Domain-specific and domain-general precursors of mathematical achievement: A longitudinal study from kindergarten to first grade

Predicting individual differences in preschoolers' numeracy and geometry knowledge: The role of understanding abstract relations between objects and quantities

Preschoolers' mathematics knowledge develops early and varies substantially. The current study focused on two ontogenetically early emerging cognitive skills that may be important predictors of later math skills (i.e., geometry and numeracy): children's understanding of abstract relations between objects and quantities as evidenced by their patterning skills and the approximate number system (ANS). Children's patterning skills, the ANS, numeracy, geometry, nonverbal intelligence (IQ), and executive functioning (EF) skills were assessed at age 4 years, and their numeracy and geometry knowledge was assessed again a year later at age 5 (N = 113). Above and beyond children's initial knowledge in numeracy and geometry, as well as IQ and EF, patterning skills and the ANS at age 4 uniquely predicted children's geometry knowledge at age 5, but only age 4 patterning uniquely predicted age 5 numeracy. Thus, although patterning and the ANS are related, they differentially explain variation in later geometry and numeracy knowledge. Results are discussed in terms of implications for early mathematics theory and research.

Inhibitory control and academic achievement - a study of the relationship between Stroop Effect and university students' academic performance

While previous research has identified executive functions as predictors of academic performance in school children, similar studies conducted among adults show mixed results. One of the reasons given for executive functions having a limited effect on academic achievements in adulthood is that they are usually fully developed by that time. Since these executive functions are at their peak at that age, the individual differences in these as well as their influence on academic performance in adults are harder to trace. The paper describes a study conducted among 107 university students the goal of which was to find out whether there is any relationship between the adult students' inhibitory control values measured with the Stroop Test and their academic achievements. Although the results indicate a weak correlation between the Stroop Effect and the students' academic performance of low statistical significance, which seems to confirm the outcomes of the previous studies focusing on adults, the study reveals an unexpected statistically significant correlation between the students' grade averages and the number of their incorrect color identifications. This phenomenon appears to be worth pursuing in future research since it suggests the existence of another, relatively quickly measurable, variable possibly reflecting other predictors of academic performance in adults such as a degree of their manifested conscientiousness, their ability to concentrate on an assigned, relatively short, one-off task and their attitude to fulfilling this task. The Stroop Test, despite not being originally designed for this purpose, might thus be used as a simple tool suitable for providing information about these variables via the subject's number of color identification errors. Such information can subsequently inform the activities that educators may include in their curricula to foster conscientiousness and concentration in the students lacking these.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

Mathematics abilities associated with adaptive functioning in preschool children born preterm

It is well known that infants born very preterm (VPT) often demonstrate deficits in mathematical abilities in early childhood which are associated with poorer academic outcomes. Mathematic skills are also critical for other areas of functioning. However, it is not known whether mathematics skills are associated with adaptive functioning in children born preterm. Infants born at ≤31 weeks gestation and full term were recruited at birth and followed over time. At the 36-month corrected age assessment, children were administered the Early Number Concepts subtest of the Differential Abilities Scale, Second Edition, and caregivers completed the Adaptive Behavior Assessment System, Third Edition. After controlling for age, sex, cognitive abilities, and caregiver education, performance on the mathematics measure was uniquely and positively associated with adaptive behavior for preschool children in the VPT group only. Exploratory analyses revealed this association to be specifically related to the Practical and Social composites. Knowledge of concepts of number and quantity were associated with better adaptive functioning, particularly for behaviors related to functioning at home and in the community and play/social functioning, for children born VPT. Although replication is warranted, it would appear that mathematical skills may be an important early intervention target for children born VPT.

Influences of cognitive control on number processing: New evidence from switching between two numerical tasks

A growing body of research suggests that basic numerical abilities such as number magnitude and number parity processing are influenced by cognitive control. So far, however, evidence for number processing being influenced by cognitive control came primarily from observed adaptations to stimulus set characteristics (e.g., ratio or order of specific stimulus types) and switches between a numerical and non-numerical task. Complementing this previous research, the present study employed a task switching paradigm exclusively involving numerical tasks (i.e., magnitude comparisons and parity judgements) to examine how cognitive control processes influence number processing. Participants were presented with a single-digit number and had to either judge its parity or compare its magnitude with a standard of 5, depending on a preceding cue. Based on previous results, we expected the numerical distance effect and the spatial-numerical association of response codes (SNARC) effect to be modulated in switch trials requiring the exertion of cognitive control. Partly in line with our expectations, the numerical distance effect was reduced in switch trials. However, no modulation of the SNARC effect was observed. The results pattern suggests that number processing is influenced by cognitive control, depending on task requirements and the type of numerical information (i.e., numerical magnitude vs spatial association of numbers) that is processed. To reconcile the present and previous results, we propose an information prioritisation account, suggesting that cognitive control primarily influences the processing of the information type that requires the most explicit processing.

