The relation between spatial skill and early number knowledge: the role of the linear number line

Spatial associations of number and pitch in human newborns

Humans use space to think, reason about, externally represent, and even talk about many dimensions (e.g., time, pitch height). One dimension that appears to exploit spatial resources is the mental representation of the numerosity of a set in the form of a mental number line. Although the horizontal number-space mapping is present from birth (small-left vs. large-right), it is unknown whether it extends to other spatial axes from birth or whether it is later acquired through development/experience. Moreover, newborns map changes in pitch height onto a vertical axis (low pitch-bottom vs. high pitch-top), but it is an open question whether it extends to other spatial axes. We presented newborns (N = 64 total, n = 16 per experiment, 0-4 days) with an auditory increase/decrease in magnitude along with a visual figure on a vertically oriented screen (bottom vs. top, change in number: Experiments 1 and 2; change in pitch: Experiment 3) or on a horizontally oriented screen (left vs. right, change in pitch: Experiment 4). Newborns associated changes in magnitude with a vertical axis only when experiencing an increase in magnitude (increase/up); however, the possibility that visuospatial biases could account for this asymmetric pattern are discussed. Newborns did not map changes in pitch horizontally (Experiment 4), in line with previous work showing that the horizontal mapping of number at birth does not generalize to other dimensions. These findings suggest that the flexible use of different spatial axes to map magnitude is not functional at birth and that the horizontal mapping of number might be privileged.

Exploring the Complexity of Children's Math and Vocabulary Learning: The Role of Cognitive, Dispositional, and Parental Factors

Early mathematical and vocabulary skills serve as critical foundations for academic success, yet the mechanisms underlying their development remain complex. This study examines the role of parents' education, children's attentional control, and learning approaches as predictors of kindergarteners' mathematics and vocabulary performance. Using a sample of 149 children aged 60-72 months in Shanghai, China, we conducted a path analysis to explore direct and indirect relationships among these factors. Findings indicate that parental education indirectly predicts math ability through children's learning approaches and attentional control, emphasizing the role of both cognitive and behavioral pathways. Conversely, vocabulary development is directly influenced by parental education and learning approaches, suggesting distinct developmental trajectories for math and language acquisition. These results highlight the interconnected nature of cognitive, behavioral, and environmental influences on early academic performance. Implications for early childhood education emphasize the need for targeted interventions that not only engage parents in fostering language-rich and cognitively stimulating environments but also support children's motivation, persistence, and attentional capacities.

Mental arithmetic skill development in primary school: The importance of number processing abilities and general cognitive abilities

The purpose of this study was to pinpoint which mixture of cognitive abilities and number abilities underlies young children's early mental arithmetic learning (i.e., skill development) and to examine to what extent this mixture is akin to the mixture underlying children's early arithmetic performance. A total of 265 children were assessed on counting knowledge, symbolic magnitude comparison, number line estimation, logical reasoning, verbal working memory, spatial processing, phonological processing, and general processing speed. One year later in first grade, the children's mental arithmetic ability was assessed, and it was then reassessed in second grade. A latent change score model showed that arithmetic performance was supported by counting knowledge, number line estimation, logical reasoning, spatial processing, phonological processing, and general processing speed, whereas arithmetic development was only supported by verbal working memory. These results demonstrate that the mixture of abilities underlying arithmetic development and arithmetic performance are rather different. Mental arithmetic performance in Grade 1 is equally dependent on a combination of both number abilities and cognitive abilities, whereas mental arithmetic development between first grade and second grade is only supported by one cognitive ability, verbal working memory.

Spatial Reasoning and Its Contribution to Mathematical Performance Across Different Content Domains: Evidence from Chinese Students

Recent studies have provided convincing evidence highlighting the strong relationship between spatial reasoning and mathematical performance. However, there is a limited body of research exploring the contributions of different spatial reasoning constructs to mathematical performance across various content domains, particularly within non-Western contexts. This study investigates the relationship between spatial reasoning skills-including mental rotation, spatial visualization, and spatial orientation-and mathematical performance across various domains (number, geometric shapes and measures and data display) among Chinese elementary school students in grade four (ages 9-10). The results indicate that overall spatial reasoning significantly predicts mathematical performance across various domains. All three spatial reasoning constructs significantly contribute to performance in the number and geometric shapes and measures domains, with mental rotation and spatial orientation being the strongest predictors of performance in these respective content domains. For data display performance, spatial orientation and spatial visualization significantly contribute, with spatial visualization being the strongest predictor. Although no significant gender differences were found in the overall link between spatial reasoning and mathematical performance, subgroup regression analysis showed variations. For male students, spatial orientation was the main predictor across content areas. For female students, mental rotation was the key predictor for number and geometry, while spatial visualization was most significant for data display.

