A longitudinal analysis of sex differences in math and spatial skills in primary school age children

Visual-Motor Integration Deficits in 3q29 Deletion Syndrome

3q29 deletion syndrome (3q29del) is associated with neuropsychiatric and neurodevelopmental phenotypes. We previously reported that graphomotor weakness is present in up to 78% of individuals with 3q29del. We have now explored nuances of the graphomotor phenotype and its association with other comorbidities in this population. Participants were recruited from the online 3q29 registry (3q29deletion.org) for two days of deep phenotyping. 32 individuals with 3q29del (62.5% male) were evaluated with the Beery-Buktenica Developmental Test of Visual-Motor Integration (VMI) to assess visual-motor integration. Participants were also evaluated with measures of cognitive ability, executive function, adaptive behavior, and school function. Males with 3q29del performed significantly worse than females on the VMI and Motor Coordination subtest. VMI performance was significantly associated with ADHD diagnosis and cognitive ability. Compared to published data from individuals with 22q11.2 deletion syndrome, individuals with 3q29del showed significantly more impairment. The 3q29 deletion is associated with substantial deficits in visual-motor integration, Visual Perception, and Motor Coordination. Our data suggests that 3q29del may qualify as a nonverbal learning disability. Future studies should assess whether individuals with 3q29del would benefit from early interventions, including occupational therapy.

Educational achievement and bullying: The mediating role of psychological difficulties

BACKGROUND

Bullying has a profound and enduring impact on academic achievement. However, there is a lack of clarity surrounding the specific mechanisms of this relationship.

AIMS

This study examined the link between bullying at age 9 and Numeracy/Literacy achievement at age 15 to determine if this relationship is partially or fully explained by psychological difficulties at age 13.

SAMPLE

Secondary data analysis was completed on waves 1, 2 and 3 of child cohort (Cohort'98) of the Growing Up in Ireland (GUI) study, respectively, at 9 years (N = 8568), 13 years (N = 7527) and 15 years of age (N = 6216).

RESULTS

Longitudinal path mediation model was conducted with bullying at age 9 as the predictor, total (emotional and behavioural) difficulties at age 13 as the mediator and Numeracy/Literacy scores at age 15 as outcomes revealing significant indirect effects of bullying on achievement, via psychological difficulties.

CONCLUSIONS

We discuss the impact of bullying on the student's psychological well-being, the relationship between bullying and academic attainment and how this may be tackled to avoid consequences throughout education and later in life.

EDUCATIONAL IMPACT AND IMPLICATIONS

This study emphasizes the need for schools to address the emotional and behavioural difficulties occurring as a result of bullying in order to improve the overall educational experience of a child. Existing interventions can be built upon by focusing on the continuous remediation of such psychological difficulties.

The neural substrates of visual organization in children and adolescents: An fMRI study

Deficient visual organization ability not only indicates possible brain dysfunctions but further affects an individual's daily activities. This study aimed to use functional magnetic resonance imaging (fMRI) to investigate the neural network contributing to visual organization abilities in children and adolescents. A two-choice version of the Hooper Visual Organization Test (T-HVOT) was adapted as the fMRI task for the present study. The effects of age and gender on overall visual perceptual functions and related neural foundations were also analyzed. Seventy children and adolescents were administered with the Test of Visual Perceptual Skill-Third Edition and 41 completed the fMRI scans. The whole-brain fMRI mapping results showed the cortical activation of multiple brain areas relating to visual organization. The greatest cortical activities were seen in the middle occipital gyrus, middle temporal gyrus, middle frontal gyrus and inferior frontal gyrus, and two age groups showed significant differences in cortical activation patterns as well. Gender had no significant effects on visual perceptual functions nor related cortical activation patterns. The overall visual perception functions improve with age, and the different cortical activation patterns indicated that the two groups adopt different strategies while performing visual organization tasks. The sensitivity and spatial resolution of fMRI allowed us to make specific conclusions about cortical regions involved in visual organization function and to provide a reference for objectively judging rehabilitative outcomes.