Relative Contributions of g and Basic Domain-Specific Mathematics Skills to Complex Mathematics Competencies

Meta-analytic structural equation modeling was used to estimate the relative contributions of general cognitive ability or g (defined by executive functions, short-term memory, and intelligence) and basic domain-specific mathematical abilities to performance in more complex mathematics domains. The domain-specific abilities included mathematics fluency (e.g., speed of retrieving basic facts), computational skills (i.e., accuracy at solving multi-step arithmetic, algebra, or geometry problems), and word problems (i.e., mathematics problems presented in narrative form). The core analysis included 448 independent samples and 431,344 participants and revealed that g predicted performance in all three mathematics domains. Mathematics fluency contributed to the prediction of computational skills, and both mathematics fluency and computational skills predicted word problem performance, controlling g. The relative contribution of g was consistently larger than basic domain-specific abilities, although the latter may be underestimated. The patterns were similar across younger and older individuals, individuals with and without a disability (e.g., learning disability), concurrent and longitudinal assessments, and family socioeconomic status, and have implications for fostering mathematical development.

The Role of Working Memory in Early Literacy and Numeracy Skills in Kindergarten and First Grade

The working memory system supports learning processes such as acquiring new information and the development of new skills. Working memory has been found to be related to both early literacy and early numeracy in kindergarten and to linguistic and mathematical academic skills at older ages, but the contribution of each of the memory components at these ages is not yet clear. The purpose of this study is to examine the unique connections among the various systems of WM, early literacy, and early numeracy using various assessment tests of simple WM and complex WM, as well as a variety of tasks in math and language skills administered to the same 250 children in kindergarten and 150 children in first grade. Consistent with the predictions, significant relations among all components of memory and mathematics and language knowledge at both ages were found, although these connections were differential for the different types of tasks and memory systems. The connection of complex WM was stronger in its contribution and more significant in first grade in both mathematics and language domains. Complex WM resources were more important in early literacy at kindergarten age, while simple WM seems to be important in early numeracy. The theoretical and educational implications of these results are discussed accordingly.

Visuo-Spatial Working Memory and Mathematical Skills in Children: A Network Analysis Study

Visuo-spatial working memory is one of the main domain-general cognitive mechanisms underlying mathematical abilities and their development in children. However, if visuo-spatial working memory involves different processes and components, then the term 'mathematics' refers to a broad concept that includes multiple domains and skills. The aim of this present study was to investigate the relationship between different visuo-spatial working memory components and several mathematical abilities in a sample of third- to fifth-grade Italian children. To assess the relationships between different visuo-spatial working memory components and different mathematical abilities, we relied on Network Analysis (NA). Results indicate that some but not all visuo-spatial working memory components are associated with some mathematical abilities.

Math self-efficacy or anxiety? The role of emotional and motivational contribution in math performance

Various studies have highlighted the important influence of math ability in a numerate society. In this study, we investigated the influence of emotional (math anxiety and math enjoyment) and cognitive-motivational (math self-efficacy) factors on math performance. Participants were 145 fifth-grade students (84 boys and 61 girls). The results showed that math performance was negatively correlated with math anxiety and positively correlated with math enjoyment and math self-efficacy. Moreover, math anxiety was negatively associated with enjoyment in math and math self-efficacy, whereas math enjoyment was positively correlated with math self-efficacy. Hierarchical regression analysis showed a significant influence of math anxiety and math self-efficacy on math performance in fifth-grade students. Results are discussed in terms of a new perspective in emotional and motivational factors to train in school contexts.

A sequential model of the contribution of preschool fluid and crystallized cognitive abilities to later school achievement

The present study documented in two distinct population-based samples the contribution of preschool fluid and crystallized cognitive abilities to school achievement in primary school and examined the mediating role of crystallized abilities in this sequence of predictive associations. In both samples, participants were assessed on the same cognitive abilities at 63 months (sample 1, n = 1072), and at 41 and 73 months (sample 2, n = 1583), and then with respect to their school achievement from grade 1 (7 years) to grade 6 (12 years). Preschool crystallized abilities were found to play a key role in predicting school achievement. They contributed substantially to school achievement in the early school years, but more modestly in the later years, due to the strong auto-regression of school achievement. They also mediated the association between fluid abilities and later school achievement in the early grades of school, with the former having modest direct contribution to the latter in the later grades. These findings are discussed regarding their implication for preventive interventions.

Early number word learning: Associations with domain-general and domain-specific quantitative abilities

Cardinal number knowledge-understanding “two” refers to sets of two entities-is a critical piece of knowledge that predicts later mathematics achievement. Recent studies have shown that domain-general and domain-specific skills can influence children’s cardinal number learning. However, there has not yet been research investigating the influence of domain-specific quantifier knowledge on children’s cardinal number learning. The present study aimed to investigate the influence of domain-general and domain-specific skills on Mandarin Chinese-speaking children’s cardinal number learning after controlling for a number of family background factors. Particular interest was paid to the question whether domain-specific quantifier knowledge was associated with cardinal number development. Specifically, we investigated 2–5-year-old Mandarin Chinese-speaking children’s understanding of cardinal number words as well as their general language, intelligence, approximate number system (ANS) acuity, and knowledge of quantifiers. Children’s age, gender, parental education, and family income were also assessed and used as covariates. We found that domain-general abilities, including general language and intelligence, did not account for significant additional variance of cardinal number knowledge after controlling for the aforementioned covariates. We also found that domain-specific quantifier knowledge did not account for significant additional variance of cardinal number knowledge, whereas domain-specific ANS acuity accounted for significant additional variance of cardinal number knowledge, after controlling for the aforementioned covariates. In sum, the results suggest that domain-specific numerical skills seem to be more important for children’s development of cardinal number words than the more proximal domain-general abilities such as language abilities and intelligence. The results also highlight the significance of ANS acuity on children’s cardinal number word development.

