the relation between visuospatial abilities and verbal number skills by examining the role of spatial language. Because spatial language encompasses the verbalization of spatial thinking, it is a key candidate supporting the interplay between visuospatial and verbal processes. Regression analysis indicated that both visuospatial and verbal abilities, as assessed by spatial perception and phonological awareness, respectively, uniquely predicted verbal number skills when controlling for their respective influences, age, gender, and socioeconomic status. This confirms the spatial grounding of verbal number skills. Interestingly, adding spatial language to the model abolished the predictive effects of visuospatial and verbal abilities, whose influences were completely mediated by spatial language. Verbal number skills thus concurrently depend on specifically those visuospatial and verbal processes jointly indexed through spatial language. The knowledge of spatial terms might promote verbal number skills by advancing the understanding of the spatial relations between numerical magnitudes on the mental number line. Promoting spatial language in preschool thus might be a successful avenue for stimulating mathematical development prior to formal schooling. Moreover, measures of spatial language could become an additional promising tool to screen preschool children for potential upcoming difficulties with mathematical learning.

Visual Processing Matters in Chinese Reading Acquisition and Early Mathematics

The main purpose of the present study was to investigate whether visual processing uniquely contributed to character reading and early mathematics in Chinese children. Eighty-two Chinese kindergarteners at K3 (mean age = 68 months, SD = 0.30) were followed up to grade one (mean age = 82 months, SD = 0.35) with an interval of 14 months. Nonverbal intelligence, inhibitory control, sustained attention, character reading, and mathematics were measured at kindergarten. Character reading and mathematics were assessed again at grade one. Results showed visual processing at kindergarten significantly predicted character reading at grade one after controlling for prior reading performance, inhibitory control, sustained attention, age, gender, and nonverbal IQ. Similarly, visual processing at kindergarten explained unique variance in early mathematics at grade one when prior mathematics performance and other covariates at kindergarten were controlled. These findings suggest that visual processing should serve as a domain-general precursor of children's performance in character reading and early mathematics and an important cognitive factor for later academic learning.

Make-A-Dice Test: Assessing the intersection of mathematical and spatial thinking

Individuals with better spatial thinking have increased interest and greater achievement in science, technology, engineering, and mathematics (STEM) disciplines (Wai, Lubinski, & Benbow in Journal of Educational Psychology, 101, 817-835, 2009). This relationship means that STEM education may benefit from leveraging spatial thinking, but measures of spatial thinking as they relate to specific STEM disciplines are needed. The present work presents an assessment of spatial and mathematical reasoning, called Make-A-Dice. In Make-A-Dice, individuals are presented with a cube net (i.e., a flattened cube) with numbers on two sides. Their goal is to "make a dice" by filling in the blank sides using two rules: opposite sides add to 7, and the numbers 1 through 6 should be used once each. Make-A-Dice was given to adults (Study 1) and elementary students (Studies 2 and 3) along with math, spatial, and other measures, across two sessions in all studies. Make-A-Dice had both internal and test-retest reliability, with items ordered by difficulty. Furthermore, performance was related to spatial and mathematical reasoning. In Study 1, adults reported a range of strategies used to complete Make-A-Dice, and one strategy predicted performance. Studies 2 and 3 showed that Make-A-Dice is age-appropriate for elementary students. Make-A-Dice shows promise as an individual-difference measure linking spatial and mathematical thinking and has the potential to identify elementary-aged children who may benefit from spatial training.

Young Chinese Children's Academic Skill Development: Identifying Child-, Family-, and School-Level Factors

This chapter addresses how child-, family-, and school-level characteristics are associated with Chinese children's academic skill development during their preschool years. Academic skills are defined in terms of young children's emergent competencies in academic domains including literacy, mathematics, and science. First, we review the relations of young Chinese children's cognition (language, visuospatial, and executive functioning), behavior (social behavior and behavioral regulation), and affect (interest and attitude) to their performance in these academic domains. Second, we review the roles of familial variables, including family socioeconomic status and broad and specific aspects of parenting practices and parental involvement. Third, we review school- and classroom-level factors, with a special emphasis on preschool and classroom quality that is particularly relevant to young Chinese children's academic skills. We discuss the educational implications of these study findings and identify methodological limitations that may threaten their internal and external validity. Our aim is to bring attention to the growing body of research on young Chinese children's academic skill development and to highlight several areas that need further research.

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes. Start-of-year language was a significantly stronger predictor of both year-end WP outcomes than of calculations, whereas start-of-year arithmetic was a significantly stronger predictor of calculations than of either WP measure. Implications are discussed in terms of WP solving as a form of TC and a theoretically coordinated approach, focused on language, for addressing TC and WP-solving instruction.

The contribution of parent-child numeracy activities to young Chinese children's mathematical ability

BACKGROUND

A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities.

AIMS

This study aimed to examine both mother-child and father-child numeracy activities in Hong Kong Chinese families and both parents' unique roles in predicting young Chinese children's mathematics ability.

SAMPLE

A sample of 104 Hong Kong Chinese children aged approximately 5 years and their mothers and fathers participated in this study.

METHODS

Mothers and fathers independently reported the frequency of their own numeracy activities with their children. Children were assessed individually using two measures of mathematical ability. Hierarchical regression models were used to investigate the contribution of parent-child numeracy activities to children's mathematical ability.

RESULTS

Mothers' participation in number skill activities and fathers' participation in number game and application activities significantly predicted their children's mathematical performance even after controlling for background variables and children's language ability.

CONCLUSIONS

This study extends previous research with a sample of Chinese kindergarten children and shows that parent-child numeracy activities are related to young children's mathematical ability. The findings highlight the important roles that mothers and fathers play in their young children's mathematical learning.

The space-math link in preschool boys and girls: Importance of mental transformation, targeting accuracy, and spatial anxiety

Spatial abilities are pertinent to mathematical competence, but evidence of the space-math link has largely been confined to older samples and intrinsic spatial abilities (e.g., mental transformation). The roles of gender and affective factors are also unclear. This study examined the correlations between counting ability, mental transformation, and targeting accuracy in 182 Hong Kong preschoolers, and whether these relationships were weaker at higher spatial anxiety levels. Both spatial abilities related with counting similarly for boys and girls. Targeting accuracy also mediated the male advantage in counting. Interestingly, spatial anxiety moderated the space-math links, but differently for boys and girls. For boys, spatial abilities were irrelevant to counting at high anxiety levels; for girls, the role of anxiety on the space-math link is less clear. Results extend the evidence base of the space-math link to include an extrinsic spatial ability (targeting accuracy) and have implications for intervention programmes. Statement of contribution What is already known on this subject? Much evidence of a space-math link in adolescent and adult samples and for intrinsic spatial abilities. What does this study add? Extended the space-math link to include both intrinsic and extrinsic spatial abilities in a preschool sample. Showed how spatial anxiety moderated the space-math link differently for boys and girls.