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.

Sex differences in the association of math achievement with visual-spatial and verbal working memory: Does the type of math test matter?

Previous research on sex differences in mathematical achievement shows mixed findings, which have been argued to depend on types of math tests used and the type of solution strategies (i.e., verbal versus visual‐spatial) these tests evoke. The current study evaluated sex differences in (a) performance (development) on two types of math tests in primary schools and (b) the predictive value of verbal and visual‐spatial working memory on math achievement. Children (N = 3175) from grades 2 through five participated. Visual‐spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed five times during two school years using a speeded arithmetic test (math fluency) and a word problem test (math problem solving). Results from Multilevel Multigroup Latent Growth Modeling, showed that sex differences in level and growth of math performance were mixed and very small. Sex differences in the predictive value of verbal and visual‐spatial working memory for math performance suggested that boys seemed to rely more on verbal strategies than girls. Explanations focus on cognitive and emotional factors and how these may interact to possibly amplify sex differences as children grow older.

Psychometric properties of the Korean Motor-free Visual Perception Test-4 in healthy people

Objective

This study was conducted to cross-culturally adapt the Motor-free Visual Perception Test 4 (MVPT-4) for use in Korean contexts and examine its psychometric properties.

Methods

The Korean MVPT-4 (K-MVPT-4) was developed via the process of translation, back-translation, and expert committee review. To establish internal consistency, test-retest reliability, concurrent validity and construct validity of the K-MVPT-4, 295 healthy people aged 10 to 79 years participated in this study. Participants completed the measures for the test-retest reliability on two occasions, 2 weeks apart.

Results

After three steps of cross-cultural adaptation, the K-MVPT-4 was revised to improve its alignment with Korean cultural norms. Cronbach's α for internal consistency was .857 and intra-class correlation coefficient for test-retest reliability was .949. The K-MVPT-4 scores were significantly correlated with those of three motor-reduced subscales of the Korean Developmental Test of Visual Perception-Adolescent (K-DTVP-A) (r = .44-.46, p < .01). Participants' age significantly influenced the K-MVPT-4 scores (p < .001) while their gender did not affect those scores (p = .409). As the age increased, the K-MVPT-4 scores decreased.

Conclusions

The findings indicated that the K-MVPT-4 is a reliable and valid test that Korean rehabilitation service providers can use with confidence to assess clients' visual perceptual abilities.

Inattention, hyperactivity/impulsivity, and mathematics: Exploring gender differences in a nonclinical sample

In this study, we considered two subscales of attention problem (AP) behaviour, inattentiveness and hyperactivity/impulsivity, as latent traits, extreme values of which indicate attention deficit hyperactivity disorder (ADHD). We examined gender differences in these traits in a community sample of Russian schoolchildren and estimated the extent to which the association of AP behaviour and math achievement varied for boys and girls. The data from a three-wave longitudinal study of math achievement of 958 children (49 % girls) were used, and growth in math achievement was estimated. The levels of inattentiveness and hyperactivity/impulsivity of each child were measured based on teachers' responses using the Behaviour Rating Scale (BRS). The results demonstrated that inattentiveness had a negative association with math achievement, while hyperactivity/impulsivity was positively associated with math achievement when inattentiveness was controlled for. Inattentiveness was negatively associated with math achievement in both boys and girls. However, the size of this association decreased over time for boys, so the gap between boys with high inattentiveness and low inattentiveness decreased from grade 1 to grade 2. Meanwhile, for girls, the association between inattentiveness and math remained stable, so the gap between girls with high inattentiveness and girls with low inattentiveness did not change.