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.

Contributions of the psychology of mathematical cognition in early childhood education using apps

Educational interventions are necessary to develop mathematical competence at early ages and prevent widespread mathematics learning failure in the education system as indicated by the results of European reports. Numerous studies agree that domain-specific predictors related to mathematics are symbolic and non-symbolic magnitude comparison, as well as, number line estimation. The goal of this study was to design 4 digital learning app games to train specific cognitive bases of mathematical learning in order to create resources and promote the use of these technologies in the educational community and to promote effective scientific transfer and increase the research visibility. This study involved 193 preschoolers aged 57–79 months. A quasi-experimental design was carried out with 3 groups created after scores were obtained in a standardised mathematical competence assessment test, i.e., low-performance group (N = 49), high-performance group (N = 21), and control group (N = 123). The results show that training with the 4 digital learning app games focusing on magnitude, subitizing, number facts, and estimation tasks improved the numerical skills of the experimental groups, compared to the control group. The implications of the study were, on the one hand, provided verified technological tools for teaching early mathematical competence. On the other hand, this study supports other studies on the importance of cognitive precursors in mathematics performance.

The role of working memory updating, inhibition, fluid intelligence, and reading comprehension in explaining differences between consistent and inconsistent arithmetic word-problem-solving performance

Children's performance in arithmetic word problems (AWPs) predicts their academic success and their future employment and earnings in adulthood. Understanding the nature and difficulties of interpreting and solving AWPs is important for theoretical, educational, and social reasons. We investigated the relation between primary school children's performance in different types of AWPs and their basic cognitive abilities (reading comprehension, fluid intelligence, inhibition, and updating processes). The study involved 182 fourth- and fifth-graders. Participants were administered an AWP-solving task and other tasks assessing fluid intelligence, reading comprehension, inhibition, and updating. The AWP-solving task included comparison problems incorporating either the adverb more than or the adverb less than, which demand consistent or inconsistent operations of addition or subtraction. The results showed that consistent problems were easier than inconsistent problems. Efficiency in solving inconsistent problems is related to inhibition and updating. Moreover, our results seem to indicate that the consistency effect is related to updating processes' efficiency. Path analyses showed that reading comprehension was the most important predictor of AWP-solving accuracy. Moreover, both executive functions-updating and inhibition-had a distinct and significant effect on AWP accuracy. Fluid intelligence had both direct and indirect effects, mediated by reading comprehension, on the overall measure of AWP performance. These domain-general factors are important factors in explaining children's performance in solving consistent and inconsistent AWPs.

Numeracy skills in young children as predictors of mathematical competence

As mathematical competence is linked to educational success, professional achievement, and even a country's economic growth, researchers have been interested in early predictors for quite some time. Although there have been numerous studies on domain-specific numerical abilities predicting later mathematical competence in preschool children, research in toddlers is scarce, especially regarding additional influential aspects, such as domain-general cognitive abilities and the children's social background. Using a large-scale dataset, the present study examined predictive effects of numeracy skills in 17-month-olds for later mathematical achievement. We found small, positive effects, even when controlling for child-related variables (i.e., age and sex) and the children's social background (i.e., maternal education and household language). Additionally, we compared results with a domain-general categorization task and found no distinct effect on mathematical competence. The present results are discussed with regard to the specificities of the dataset, as well as implications for future studies on predictors of mathematical competence.

The contributions of working memory domains and processes to early mathematical knowledge between preschool and first grade

Working Memory (WM) plays a crucial role in supporting children's mathematical learning. However, there is no consensus on the relative contributions of different WM domains (i.e., verbal, visuo-spatial, and numerical-verbal) and processes (i.e., low-control and high-control) to mathematical performance, specifically before and after the onset of formal education. This cross-sectional study examined the relations between WM domains and processes and early mathematical knowledge, comparing a group of children in the second year of preschool (N = 66) to a group of first graders (N = 110). Results of multigroup path analysis showed that whereas visuo-spatial low-control WM significantly predicted early mathematical knowledge only among preschoolers, verbal low-control WM was a significant predictor only among first graders. Instead, the contribution of visuo-spatial high-control WM emerged as significant for both age groups, as well as that of numerical-verbal WM, although the latter to a greater extent among preschoolers. These findings provide new insights into the WM domains and processes most involved in early mathematical knowledge at different developmental stages, with potential implications for the implementation of age-appropriate training interventions targeting specific WM skills before and after the onset of formal education.

Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature

Mathematical performance implies a series of numerical and mathematical skills (both innate and derived from formal training) as well as certain general cognitive abilities that, if inadequate, can have a cascading effect on mathematics learning. These latter skills were the focus of the present systematic review. Method: The reviewing process was conducted according to the PRISMA statement. We included 46 studies comparing school-aged children’s performance with and without math difficulties in the following cognitive domains: processing speed, phonological awareness, short- and long-term memory, executive functions, and attention. Results: The results showed that some general cognitive domains were compromised in children with mathematical difficulties (i.e., executive functions, attention, and processing speed). Conclusions: These cognitive functions should be evaluated during the diagnostic process in order to better understand the child’s profile and propose individually tailored interventions. However, further studies should investigate the role of skills that have been poorly investigated to date (e.g., long-term memory and phonological awareness).