Playful activities mitigate relations between parental mental health difficulties and child verbal outcomes

This study examined the role of parental involvement in the home learning environment in the association between parental mental health and child cognitive performance. In a sample of 174 three- to five-year-old children (52% female, 97% White, 7% Hispanic, 2019-2022), playful activities moderated the relation between parental general depression and child verbal reasoning and acquired verbal knowledge. However, there was no evidence that parental involvement moderated the association between parental mental health and child spatial reasoning. These results improve our understanding of the pathways by which parental mental health, even in a non-clinical community sample, relate to child outcomes and raise the possibility of leveraging playful activities as one mechanism to alleviate the potential role of parental mental health difficulties.

The relation of verbal and nonverbal skills to basic numerical processing of preterm versus term-born preschoolers

Verbal and nonverbal skills significantly contribute to individual differences in children's numerical development at the group level. However, less is known about whether the nature of the relations between verbal and nonverbal systems and numerical cognition varies depending on the unique characteristics children bring into numerical learning. To better delineate these associations, we examined the association between verbal and nonverbal skills and symbolic numerical development in preterm-born (PTB; n = 93; <37 weeks of gestation) children and term-born children (n = 104). We showed that PTB preschoolers, as a group, were at a higher risk of falling behind on certain numerical tasks (cardinality) but not on others (counting). There was, however, significant individual variability within the groups. Verbal and nonverbal skills contributed to the variability of children's numerical performance but did so differentially across the full spectrum of gestational age. Specifically, verbal skills moderated the association between gestational age and symbolic number performance (cardinality). The relation between verbal and cardinality skills was stronger at higher gestational ages compared with lower gestational ages. In addition, at higher gestational ages, children more frequently used retrieval strategy and less often relied solely on finger counting for the cardinality task. Shifting the focus from group differences to understanding individuals and their unique developmental pathways may enhance our insight into the risk and protective factors underlying the variability observed in all children.

Pathways From Spatial Skills to Mathematics: The Roles of Gender and Fluid Reasoning

There are contentious and persistent gender differences reported in some measures of spatial skills, particularly mental rotation and, to a lesser extent, perspective-taking, which may have an impact on mathematics success. Furthermore, pathways between spatial skills and mathematics may be mediated by other cognitive factors, such as fluid reasoning. Participants (N = 320, age range 8-12 years) completed measures of mental rotation, perspective-taking, fluid reasoning, and mathematics. Regression analyses were conducted to assess the mediation effect of fluid reasoning on the relations between mental rotation and perspective-taking, and mathematics. Moderated mediation was performed to assess the effects of gender and age on these relations. Mental rotation and perspective-taking both predicted performance in mathematics for the overall sample, and fluid reasoning was found to partially mediate these relations. For mental rotation, gender moderated the mediation model, with mental rotation directly predicting performance in mathematics for males but not females. The mediation model for perspective-taking and mathematics was not moderated by gender. Although a predictor of performance, age did not moderate any of the reported relations. These findings suggest that gender differences in some spatial skills, such as mental rotation, may extend to the pathways linking the skills to mathematics. Although mental rotation may be predictive of mathematics performance for boys, the same might not be so for girls. Extrinsic spatial skills, such as perspective-taking, offer new pathways to explore in the growing body of work examining the links between spatial reasoning and mathematics.