Spatial and mathematics skills: Similarities and differences related to age, SES, and gender

Performance on a range of spatial and mathematics tasks was measured in a sample of 1592 students in kindergarten, third grade, and sixth grade. In a previously published analysis of these data, performance was analyzed by grade only. In the present analyses, we examined whether the relations between spatial skill and mathematics skill differed across socio-economic levels, for boys versus girls, or both. Our first aim was to test for group differences in spatial skill and mathematics skill. We found that children from higher income families showed significantly better performance on both spatial and mathematics measures, and boys outperformed girls on spatial measures in all three grades, but only outperformed girls on mathematics measures in kindergarten. Further, comparisons using factor analysis indicated that the income-related gap in mathematics performance increased across the grade levels, while the income-related gap in spatial performance remained constant. Our second aim was to test whether spatial skill mediated any of these effects, and we found that it did, either partially or fully, in all four cases. Our third aim was to test whether the "separate but correlated" two-factor latent structure previously reported for spatial skill and mathematics skill was (Mix et al., 2016; Mix et al., 2017) replicated across grade, SES, and sex. Multi-group confirmatory factor analyses conducted for each of these subgroups indicated that the same latent structure was present, despite differences in overall performance. These findings replicate and extend prior work on SES and sex differences related to spatial and mathematics skill, but provide evidence that the relations between the domains are stable and consistent across subgroups.

Supporting preschoolers' cognitive development: Short- and mid-term effects of fluid reasoning, visuospatial, and motor training

Cognitive abilities are essential to children's overall growth; thus, the implementation of early and effective training interventions is a major challenge for developmental psychologists and teachers. This study explores whether an intervention simultaneously operating on fluid reasoning (FR), visuospatial, narrative, and motor abilities could boost these competencies in a group of Italian preschoolers (N = 108, 54 males 54 females, Age_mean = 4.04). FR and visuospatial abilities showed training‐related increases at the end of the training and 1‐year follow‐up (moderate effect size). Interestingly, positive correlations with working memory and mathematical abilities were found. Beyond their scientific relevance, the short‐ and long‐term effects provide fundamental indications for designing and implementing educational programs dedicated to preschoolers.

Gender-Based Performance in Mathematical Facts and Calculations in Two Elementary School Samples From Chile and Spain: An Exploratory Study

Gender differences in mathematical performance are not conclusive according to the scientific literature, although such differences are supported by international studies such as the Trends in International Mathematics and Science Study (TIMSS). According to TIMSS 2019, fourth-grade male students outperformed female students in Spanish-speaking countries, among others. This work approaches the study on gender difference by examining the basic calculation skills needed to handle more complex problems. Two international samples of second and third graders from Chile and Spain were selected for this exploratory study. Tests on basic mathematical knowledge (symbolic and non-symbolic magnitude comparisons, fluency, and calculation) were administered. The tests did not show significant difference or size effect between genders for mean performance, variance in the distribution of performance, or percentiles. As noted in the existing literature on this topic and reiterated by these findings, great care should be exercised when reporting on possible gender differences in mathematical performance, as these can contribute to low self-concept among female students.

Relations among spatial skills, number line estimation, and exact and approximate calculation in young children

Decades of research have established that spatial skills correlate with numerical skills. However, because both spatial and numerical skills are multidimensional, we sought to determine how specific spatial skills relate to specific numeracy skills. We used a cohort-sequential design, assessing a large diverse sample of students (N = 612, initially in pre-kindergarten [pre-K]-3rd grade, 4-9 years of age) at four time points spanning 2 years. We examined how initial levels of five spatial skills (visuospatial working memory [VSWM], mental transformation, mental rotation, proportional reasoning, and analog magnitude system [AMS] acuity) related to initial levels and growth rates in exact and approximate calculation skills, and we further investigated number line estimation as a potential mediator. We found unique patterns of relations between spatial skills and numeracy. Initial levels of mental rotation, proportional reasoning, and AMS acuity related to initial levels of exact calculation skill; initial levels of AMS acuity related to initial levels of approximate calculation; and initial levels of proportional reasoning related to initial levels of number line estimation. VSWM and mental transformation did not relate to numeracy skills after controlling for other spatial skills. Initial levels of number line estimation related to both exact and approximate calculation after controlling for spatial skills. Notably, neither spatial skills nor number line estimation predicted growth in exact or approximate calculation skills. These results indicate that there is specificity in the time-invariant relations between spatial skills and numeracy, and they suggest that researchers and educators should treat spatial skills and numeracy as multidimensional constructs with complex and unique interrelations.