Cognitive control in number processing: new evidence from number compatibility effects in task-switching

A growing body of research suggests that basic numerical abilities such as number magnitude processing are influenced by cognitive control processes. So far, evidence for number processing being affected by cognitive control processes stems primarily from observed adaptations of numerical effects to stimulus set characteristics (e.g. order or ratio of specific stimulus types). Complementing previous research on adaptation to stimulus set characteristics as an index of influences of cognitive control, the present study employed a task-switching paradigm to examine how cognitive control processes influence number processing. Participants were presented with a two-digit number and had to either judge its parity or compare its magnitude to a standard depending on a preceding cue. We expected numerical congruency effects (i.e. the unit-decade compatibility effect for magnitude comparisons and the parity congruity effect for parity judgements) to be larger in switch trials, as persisting activation of the task set of the preceding trial should increase interference. In contrast to our expectations, both numerical congruity effects were reduced following task switches as compared to repetitions. This interaction of task-switching with numerical congruency effects suggests an influence of cognitive control on basic number processing in form of persisting inhibition of previously abandoned task sets, so that these exert less influence on current number processing demands.

Distance learning during COVID-19 lockdown: Impact on adolescents with specific learning disorders and their parents

BACKGROUND

The transition of teaching from in-person to Distance Learning (DL) due to the COVID-19 pandemic led to negative effects on students' psychological wellbeing and academic achievement. The worst consequences have been experienced by students with so-called special educational needs, as well as by their parents. However, very little emphasis has been placed on the effects of DL in students with Specific Learning Disorders (SLD). The present work aimed to evaluate the effects of DL during the COVID-19 lockdown in Italian students with SLD and in their parents.

METHODS

An online survey was administered to 92 students with SLD and their parents after the COVID-19 lockdown. The survey consisted of four sections: participants' demographic information; perceived stress related to general aspects (i.e., social and family determinants) as well as specific aspects related to DL; attitudes and feelings toward DL; and academic grades before and after DL.

RESULTS

Students with SLD perceived stress mainly from social isolation/distancing and DL (p always ≤ 0.0001), especially from online classes and oral exams (p always ≤ 0.0001). Students who did not benefit from appropriate accommodations (i.e., individualized teaching and learning methods) during DL perceived 3 times more DL-related stress than those who used them as in-person learning (OR = 3.00, CI 95%: 1.24-7.28, p = 0.015). Girls perceived more stress from online lessons (OR = 0.40, CI 95%: 0.16-0.96, p = 0.04) and use of devices (OR = 0.33, CI 95%: 0.14-0.80, p = 0.015) than boys. Negative feelings (less motivation, reduced ability to understand lessons, interact, and stay focused) and positive feelings (less anxiety and more self-confidence with its own rate of learning) toward DL emerged. Higher academic grades also was observed after DL (p ≤ 0.0001). Lastly, strong and positive correlations emerged between students' and parents' perceived stress during DL (p always < 0.001).

IMPLICATIONS

The present study prompts special considerations for students with special educational needs not only when providing conventional instruction, but especially when it is necessary to suddenly modify teaching approaches.

Examining the Differential Role of General and Specific Processing Speed in Predicting Mathematical Achievement in Junior High School

Processing speed is divided into general (including perceptual speed and decision speed) and specific processing speed (including reading fluency and arithmetic fluency). Despite several study findings reporting the association between processing speed and children's mathematical achievement, it is still unclear whether general or specific processing speed differentially predicts mathematical achievement. The current study aimed to examine the role of general and specific processing speed in predicting mathematical achievements of junior high school students. Cognitive testing was performed in 212 junior school students at the beginning of the 7th grade year, along with assessment of general and specific processing speed. Relevant academic achievement scores were also recorded at the end of the 7th and 9th grade years. Hierarchical regression analyses showed that specific processing speed made a significant unique contribution in mathematical achievement by the end of the 7th grade and could significantly predict mathematical achievements in the high school entrance examinations by end of the 9th grade after controlling for age, gender, and general cognitive abilities. However, general processing speed could not predict mathematical achievements. Moreover, specific processing speed could significantly predict all academic achievements for both the 7th and 9th grade. These results demonstrated that specific processing speed, rather than general processing speed, was able to predict mathematical achievement and made a generalised contribution to all academic achievements in junior school. These findings suggest that specific processing speed could be a reflection of academic fluency and is therefore critical for long-term academic development.

Numerical cognition in children with cerebral palsy

Children with Cerebral Palsy (CP) often perform poorly in mathematics. It is not yet clear to what extent mathematics difficulties in this clinical condition are similar to those observed in developmental dyscalculia. To better elucidate this issue, we conducted an exploratory cross-sectional study with a sample of children and adolescents with congenital brain injuries and educational history of problems in Mathematics. Fifty students aged 7-15 years, of both genders (28 males) participated in the study, 31 with typical development (TD) and 19 of whom diagnosed with spastic CP. Nine had hemiplegia and ten diplegia. Assessment procedures included a neuropsychological battery covering numerical cognition (ZAREKI-R) and working memory (AWMA) skills, and a computerized task for comparing non-symbolic magnitudes as a measure of number sense. Despite average intelligence coefficient, participants with CP underperformed the TD in five of the 12 ZAREKI-R subtests, as well as in the number sense and working memory tasks. scores were lower among hemiplegic children compared to diplegic, numerical cognition was impaired in all CP group, unveiling a dyscalculia secondary to neurodevelopmental impairments. Therefore, we can consider that mathematical learning difficulties in CP as being heterogeneous and associated with the immaturity of neuropsychological functions, with consequences for the development of numerical cognition.