Implications of neural integration of math and spatial experiences for math ability and math anxiety

Mathematical and spatial abilities are positively related at both the behavioral and neural levels. Much of the evidence illuminating this relationship comes from classic laboratory-based experimental methods focused on cognitive performance despite most individuals also experiencing math and space in other contexts, such as in conversations or lectures. To broaden our understanding of math-space integration in these more commonplace situations, we used an auditory memory-encoding task with stimuli whose content evoked a range of educational and everyday settings related to math or spatial thinking. We used a multivariate approach to directly assess the extent of neural similarity between activity patterns elicited by these math and spatial stimuli. Results from whole-brain searchlight analysis revealed a highly specific positive relation between math and spatial activity patterns in bilateral anterior hippocampi. Examining individual variation in math-space similarity, we found that greater math-space similarity in bilateral anterior hippocampi was associated with poorer math skills and higher anxiety about math. Integration of neural responses to mathematical and spatial content may not always portend positive outcomes. We suggest that episodic simulation of quotidian contexts may link everyday experiences with math and spatial thinking-and the strength of this link is predictive of math in a manner that diverges from math-space associations derived from more lab-based tasks. On a methodological level, this work points to the value of considering a wider range of experimental paradigms, and of the value of combining multivariate fMRI analysis with behavioral data to better contextualize interpretations of brain data.

Dragging but not tapping promotes preschoolers' numerical estimating with touchscreens

When solving mathematical problems, young children will perform better when they can use gestures that match mental representations. However, despite their increasing prevalence in educational settings, few studies have explored this effect in touchscreen-based interactions. Thus, we investigated the impact on young children's performance of dragging (where a continuous gesture is performed that is congruent with the change in number) and tapping (involving a discrete gesture that is incongruent) on a touchscreen device when engaged in a continuous number line estimation task. By examining differences in the set size and position of the number line estimation, we were also able to explore the boundary conditions for the superiority effect of congruent gestures. We used a 2 (Gesture Type: drag or tap) × 2 (Set Size: Set 0-10 or Set 0-20) × 2 (Position: left of midpoint or right of midpoint) mixed design. A total of 70 children aged 5 and 6 years (33 girls) were recruited and randomly assigned to either the Drag or Tap group. We found that the congruent gesture (drag) generally facilitated better performance with the touchscreen but with boundary conditions. When completing difficult estimations (right side in the large set size), the Drag group was more accurate, responded to the stimulus faster, and spent more time manipulating than the Tap group. These findings suggest that when children require explicit scaffolding, congruent touchscreen gestures help to release mental resources for strategic adjustments, decrease the difficulty of numerical estimation, and support constructing mental representations.

Harnessing technology to measure individual differences in spatial thinking in early childhood from a relational developmental systems perspective

According to the Relational Developmental Systems perspective, the development of individual differences in spatial thinking (e.g., mental rotation, spatial reorientation, and spatial language) are attributed to various psychological (e.g., children's cognitive strategies), biological (e.g., structure and function of hippocampus), and cultural systems (e.g., caregiver spatial language input). Yet, measuring the development of individual differences in spatial thinking in young children, as well as the psychological, biological, and cultural systems that influence the development of these abilities, presents unique challenges. The current paper outlines ways to harness available technology including eye-tracking, eye-blink conditioning, MRI, Zoom, and LENA technology, to study the development of individual differences in young children's spatial thinking. The technologies discussed offer ways to examine children's spatial thinking development from different levels of analyses (i.e., psychological, biological, cultural), thereby allowing us to advance the study of developmental theory. We conclude with a discussion of the use of artificial intelligence.

The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study

Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; Mage = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns.

Direct and indirect effects of mother's spatial ability on child's spatial ability: What role does the home environment play?