Cross-cultural Validation of the Full Range Test of Visual Motor Integration Used with Children in Four Arab Countries

SIGNIFICANCE

Arab countries have a shortage of culturally sensitive psychoeducational assessments. Tests of visual-motor integration are low in their linguistic demands, yet they are not culture-free.

PURPOSE

The aim of this study was to explore the psychometric properties and the validation of the Full Range Test of Visual Motor Integration (FRTVMI) across four Arabic speaking countries, namely, Sultanate of Oman, Kuwait, Qatar, and the Kingdom of Saudi Arabia (n = 2318).

METHODS

The FRTVMI was administered to 2318 children from four Gulf countries. Criterion measures included the Reading Observation Scale and the achievement scores in reading. All raw data obtained for the FRTVMI were analyzed using the Statistical Package for Social Sciences and R package (version 3.5.1, 2018). Construct validity was examined using confirmatory factor analysis. The internal consistency, test-retest reliability, and interrater reliability of FRTVMI were also examined.

RESULTS

The means for Cronbach α, intraclass correlation, and test-retest reliability across the four countries were 0.87, 0.87, and 0.90, respectively. Spearman ρ correlation between FRTVMI scores and Reading Observation Scale scores ranged between 0.16 and 0.51 across the four countries and were 0.57, 0.43, and 0.45 for male and female participants and the entire sample, respectively. The Spearman ρ correlations between FRTVMI scores and reading achievement scores ranged between 0.15 and 0.20 across the four countries and were 0.27, 0.29, and 0.26 for male and female participants and the entire sample, respectively. The modified model indices showed that the FRTVMI was adequate for use in the four countries and for both male and female participants. The reliability estimates for the test were high, whereas the concurrent validity estimates were moderate.

CONCLUSIONS

The unidimensionality of the test should be taken with caution, as we found some indication for the multidimensionality of the test factor structure. Implications for cross-cultural assessment 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 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.

Spatial reasoning, mathematics, and gender: Do spatial constructs differ in their contribution to performance?

BACKGROUND

The role of gender in both spatial and mathematics performance has been extensively studied separately, with a male advantage often found in spatial tasks and mathematics from adolescence. Spatial reasoning is consistently linked to mathematics proficiency, yet despite this, little research has investigated the role of spatial orientation and gender in the relationship between spatial reasoning and mathematics.

AIMS

In the present study, three spatial reasoning constructs (mental rotation, spatial visualization, and spatial orientation) were examined for their unique contributions to mathematics performance in two samples (Study 1: grade 5; Study 2: grade 8). In light of the emerging gender gap in mathematics as children develop, these relationships were explored as a function of gender.

SAMPLE

Eighty-four fifth-grade students participated in Study 1 (43 females, 41 males; mean age = 11.19 years). Nine hundred and three eighth-grade students participated in Study 2 (498 females, 405 males; mean age = 13.83 years).

METHODS

The three spatial reasoning constructs (mental rotation, spatial visualization, and spatial orientation) were examined for their unique contributions to mathematics performance for females and males in general and across different mathematical content (geometry-measurement and number sense).

RESULTS

Spatial factors accounted for 51% of the variance in math scores in Study 1 (grade 5) and 32% of the variance in math scores in Study 2 (grade 8). In both studies, spatial factors predicted a larger proportion of variance in geometry-measurement than for number sense. Spatial orientation was found to be a unique contributor in all mathematics models, object-based spatial skills (mental rotation and spatial visualization) varied in their contribution to math performance depending on mathematics content and gender.

CONCLUSIONS

The present work highlights the unique contribution of spatial orientation in the spatial-mathematics relationship and provides insights into the nature of gender differences in mathematical problem-solving as a function of spatial reasoning and mathematics content.