Boosting Numerical Cognition in Children and Adolescents with Mathematical Learning Disabilities by a Brain-Based Intervention: A Study Protocol for a Randomized, Sham-Controlled Clinical Trial

Numbers are everywhere, and supporting difficulties in numerical cognition (e.g., mathematical learning disability (MLD)) in a timely, effective manner is critical for their daily use. To date, only low-efficacy cognitive-based interventions are available. The extensive data on the neurobiology of MLD have increased interest in brain-directed approaches. The overarching goal of this study protocol is to provide the scientific foundation for devising brain-based and evidence-based treatments in children and adolescents with MLD. In this double-blind, between-subject, sham-controlled, randomized clinical trial, transcranial random noise stimulation (tRNS) plus cognitive training will be delivered to participants. Arithmetic, neuropsychological, psychological, and electrophysiological measures will be collected at baseline (T0), at the end of the interventions (T1), one week (T2) and three months later (T3). We expect that tRNS plus cognitive training will significantly improve arithmetic measures at T1 and at each follow-up (T2, T3) compared with placebo and that such improvements will correlate robustly and positively with changes in the neuropsychological, psychological, and electrophysiological measures. We firmly believe that this clinical trial will produce reliable and positive results to accelerate the validation of brain-based treatments for MLD that have the potential to impact quality of life.

The association of basic numerical abilities and math achievement: The mediating role of visuospatial and arithmetical abilities

Basic numerical abilities such as number line estimation have been observed repeatedly to be associated with mathematical achievement. Recently, it was argued that the association between basic numerical abilities and mathematical achievement is fully mediated by visuospatial abilities. However, arithmetical abilities have not yet been considered as influencing this association, even though solution strategies in number line estimation as well as mathematical achievement often involve arithmetical procedures. Therefore, we investigated the mediating role of arithmetical and visuospatial abilities on the association between number line estimation and mathematical achievement in a sample of n = 599 German elementary school students. The results indicated that arithmetical abilities as well as visuospatial abilities mediated the association between number line estimation and mathematical achievement. However, neither visuospatial nor arithmetical abilities fully mediated the association between number line estimation and mathematical achievement when considered in isolation. This substantiates the relevance of the intertwined development of visuospatial and arithmetical abilities as well as basic numerical abilities such as number line estimation (i.e., the combination of domain-specific numerical and domain-general abilities) driving mathematical achievement.

The relation between working memory, number sense, and mathematics throughout primary education in children with and without mathematical difficulties

Number sense and working memory contribute to mathematical development throughout primary school. However, it is still unclear how the contributions of each of these predictors may change across development and whether the cognitive contribution is the same for children with and without mathematical difficulties. The aim of the two studies in this paper was to shed light on these topics. In a cross-sectional design, a typically developing group of children (study 1; N = 459, Grades 1-4) and a group with mathematical difficulties (study 2; N = 61, Grades 4-6) completed a battery of number sense and working memory tests, as well as a measure of arithmetic competence. Results of study 1 indicated that number sense was important in first grade, while working memory gained importance in second grade, before predictive value of both predictors waned. Number sense and working memory supported mathematics development independently from one another from Grade 1. Analysis of task demands showed that typically developing children rely on comprehension and visualization of quantity-to-number associations in early development. Later in development, pupils rely on comparing larger numerals and working memory until automatization. Children with mathematical difficulties were less able to employ number sense during mathematical operations, and thus might remain dependent on their working memory resources during arithmetic tasks. This suggests that children with mathematical difficulties need aid to employ working memory for mathematics from an early age to be able to automatize mathematical abilities later in development.

How do phonological awareness, rapid automatized naming, and vocabulary contribute to early numeracy and print knowledge of Filipino children?

The current study investigated the contributions of phonological awareness, rapid automatized naming (RAN), and vocabulary to early numeracy and print knowledge developmental trajectories. A total of 128 young Filipino children were tracked three times at mean ages of 4.5, 5.0, and 5.5 years. The initial level (the intercept) and the growth rate (the slope) of early numeracy and print knowledge were estimated. Results showed that phonological awareness, vocabulary, and age significantly predicted the initial level of early numeracy. RAN and vocabulary explained significant variance in the growth rate of early numeracy. Phonological awareness, RAN, and vocabulary accounted for unique variance in the initial level of print knowledge. Results highlight the differential roles of phonological awareness, RAN, and vocabulary knowledge in the development of early numeracy and print knowledge among Filipino children.

Fostering early numerical competencies by playing conventional board games

Recent evidence indicates that playing numerical board games is beneficial for the numerical development of preschoolers. However, board games used in these studies were often specifically developed for training numerical skills. Therefore, we examined whether similar beneficial effects could be observed for playing conventional board games such as Parcheesi. In an intervention study with seven 30-min training sessions over a period of 4 weeks, we observed that 4- to 6-year-old children (M_age = 4 years 11 months) who played conventional board games with traditional number dice (with dot faces numbered from one to six) benefitted more from the board games than children who played board games with color or non-numerical symbol dice. Pretest-posttest comparisons indicated differential effects on counting skills and the ability to recognize and use structures. Beyond these immediate training effects observed in posttest, the differential beneficial effects of playing board games using traditional dot dice on recognizing and using structures was still present in a follow-up test 1 year after the intervention. Thus, playing conventional board games using traditional number dice seems to be an effective low-threshold intervention to foster early numerical competencies.