Individual differences in spatial thinking are predictive of children's math and science achievement and later entry into Science, Technology, Engineering, and Mathematics (STEM) disciplines. Little is known about whether parent characteristics predict individual differences in children's spatial thinking. This study aims to understand whether, and to what extent, mother's intrinsic (i.e., mental rotation) and extrinsic (i.e., spatial scaling) spatial ability directly and indirectly, via the variation in home spatial environment, predicts children's intrinsic and extrinsic spatial ability. A total of 165 mothers and their 4-6-year-old children were recruited to participate in a remote video session with an experimenter. Mothers were administered a forced-choice Intrinsic Spatial Toy Preference Task gauging their preference for highly spatial versus less spatial toys and asked questions with the Home Intrinsic Spatial Environmental Questionnaire about the frequency with which they engage their child in spatial activities at home. Mothers completed a Mental Rotations Test and a Spatial Scaling Task adapted for adults. Children were administered the Picture Rotation Task, the Spatial Scaling Task, and the Peabody Picture Vocabulary Test. Structural equation modeling was used to examine direct and indirect, via home spatial environment and toy choices, influences of mother spatial ability on child spatial ability. Contrary to our predictions, we did not find direct, nor indirect, relations between mother and child spatial ability. These findings suggest that researchers should consider alternative conceptualizations of the early home spatial environment beyond the frequency of spatial play in the home. RESEARCH HIGHLIGHTS: The identification of factors that predict individual differences in children's spatial ability is important in order to maximize STEM learning outcomes. Data collection was conducted remotely rather than in traditional preschool or laboratory settings. Contrary to our pre-registered hypotheses, no significant relations between mother spatial ability, the early home spatial environment, and children's development of spatial skills were found. Future research should consider examining the amount of spatial language used in the home or the quality of parent-child interactions during spatial play as potential explanations for individual differences in children's spatial ability.

Unpacking associations among children's spatial skills, mathematics, and arithmetic strategies: decomposition matters

Several studies revealed links between mental rotation and mathematical tasks, but the intervening processes in this connection remain rather unexplored. Here, we aimed to investigate whether children's mental rotation skills relate to their accuracy in solving arithmetic problems via their usage of decomposition strategies, thus probing one potential intervening process. To this end, we examined a sample of 6- to 8-year-olds (N = 183) with a chronometric mental rotation task, and asked children to solve several arithmetic problems while assessing their solution strategies. After each arithmetic problem, children were asked about their strategy to solve the respective arithmetic problem and these were classified as either counting, decomposition, or retrieval strategies. Analyses were controlled for age, sex, fluid and verbal reasoning. Results indicated that children's response times and accuracy in the mental rotation task were best explained by linear functions of rotation angle, suggesting the usage of dynamic mental transformation strategies. A multiple mediation model revealed that children with higher mental rotation skills were more inclined to use higher-level mental strategies such as decomposition which in turn increased their accuracy of solving arithmetic problems. None of the other arithmetic strategies revealed significant indirect effects. These findings suggest that children with higher mental rotation skills may profit from visualizing and flexibly transforming numerical magnitudes, increasing the frequency of decomposition strategies. Overall, decomposition may play a unique role in the connection between children's mental rotation and arithmetic skills, which is an essential information for planning future training and experimental studies.

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

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

Individual differences in preschoolers' spatial thinking: Comprehension of dimensional adjectives and their relation to children's performance on non-verbal spatial tasks

The current study explores whether individual differences in the dimensional adjectives (e.g., big, tall) children understand, relates to individual differences in two non-verbal spatial abilities, spatial scaling and mental transformations, in bilingual children. The inclusion of English-Spanish bilingual children broadens the work in this area which has previously focused strictly on English language. Ninety-two English-Spanish bilingual children between 37.65 and 71.87 months (42 male) participated in the study. Results show number of dimensional adjectives preschool children comprehend utilizing a new interactive, tablet-based task relates to performance on non-verbal spatial tasks. This research supports hypothesized relations between spatial language comprehension and spatial abilities, introduces an effective tool for examining spatial language comprehension in young children, and improves generalizability by including a bilingual sample and testing comprehension in both English and Spanish.

Assessing the impact of LEGO® construction training on spatial and mathematical skills

Lego construction ability is associated with a variety of spatial skills and mathematical outcomes. However, it is unknown whether these relations are causal. We aimed to establish the causal impact of Lego construction training on: Lego construction ability; a broad range of spatial skills; and on mathematical outcomes in 7-9-year-olds. We also aimed to identify how this causal impact differs for digital versus physical Lego construction training. One-hundred and ninety-eight children took part in a six-week training programme, delivered twice weekly as a school lunch time club. They completed either physical Lego training (N = 59), digital Lego training (N = 64), or an active control condition (crafts; N = 75). All children completed baseline and follow-up measures of spatial skills (disembedding, visuo-spatial working memory, spatial scaling, mental rotation, and performance on a spatial-numerical task, the number line task), mathematical outcomes (geometry, arithmetic, and overall mathematical skills) and Lego construction ability. Exploratory analyses revealed evidence for near transfer (Lego construction ability) and some evidence for far transfer (arithmetic) of Lego training, but overall transfer was limited. Despite this, we identified key areas for further development (explicit focus on spatial strategies, training for teachers, and embedding the programme within a mathematical context). The findings of this study can be used to inform future development of Lego construction training programmes to support mathematics learning.