Spatial anxiety mediates the sex difference in adult mental rotation test performance

Mental rotation ability is associated with successful advances in STEM (science, technology, engineering, and mathematics) education and occupations. Meta-analyses have shown consistent sex disparities in mental rotation, where men outperform women on one measure of mental rotation ability, the Mental Rotations Test (MRT). Spatial anxiety, or the fear and apprehension felt when completing a task that requires spatial thinking, was proposed as a mechanism explaining the relation between sex and mental rotation test performance. This study modified the Spatial Anxiety Scale (SAS) to include questions about how anxious individuals feel when they must mentally rotate items to accomplish a task (e.g., playing Tetris). An exploratory factor analysis was conducted to assess the factorial structure of the modified spatial anxiety scale. Three factor loadings were extracted representing the ability to navigate, mentally rotate objects, and visualize objects. Furthermore, we analyzed the role of spatial anxiety and trait anxiety as potential mediators of the relation between participant sex and mental rotation performance. Spatial anxiety partially mediated the link between the sex of the participants and the MRT performance controlling for trait anxiety. Only navigation and mental rotation anxiety significantly mediated the relation between participant sex and mental rotation performance. We posit spatial anxiety as a barrier to efficient and accurate spatial thinking, and suggest that reducing spatial anxiety has the potential to improve spatial skills and reduce sex differences in mental rotation test performance. To ascertain this, an experimental design can determine whether a reduction in spatial anxiety causes changes in mental rotation test scores.

Gender differences in the development of semantic and spatial processing of numbers

This study recruited kindergarteners and first graders to investigate gender and grade differences in semantic and spatial processing of number magnitude. Results based on the Bayesian statistics showed that (1) there was extreme evidence in favour of grade differences in both semantic processing and spatial processing; (2) there were no gender differences in semantic processing; and (3) boys developed earlier than girls in spatial processing of numbers, especially for the more difficult task. These results are discussed in terms of gender differences in cognitive mechanisms underlying semantic and spatial processing of number magnitude.

Preschoolers and multi-digit numbers: A path to mathematics through the symbols themselves

Numerous studies from developmental psychology have suggested that human symbolic representation of numbers is built upon the evolutionally old capacity for representing quantities that is shared with other species. Substantial research from mathematics education also supports the idea that mathematical concepts are best learned through their corresponding physical representations. We argue for an independent pathway to learning "big" multi-digit symbolic numbers that focuses on the symbol system itself. Across five experiments using both between- and within-subject designs, we asked preschoolers to identify written multi-digit numbers with their spoken names in a two-alternative-choice-test or to indicate the larger quantity between two written numbers. Results showed that preschoolers could reliably map spoken number names to written forms and compare the magnitudes of two written multi-digit numbers. Importantly, these abilities were not related to their non-symbolic representation of quantities. These findings have important implications for numerical cognition, symbolic development, teaching, and education.

Sex Differences in Gains Among Hispanic Pre-kindergartners' Mental Rotation Skills

The current study explores change in mental rotation skills throughout the pre-kindergarten year in a Hispanic population to better understand the development of early sex differences in mental rotation. Ninety-six Hispanic children (M = 4 years 8 months) completed a mental rotation task at the beginning and end of pre-kindergarten. Results suggest Hispanic boys and girls differed in gains on mental rotation ability, with boys improving significantly more than girls during pre-kindergarten on a mental rotation task. This study highlights the significance of studying mental rotation abilities in a Hispanic population of pre-kindergarten aged children and suggests the importance of examining sex differences in mental rotation over time, rather than at one time-point, to better understand when sex differences in spatial skills develop. We discuss various factors that potentially affect the growth of spatial skills including the role of early education, spatial experiences, and spatial language input.