The relationship of working memory and inhibition with different number knowledge skills in preschool children

The purpose of this study was to analyze the contribution of specific executive function (EF) components to different number knowledge skills. A sample of 143 children attending the last year of preschool educational services (M_age = 65.01 months, SD = 3.57) were tested on five number knowledge tasks from the Numerical Intelligence Battery and four EF tasks assessing working memory (WM) and inhibition. First, we examined the interrelationship between different number skills; the results suggested that the relationship between basic informal skills (set comparison and number sequence) and formal skills (seriation of Arabic numerals and number comparison) was mediated by the ability to link sets to numerals. Next, we explored the contribution of WM and inhibition to different number knowledge skills. The structural equation model showed that WM and inhibition were differentially related to specific number knowledge skills. Specifically, WM predicted most components of number knowledge, including the two basic informal skills and the number comparison, whereas inhibition contributed to the seriation of Arabic numerals. The ability to link sets to numerals was predicted only by number sequence, not by EF components.

The role of numeracy skills on the Wisconsin card sorting test (WCST) performances of 5- to 8-Year-old turkish children

The Wisconsin Card Sorting Test (WCST) is one of the most widely used complex EF task for various populations. However, it seems questionable to employ the task for preschool-aged children due to their lack of numerical efficiency while sorting cards according to the number dimension. The present study aimed to examine the association of numeracy skills with different EF-related abilities as measured by the WCST. For the assessment of numeracy skills, we used the Early Numeracy Test (ENT). One hundred and fourteen Turkish children between the ages of 5 and 8 were administered the WCST and ENT in a counterbalanced order. Results revealed a significant correlation only between the three ENT scores and the concept formation factor of the WCST, indicating a significant relationship between the WCST performance and numeracy skills in terms of concept formation. This finding highlights the specific relation between numeracy skills and subcomponents of the WCST and points to potential interfering variables that should be taken into account while evaluating the scores of the sorting tasks for children between the ages of 5 and 8.

Cognitive control in number processing: new evidence from task switching

Recently, it was demonstrated that even basic numerical cognition such as the processing of number magnitude is under cognitive control. However, evidence so far primarily came from adaptation effects to stimulus characteristics (e.g., relative frequency of specific stimulus categories). Expanding this approach, we evaluated a possible influence of more active exertion of cognitive control on basic number processing in task switching. Participants had to perform a magnitude comparison task while we manipulated the order of compatible and incompatible input–output modalities (i.e., auditory/vocal input–visual/manual output vs. auditory/visual input–manual/vocal output, respectively) on the trial level, differentiating repeat vs. switch trials. Results indicated that the numerical distance effect but not the problem size effect was increased after a switch in input–output modality compatibility. In sum, these findings substantiate that basic number processing is under cognitive control by providing first evidence that it is influenced by the active exertion of cognitive control as required in task switching.

Cognitive flexibility in critical CHD: a target for intervention

Most children born with even the most critical forms of CHD are now surviving well into adulthood. However, with increased survival has come increased recognition of the diverse neurobehavioural and psychosocial challenges these children experience. Among these challenges are deficits in executive function skills, including inhibitory control, working memory, and cognitive flexibility. Over the past several years, whereas inhibitory control and working memory deficits have garnered particular attention among clinicians and interventionists, relatively less attention has been paid to cognitive flexibility. This is unfortunate given both the high prevalence of cognitive flexibility deficits observed in children and adolescents with critical CHD, and also the far-reaching relevance of cognitive flexibility in helping individuals achieve optimal quality of life across the lifespan. This paper reviews the construct of cognitive flexibility, including its definition, development, measurement, and neuroanatomical basis, provides a summary of how cognitive flexibility is affected by CHD, and offers evidence-based recommendations to systematically support the development of cognitive flexibility within the context of CHD.

Number Magnitude Processing and Verbal Working Memory in Children with Mild Intellectual Disabilities

This study examined if children (M_age = 14.60) with Mild Intellectual Disabilities (MID) display weaknesses in number processing and verbal working memory. An age-matched and mental age-matched (MA, M_age = 6.17) design extended by a group of 9-10-year-olds, and a group of 11-12-year-olds were used. The MID children's working memory was equal to the MA group but poorer than the other groups. On number tasks, the MID group was faster than the MA group but slower than the other groups. All groups obtained equal Weber fraction scores and distance effects on the number comparison tasks. The MID group performed subitizing and counting faster than the MA group, but slower than the 11-12-year-olds. The results demonstrate that number processing and working memory in children with MID is characterized by a developmental delay, not a deficit. Their main problem is to access the quantitative meaning of Arabic numerals. The development of different types of cognitive abilities is differently affected by educational experience and intellectual ability. The innate number system appears to be unaffected by intellectual capacity or educational experience, while the innate working memory ability is affected by intellectual capacity but not by educational experience. Culturally acquired symbolic number abilities are strongly affected by educational experience.