How Can We Best Assess Spatial Skills? Practical and Conceptual Challenges

Spatial thinking skills are associated with performance, persistence, and achievement in science, technology, engineering, and mathematics (STEM) school subjects. Because STEM knowledge and skills are integral to developing a well-trained workforce within and beyond STEM, spatial skills have become a major focus of cognitive, developmental, and educational research. However, these efforts are greatly hampered by the current lack of access to reliable, valid, and well-normed spatial tests. Although there are hundreds of spatial tests, they are often hard to access and use, and information about their psychometric properties is frequently lacking. Additional problems include (1) substantial disagreement about what different spatial tests measure-even two tests with similar names may measure very different constructs; (2) the inability to measure some STEM-relevant spatial skills by any existing tests; and (3) many tests only being available for specific age groups. The first part of this report delineates these problems, as documented in a series of structured and open-ended interviews and surveys with colleagues. The second part outlines a roadmap for addressing the problems. We present possibilities for developing shared testing systems that would allow researchers to test many participants through the internet. We discuss technological innovations, such as virtual reality, which could facilitate the testing of navigation and other spatial skills. Developing a bank of testing resources will empower researchers and educators to explore and support spatial thinking in their disciplines, as well as drive the development of a comprehensive and coherent theoretical understanding of spatial thinking.

Cognitive Foundations of Early Mathematics: Investigating the Unique Contributions of Numerical, Executive Function, and Spatial Skills

There is an emerging consensus that numerical, executive function (EF), and spatial skills are foundational to children's mathematical learning and development. Moreover, each skill has been theorized to relate to mathematics for different reasons. Thus, it is possible that each cognitive construct is related to mathematics through distinct pathways. The present study tests this hypothesis. One-hundred and eighty 4- to 9-year-olds (Mage = 6.21) completed a battery of numerical, EF, spatial, and mathematics measures. Factor analyses revealed strong, but separable, relations between children's numerical, EF, and spatial skills. Moreover, the three-factor model (i.e., modelling numerical, EF, and spatial skills as separate latent variables) fit the data better than a general intelligence (g-factor) model. While EF skills were the only unique predictor of number line performance, spatial skills were the only unique predictor of arithmetic (addition) performance. Additionally, spatial skills were related to the use of more advanced addition strategies (e.g., composition/decomposition and retrieval), which in turn were related to children's overall arithmetic performance. That is, children's strategy use fully mediated the relation between spatial skills and arithmetic performance. Taken together, these findings provide new insights into the cognitive foundations of early mathematics, with implications for assessment and instruction moving forward.

A meta-analysis of mental rotation in the first years of life

Mental rotation, the cognitive process of moving an object in mind to predict how it looks in a new orientation, is coupled to intelligence, learning, and educational achievement. On average, adolescent and adult males solve mental rotation tasks slightly better (i.e., faster and/or more accurate) than females. When such behavioral differences emerge during development, however, remains poorly understood. Here we analyzed effect sizes derived from 62 experiments conducted in 1705 infants aged 3-16 months. We found that male infants recognized rotated objects slightly more reliably than female infants. This difference survives correction for small degrees of publication bias. These findings indicate that gender differences in mental rotation are small and not robustly detectable in the first months of postnatal life. RESEARCH HIGHLIGHTS: We analyzed effect sizes of 62 mental rotation experiments including 1705 infants. Looking time reveals that 3-16-months-old infants are able to perform mental rotation. Mental rotation is slightly more reliable in male infants compared to female infants. Gender difference in mental rotation is robust to small degrees of publication bias.