Relationships Between Motor Proficiency and Academic Performance in Mathematics and Reading in School-Aged Children and Adolescents: A Systematic Review

Positive associations exist between physical activity, cognition, and academic performance in children and adolescents. Further research is required to examine which factors underpin the relationships between physical activity and academic performance. This systematic review aimed to identify, critically appraise, and synthesize findings of studies examining relationships between motor proficiency and academic performance in mathematics and reading in typically developing school-aged children and adolescents. A systematic search of electronic databases was performed to identify relevant studies. Fifty-five eligible articles were critically appraised and key data was extracted and synthesized. Findings support associations between several components of motor proficiency and academic performance in mathematics and reading. There was evidence that fine motor proficiency was significantly and positively associated with academic performance in mathematics and reading, particularly during the early years of school. Significant positive associations were also evident between academic performance and components of gross motor proficiency, specifically speed and agility, upper-limb coordination, and total gross motor scores. Preliminary evidence from a small number of experimental studies suggests motor skill interventions in primary school settings may have a positive impact on academic performance in mathematics and/or reading. Future research should include more robust study designs to explore more extensively the impact of motor skill interventions on academic performance.

Influence of Different Visual Perceptual Constructs on Academic Achievement Among Learners in the NW-CHILD Study

Visual perception plays an important and integrating role in the development of cognitive abilities and perceptual-motor skills. Visual perception comprises different independent constructs that may function in an integrative manner. This study aimed to determine whether (and the extent to which) various visual-perceptual constructs influence the academic achievement of 12-year-old school children. In a cross-sectional analysis, we extracted only 2016 data from 581 learners (mean age = 12.92 years, SD = 0.42) who were participants in the North-West Child Health, Integrated with Learning and Development longitudinal study (2010-2016). We used the Test of Visual Perceptual Skills, Third Edition, the North-West Provincial Assessment and mid-year school examination reports to determine visual perceptual abilities and academic achievement of this participant group. We calculated correlations between visual perceptual constructs and academic performance using Spearman rank order correlations and separately analyzed the influence of gender and socioeconomic status with independent T tests. Different visual perceptual constructs did have significant influences on specific areas of academic learning and on academic achievement generally ( r = .26 to r = .41). Spatial relationships showed slightly greater correlations with academic achievement ( r = .15 to r = .33) than did other basic visual perceptual constructs, possibly because spatial relationships are not completely developed at age 12. Complex and basic visual perceptual skills had medium significant retrospective correlations with grade point average ( r = .40 and r = .41) and first additional language ( r = .30 and r = .33). We concluded that basic and complex visual perceptual constructs remain important for academic achievement in this age-group, while gender and socioeconomic status influence both visual perceptual abilities and academic achievement.

Let the Data Speak: Gender Differences in Math Curriculum–Based Measurement

Numerous studies have identified differences between males and females in academic performance across the areas of reading, writing, and mathematics. The current study examined whether or not gender differences exist when math curriculum–based measures (M-CBMs) are used to assess basic math computation skills in a sample of third- through eighth-grade students. Participants included 1,626 general and special education students from five schools in a rural southeastern school district. Two-way repeated measures ANOVAs were used to determine significance across genders at each grade level. Statistically significant differences in favor of females were found in Grades 5, 7, and 8. The discussion highlights applied and theoretical implications of these findings.

Who Is At Risk for Persistent Mathematics Difficulties in the United States?

We analyzed two nationally representative, longitudinal data sets of U.S. children to identify risk factors for persistent mathematics difficulties (PMD). Results indicated that children from low socioeconomic households are at elevated risk of PMD at 48 and 60 months of age, as are children with cognitive delays, identified developmental delays or disabilities, and vocabulary difficulties. In contrast, children attending preschool either in Head Start or non-Head Start classrooms are at initially lower risk of PMD. Kindergarten-aged children experiencing either low socioeconomic status or mathematics difficulties are at greatest risk for PMD across third, fifth, and eighth grades. Also at risk for PMD between third and eighth grades are children displaying reading difficulties or inattention and other learning-related behaviors problems, children with identified disabilities, and those who are retained. Educationally relevant and potentially malleable factors for decreasing young children's risk for PMD may include increasing children's access to preschool, decreasing their risk of experiencing vocabulary or reading difficulties, and avoiding use of grade retention.