Development of early domain-specific and domain-general cognitive precursors of high and low math achievers in grade 6

This study investigated from a longitudinal retrospective perspective what characterizes and predicts 6th graders (M_age = 12.95, SD = 0.27) with low (LMA) or high (HMA) math achievement concerning the development of early domain-specific and domain-general cognitive abilities. They were examined and compared to average achievers (n = 88) at four-time points from kindergarten (M_age = 6.58, SD = 0.36) to third grade (M_age = 9.53, SD = 0.33). The LMA (n = 27) or HMA (n = 41) children exhibited persistent multi-weakness and multi-strength profiles, respectively, present already prior to formal schooling. The cognitive profiles of the two groups, and their development, were mostly qualitatively similar, but there were also important qualitative differences. Logistic regression analyzes showed that superior verbal arithmetic, logical reasoning, and executive functions are vital for developing superior mathematical skills while inferior verbal arithmetic, logical reasoning, and spatial processing ability constitute unique potential risk factors for low mathematical skills.

Talent Development in Achievement Domains: A Psychological Framework for Within- and Cross-Domain Research

Achievement in different domains, such as academics, music, or visual arts, plays a central role in all modern societies. Different psychological models aim to describe and explain achievement and its development in different domains. However, there remains a need for a framework that guides empirical research within and across different domains. With the talent-development-in-achievement-domains (TAD) framework, we provide a general talent-development framework applicable to a wide range of achievement domains. The overarching aim of this framework is to support empirical research by focusing on measurable psychological constructs and their meaning at different levels of talent development. Furthermore, the TAD framework can be used for constructing domain-specific talent-development models. With examples for the application of the TAD framework to the domains of mathematics, music, and visual arts, the review provided supports the suitability of the TAD framework for domain-specific model construction and indicates numerous research gaps and open questions that should be addressed in future research.

Math anxiety and math achievement: The effects of emotional and math strategy training

Math anxiety (MA) is a specific feeling of tension generated by the manipulation of numerical stimuli in daily life and academic situations (Richardson & Suinn, 1972). This condition has significant repercussions on the individual's life at personal, social, and economic level. Literature on the topic of MA alleviation, however, is still scarce. This study aims at contributing to this field by addressing MA prevention in school-age children. We have developed two different training methods administered to two groups of fourth graders: (a) MA training focusing on identifying and copying with MA-related feelings (N = 76); and (b) Math strategy training focusing on supplementary exercises to enhance calculation strategies (N = 76). We also carried out a Control training involving a range of activities, such as reading comic strips, describing characters in the story, and combining text and images to obtain an original narrative text (N = 72). We evaluated the differential effects of these training methods on MA, general anxiety, and math achievement before and after the training. Results indicate that MA training contributes to a decrease in MA level, although it does not appear to affect math achievement; Math strategy training, on the other hand, results in far transfer on a reduction of MA level as well as near transfer on the improvement of math achievement. Data are discussed in terms of specific mechanisms underlying each type of training method, and with specific focus on the evaluation of educational and developmental opportunities linked to MA prevention and improvement of math abilities in school-age children.

Exploring EFs and Math Abilities in Highly Deprived Contexts

Executive functions (EFs)’ development is critically affected by childhood adversity exposure. Although recent studies underlined the deleterious effects of early life stresses on working memory (WM) and inhibitory control, they were scarcely investigated in war context especially in relation with learning abilities. In order to fill this gap, we designed a research with the aim to evaluate EFs together with early math skills. In particular, we conducted a study involving 150 children divided into three groups: 48 Yazidis (M_age = 71 months, SD = 6.59), 47 Syrian refugees (M_age = 68.77 months, SD = 7, age), and 55 Italians (M_age = 68.65 months, SD = 2.88) attending the third year of kindergarten in Italy or inserted in Psyco-Social-Support activities in Iraq. The children were evaluated with a variety of tasks assessing WM, inhibitory control, counting, digit-quantity mapping, and digit naming skills. The results indicated substantial differences both in EFs and early numerical abilities between the deprived groups and the Italian children. Data are discussed in terms of implications for children both exposed to mainstream school environments and living in socio-economically disadvantaged and deprived contexts.

Temporo-frontal activation during phonological processing predicts gains in arithmetic facts in young children

Behavioral studies have shown discrepant results regarding the role of phonology in predicting math gains. The objective of this study was to use fMRI to study the role of activation during a rhyming judgment task in predicting behavioral gains on math fluency, multiplication, and subtraction skill. We focused within the left middle/superior temporal gyrus and left inferior frontal gyrus, brain areas associated with the storage of phonological representations and with their access, respectively. We ran multiple regression analyses to determine whether activation predicted gains in the three math measures, separately for younger (i.e. 10 years old) and older (i.e 12 years old) children. Results showed that activation in both temporal and frontal cortex only predicted gains in fluency and multiplication skill, and only for younger children. This study suggests that both temporal and frontal cortex activation during phonological processing are important in predicting gains in math tasks that involve the retrieval of facts that are stored as phonological codes in memory. Moreover, these results were specific to younger children, suggesting that phonology is most important in the early stages of math development. When the math task involved subtractions, which relies on quantity representations, phonological processes were not important in driving gains.