Unlocking the Power of Gesture: Using Movement-Based Instruction to Improve First Grade Children's Spatial Unit Misconceptions

Gestures are hand movements that are produced simultaneously with spoken language and can supplement it by representing semantic information, emphasizing important points, or showing spatial locations and relations. Gestures' specific features make them a promising tool to improve spatial thinking. Yet, there is recent work showing that not all learners benefit equally from gesture instruction and that this may be driven, in part, by children's difficulty understanding what an instructor's gesture is intended to represent. The current study directly compares instruction with gestures to instruction with plastic unit chips (Action) in a linear measurement learning paradigm aimed at teaching children the concept of spatial units. Some children performed only one type of movement, and some children performed both: Action-then-Gesture [AG] or Gesture-then-Action [GA]. Children learned most from the Gesture-then-Action [GA] and Action only [A] training conditions. After controlling for initial differences in learning, the gesture-then-action condition outperformed all three other training conditions on a transfer task. While gesture is cognitively challenging for some learners, that challenge may be desirable-immediately following gesture with a concrete representation to clarify that gesture's meaning is an especially effective way to unlock the power of this spatial tool and lead to deep, generalizable learning.

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

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

Understanding the complexities of mathematical cognition: A multi-level framework

Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.

Measuring Spatial Abilities in Children: A Comparison of Mental-Rotation and Perspective-Taking Tasks

Mental rotation (MR) and perspective taking (PT) are important spatial abilities and predictive of performance in other cognitive domains. Yet, age-appropriate measures to assess these spatial abilities in children are still rare. This study examined psychometric properties of four MR tasks in 6- to 9-year-olds (N = 96). Two were developed specifically for children and two were based on established assessments for adults; one of each was a computerized and one was a paper-pencil task. Furthermore, spatial perspective taking (PT)-a different but closely related ability-was assessed to determine discriminant validity. Factor analyses showed that all MR tasks loaded on one single factor, with PT only loading weakly on the same factor, suggesting high construct validity. The computerized task for adults showed moderate factor loadings, constituted its own (but correlated) factor when a two-factor solution was forced, and showed the lowest reliabilities, suggesting that it was very difficult for children. On average, the new MR tasks had good to excellent reliabilities, differentiated well between age groups, and proved to be well-suited to assess MR in this age range. The PT task also showed good reliability and a steep developmental progression. Relations to verbal skills, gaming experience, and TV consumption are discussed.

Preliminary Adaptation of Motor Tests to Evaluate Fine Motor Skills Associated with Mathematical Skills in Preschoolers

Mathematics is the subject in which many school-age children reveal difficulties. The literature has shown that fine motor skills, namely fine motor coordination and visuomotor integration, have been more robustly associated with mathematical performance. Studies have shown the importance that instruments have to evaluate these skills, however, the characteristics of these instruments do not fit the reality of kindergartens, they are usually time consuming and expensive and are usually administered by specialists. Thus, the main objective of this study was to identify, select, adapt and validate motor tests to evaluate fine motor skills associated with mathematical skills to allow the kindergarten teachers to apply them simultaneously to the class, with few material resources, in a short period of time and without the need for a lot of training to apply, score and classify. For this purpose, firstly, it was necessary to understand the main difficulties highlighted by kindergarten teachers regarding the use of instruments to evaluate fine motor skills and, thus, elaborate criteria to identify and select the tests that best fit the reality of kindergartens. The test identified, selected and adapted to evaluate fine motor coordination was threading beads from the Movement Evaluation Battery for Children, 2nd Edition. The main adaptation of the test was related to time, that is, instead of counting the time it takes the child to string the total number of cubes on the string, we counted the number of cubes the child strung on the string in a pre-defined time. To evaluate visual-motor integration, the test identified, selected and adapted was the Visual-Motor Integration (6th Edition) test. The main adaptation was related to material resources, that is, it will be possible to apply the test using only one sheet per child instead of the seven suggested by the original test. After the preliminary adaptation of the tests, their validation was performed by means of the degree of reliability (test-retest) and predictive validity. The results indicated that the adapted tests presented an excellent degree of reliability (>0.9) and could therefore be used to administer them simultaneously to the class group. The adapted Visual-Motor Integration test seems to be the most suitable one to be used by kindergarten teachers, in a classroom context, to simultaneously evaluate students' fine motor skills and associate their results with mathematical skills.