Finger gnosis predicts a unique but small part of variance in initial arithmetic performance

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes.

Developing Numerical Ability in Children with Mathematical Difficulties Using Origami

Certain aspects of numerical processing show a connection with spatial abilities. Spatial abilities may be enhanced through the practice of origami. It is possible that the development of spatial abilities will support the development of numerical processing. The goal was to investigate whether spatial and numerical skills can be developed using origami and the folding of three-dimensional shapes. During the course of the 10-wk. training program, consisting of weekly 60-min. sessions, the performance of children with mathematical difficulties showed considerable improvement in spatial and numerical tasks as compared to the control group of children with mathematical difficulties.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1^st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement-three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1^st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ESs = .05-.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ESs = .03-.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.

Knowing right from wrong in mental arithmetic judgments: calibration of confidence predicts the development of accuracy

Does knowing when mental arithmetic judgments are right--and when they are wrong--lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the "calibration" of mental arithmetic judgments-that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25 + 50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic "fluency" is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.

Feasibility and validity of the structured attention module among economically disadvantaged preschool-age children

Rooted in the theory of attention put forth by Mirsky, Anthony, Duncan, Ahearn, and Kellam (1991), the Structured Attention Module (SAM) is a developmentally sensitive, computer-based performance task designed specifically to assess sustained selective attention among 3- to 6-year-old children. The current study addressed the feasibility and validity of the SAM among 64 economically disadvantaged preschool-age children (mean age = 58 months; 55% female); a population known to be at risk for attention problems and adverse math performance outcomes. Feasibility was demonstrated by high completion rates and strong associations between SAM performance and age. Principal Factor Analysis with rotation produced robust support for a three-factor model (Accuracy, Speed, and Endurance) of SAM performance, which largely corresponded with existing theorized models of selective and sustained attention. Construct validity was evidenced by positive correlations between SAM Composite scores and all three SAM factors and IQ, and between SAM Accuracy and sequential memory. Value-added predictive validity was not confirmed through main effects of SAM on math performance above and beyond age and IQ; however, significant interactions by child sex were observed: Accuracy and Endurance both interacted with child sex to predict math performance. In both cases, the SAM factors predicted math performance more strongly for girls than for boys. There were no overall sex differences in SAM performance. In sum, the current findings suggest that interindividual variation in sustained selective attention, and potentially other aspects of attention and executive function, among young, high-risk children can be captured validly with developmentally sensitive measures.

Charting the role of the number line in mathematical development

Individuals who do well in mathematics and science also often have good spatial skills. However, the predictive direction of links between spatial abilities and mathematical learning has not been firmly established, especially for young children. In the present research, we addressed this issue using a sample from a longitudinal data set that spanned 4 years and which includes measures of mathematical performance and various cognitive skills, including spatial ability. Children were tested once in each of 4 years (Time 1, 2, 3, and 4). At Time 3 and 4, 101 children (in Grades 2, 3, or 4 at Time 3) completed mathematical measures including (a) a number line task (0–1000), (b) arithmetic, and (c) number system knowledge. Measures of spatial ability were collected at Time 1, 2, or 3. As expected, spatial ability was correlated with all of the mathematical measures at Time 3 and 4, and predicted growth in number line performance from Time 3 to Time 4. However, spatial ability did not predict growth in either arithmetic or in number system knowledge. Path analyses were used to test whether number line performance at Time 3 was predictive of arithmetic and number system knowledge at Time 4 or whether the reverse patterns were dominant. Contrary to the prediction that the number line is an important causal construct that facilitates learning arithmetic, no evidence was found that number line performance predicted growth in calculation more than calculation predicted number line growth. However, number system knowledge at Time 3 was predictive of number line performance at Time 4, independently of spatial ability. These results provide useful information about which aspects of growth in mathematical performance are (and are not) related to spatial ability and clarify the relations between number line performance and measures of arithmetic and number system knowledge.

Developmental gains in visuospatial memory predict gains in mathematics achievement

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.