Visual and Spatial Working Memory Abilities Predict Early Math Skills: A Longitudinal Study

This study aimed to explore the influence of the visuospatial active working memory subcomponents on early math skills in young children, followed longitudinally along the first 2 years of primary school. We administered tests investigating visual active working memory (jigsaw puzzle), spatial active working memory (backward Corsi), and math tasks to 43 children at the beginning of first grade (T1), at the end of first grade (T2), and at the end of second grade (T3). Math tasks were selected according to the children’s age and their levels of formal education: the “Battery for the evaluation of numerical intelligence from 4 to 6 years of age” (BIN 4–6) at T1 to test early numerical competence and the “Test for the evaluation of calculating and problem-solving abilities” (AC-MT 6–11) to test math skills at T2 and T3. Three regression models, in which the predictors were identified through a backward selection based on the use of the Bayesian information criterion (BIC) index, were performed to study the relationship between visual and spatial working memory and math ability at the three points in time. The results show that spatial working memory influences early numerical performance at T1, while early numerical performance is the unique predictor of math performance at T2. At the end of the second grade, the regression model reveals a relationship between math performance and both visual and spatial working memory and the attenuation of the importance of domain-specific predictors. The study depicts the different implications of visual and spatial working memory predictors over the children’s development periods and brings additional evidence to the debate on the relationship between visuospatial working memory and math ability in young children.

The Relationship Between Executive Functions and Academic Performance in Primary Education: Review and Meta-Analysis

The purpose of this study was to research the relationship between executive functions and academic performance in primary education (6–12 years). Based on 21 samples (n = 7,947), a meta-analysis of random effects demonstrated a moderately significant weighted effect size (r = 0.365) and was found to be a good predictor of academic performance. For the subjects of language and mathematics, the results of the random effects model were similar and slightly higher for mathematics (r = 0.350; r = 0.365). Thus, the theory that executive functions have greater influence on mathematical performance is supported, especially in aspects such as coding, organization, and the immediate retrieval of information. Regarding the different executive function components (working memory, inhibition, cognitive flexibility, and planning), working memory had the highest presence (k = 14, n = 3,740) and predictive weight for performance, with an effect size of r = 0.370 for random effects, with a moderate level of significance. The moderating effect of variables such as gender and age were also analyzed. After performing a meta-regression, gender resulted in a value of R² = 0.49; the age variable was not significant. This result is especially important since age has traditionally been considered to be the moderating variable of executive functions. The review reveals a good predictive power of executive functions in the primary education stage, and it is even higher at the early ages, indicating its great significance in describing future performance. The study also revealed the competencies and specific aspects of the executive functions that affect the way in which its components intervene in the academic area, demonstrating the mediating effect of variables such as physical fitness, motor skills, and memory processes.

The Effect of Neurocognitive Function on Math Computation in Pediatric ADHD: Moderating Influences of Anxious Perfectionism and Gender

Predictors of math achievement in attention-deficit/hyperactivity disorder (ADHD) are not well-known. To address this gap in the literature, we examined individual differences in neurocognitive functioning domains on math computation in a cross-sectional sample of youth with ADHD. Gender and anxiety symptoms were explored as potential moderators. The sample consisted of 281 youth (aged 8-15 years) diagnosed with ADHD. Neurocognitive tasks assessed auditory-verbal working memory, visuospatial working memory, and processing speed. Auditory-verbal working memory speed significantly predicted math computation. A three-way interaction revealed that at low levels of anxious perfectionism, slower processing speed predicted poorer math computation for boys compared to girls. These findings indicate the uniquely predictive values of auditory-verbal working memory and processing speed on math computation, and their differential moderation. These findings provide preliminary support that gender and anxious perfectionism may influence the relationship between neurocognitive functioning and academic achievement.

Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense

Children’s early numerical capacities form the building blocks for later arithmetic proficiency. Linear number placements and counting skills are indicative of mapping, as an important precursor to arithmetic skills, and have been suggested to be of vital importance to arithmetic development. The current study investigated whether fostering mapping skills is more efficient through a counting or a number line training program. Effects of both programs were compared through a quasi-experimental design, and moderation effects of age and socio-economic status (SES) were investigated. Ninety kindergartners were divided into three conditions: a counting, a number line, and a control condition. Pretests and posttests included an arithmetic (addition) task and a battery of number sense tasks (comparison, number lines, and counting). Results showed significantly greater gains in arithmetic, counting, and symbolic number lines in the counting training group than in the control group. The number line training group did not make significantly greater gains than the control group. Training gains were moderated by age, but not SES. We concluded that counting training improved numerical capacities effectively, whereas no such improvements could be found for the number line training. This suggests that only a counting approach is effective for fostering number sense and early arithmetic skills in kindergarten. Future research should elaborate on the parameters of training programs and the consequences of variation in these parameters.

Low performance on mathematical tasks in preschoolers: the importance of domain-general and domain-specific abilities

BACKGROUND

Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether this also holds for preschool low achievers (LAs) and how domain-specific and domain-general abilities contribute to mathematical difficulties at a young age. The aim of this study was to explore the cognitive characteristics of a sample of preschool LAs and identify sub-types of LAs.

METHODS

81 children were identified as LAs from 283 preschoolers aged 3 to 5 years old and were assessed on a number of domain-general and domain-specific tasks.

RESULTS

Cluster analysis revealed four subgroups of LAs in mathematics: (1) a weak processing sub-type; (2) a general mathematical LAs sub-type; (3) a mixed abilities sub-type; and (4) a visuo-spatial deficit sub-type. Whilst two of the groups showed specific domain-general difficulties, none showed only domain-specific difficulties.

CONCLUSIONS

Current findings suggest that preschool LAs constitute a heterogeneous group and stress the importance of domain-general factors for the development of mathematical abilities during the preschool years.