Spatial Visualization Supports Students' Math: Mechanisms for Spatial Transfer

The present study conducted a randomized control trial to assess the efficacy of two spatial intervention programs aimed to improve Grade 4 (N = 287) students' spatial visualization skills and math performance. The first treatment (N = 98) focused on isolated spatial training that included 40 min of digital spatial training across fourteen weeks. The second treatment (N = 92) embedded spatial visualization skill development into math lessons, along with the digital spatial training that provided practice of the newly acquired skills. A business-as-usual group acted as a control (N = 97). Engagement with the embedded intervention program (i.e., both lessons and digital training) showed large additive effects, highlighting the role of spatial reasoning tools to support the transfer of spatial reasoning to math. The isolated intervention program with the digital spatial training had a transfer effect on math, compared to a business-as-usual control, while spatial reasoning improvements for this group were mixed. The spatial skills targeted in the digital training had a mediation effect on math performance, despite not increasing in the pre-post-test design. The effects of the digital training cohort were moderated by initial spatial skill, with students with lower spatial reasoning making the least gains in math.

Practitioners' perspectives on spatial reasoning in educational practice from birth to 7 years

BACKGROUND

There is a growing evidence base for the importance of spatial reasoning for the development of mathematics. However, the extent to which this translates into practice is unknown.

AIMS

We aimed to understand practitioners' perspectives on their understanding of spatial reasoning, the extent to which they recognize and implement spatial activities in their practice, and the barriers and opportunities to support spatial reasoning in the practice setting.

SAMPLE

Study 1 (questionnaire) included 94 participants and Study 2 (focus groups) consisted of nine participants. Participants were educational practitioners working with children from birth to 7 years.

METHODS

The study was mixed methods and included a questionnaire (Study 1) and a series of focus groups (Study 2).

RESULTS

We found that whilst practitioners engage in a variety of activities that support spatial reasoning, most practitioners reported little confidence in their understanding of what spatial reasoning is.

CONCLUSION

Informative and accessible resources are needed to broaden understanding of the definition of spatial reasoning and to outline opportunities to support spatial reasoning.

The Impact of School Closures during COVID-19 Lockdown on Visual-Motor Integration and Block Design Performance: A Comparison of Two Cohorts of Preschool Children

The COVID-19 outbreak has led to the closure of educational institutions, which may prevent children from attaining skills essential for learning, such as visual-motor integration (VMI) and visuospatial constructional ability (often reflected with the Block Design Test, BDT). This study compares VMI and BDT performance between a pre-pandemic cohort (children who attended preschool in late 2019) and a post-pandemic cohort (those physically attending preschool for the first time at the end of 2021). Participants were children attending government preschools with similar syllabi catered for low-income families. The pre-pandemic cohort was part of an earlier study (n = 202 for VMI and n = 220 for BDT) before lockdowns commenced in March 2020. The post-pandemic cohort comprised 197 children who completed the Beery-VMI and 93 children who completed the BDT. Compared to the pre-pandemic cohort, the post-pandemic cohort had significantly lower mean Beery-VMI scores (t(397) = 3.054, p = 0.002) and was 3.162-times more likely to have a below average Beery-VMI score (OR = 3.162 (95% CI 1.349, 7.411)). The post-pandemic cohort also had significantly lower BDT scores than the pre-pandemic cohort (t(311) = -5.866, p < 0.001). In conclusion, children with disrupted conventional preschool education due to the COVID-19 lockdowns were more likely to have below-average VMI and lower BDT scores.

Spatial-Numerical Magnitude Estimation Mediates Early Sex Differences in the Use of Advanced Arithmetic Strategies

An accumulating body of literature points to a link between spatial reasoning and mathematics learning. The present study contributes to this line of research by investigating sex differences both in spatial representations of magnitude and in the use of arithmetic strategies, as well as the relation between the two. To test the hypothesis that sex differences in spatial-numerical magnitude knowledge mediate sex differences in the use of advanced strategies (retrieval and decomposition), two studies were conducted. Study 1 included 96 US first graders (53% girls); Study 2 included 210 Russian first graders (49% girls). All participants completed a number line estimation task (a spatially based measure of numerical magnitude knowledge) and an arithmetic strategy task (a measure of strategy choice). The studies showed parallel results: boys produced more accurate numerical magnitude estimates on the number line estimation task and used advanced strategies more frequently on the arithmetic task. Critically, both studies provide support for the mediation hypothesis (although there were some differences in the pattern obtained for the two strategies). The results are discussed in the context of broader research about the relation between spatial and mathematical skills.

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

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

Symbolic and non-symbolic predictors of number line task in Italian kindergarteners

The number line estimation task (NLE) is often used as a predictor for broader measures of mathematical achievement. In spite of its popularity, it is still not clear whether the task is based on symbolic or non-symbolic numerical competence. In particular, there is only a very limited amount of studies investigating the relationship between NLE performance and symbolic vs. non-symbolic math skills in children who have not yet begun formal schooling. This study investigates the strength of the association between NLE performance and symbolic and non-symbolic tasks in young kindergarteners. Ninety two 5-year-old children completed the NLE task (range 0-100) and a battery of early numerical competence tests including symbolic-lexical tasks, symbolic semantic tasks, and non-symbolic semantic tasks. The relationship between symbolic and non-symbolic early numerical competence and NLE performance was analyzed using a regression model based on the Bayesian Information Criterion (BIC). Results show that only symbolic semantic tasks are significant predictors of NLE performance. These results suggest that symbolic numerical knowledge is involved in number line processing among young children, whilst non-symbolic knowledge is not. This finding brings new data to the debate on the relationship between non-symbolic numeral knowledge and symbolic number processing and supports the evidence of a primary role of symbolic number processing already in young kindergarteners.

Longitudinal relationship between number line estimation and other mathematical abilities in Chinese preschool children

Many cross-sectional studies have shown that number line estimation is associated with other mathematical skills, but there has been limited longitudinal research. To systematically examine such associations longitudinally at the earliest stage of mathematical learning, the current study tested 40 Chinese preschoolers (mean age = 4.97 years, SD = 0.18) and followed them up 8 months later. For both waves of data collection, children were administered six tasks: number line estimation, dot counting, comparison of two dot arrays, comparison of triple dot arrays, symbolic number comparison, and simple addition. Results of two-wave cross-lagged panel analysis showed that (a) dot counting and non-symbolic numerical comparison at Time 1 had significant longitudinal associations with number line estimation at Time 2, (b) number line estimation had bidirectional associations with symbolic number comparison, and (c) number line estimation at Time 1 had a marginally significant longitudinal association with simple addition at Time 2. These results extend the small but accumulating literature on the longitudinal relations between number line estimation and other mathematical skills and specify the important role of number line estimation in the early development of mathematical skills.

Children grow upwards, and so does the number line: Evidence from a directional number line paradigm

Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.

Cognitive predictors of children's arithmetic principle understanding

The understanding of arithmetic principles (APs) is an important component of our conceptual mathematical knowledge, but we have limited knowledge about how children acquire APs. The current study examined this issue through a longitudinal study with 273 Chinese fourth graders. These children were assessed on various cognitive capacities (e.g., verbal and visuospatial working memory, processing speed, inhibition skill, numerical magnitude representation) in Grade 4 as well as on their AP understanding using multifaceted assessment and their arithmetic competence in Grade 5. Results from structural equation modeling suggested that verbal memory and inhibition skill directly predicted AP understanding, which in turn predicted arithmetic competence. Visuospatial working memory predicted AP understanding through numerical magnitude representation. The findings allow researchers to better account for the individual differences in AP understanding.

Explaining World-Wide Variation in Navigation Ability from Millions of People: Citizen Science Project Sea Hero Quest

Navigation ability varies widely across humans. Prior studies have reported that being younger and a male has an advantage for navigation ability. However, these studies have generally involved small numbers of participants from a handful of western countries. Here, we review findings from our project Sea Hero Quest, which used a video game for mobile and tablet devices to test 3.9 million people on their navigation ability, sampling across every nation-state and from 18 to 99 years of age. Results revealed that the task has good ecological validity and across all countries sufficiently sampled (N = 63), age is linked to a near-linear decline in navigation ability from the early 20s. All countries showed a male advantage, but this varied considerably and could be partly predicted by gender inequality. We found that those who reported growing up in a city were on average worse at navigating than those who grew up outside cities and that navigation performance helped identify those at greater genetic risk of Alzheimer's disease. We discuss the advantages and challenges of using a mobile app to study cognition and the future avenues for understanding individual differences in navigation ability arising from this research.

How Memory Counts in Mathematical Development

Memory has been well-established as a predictor of mathematics achievement in child development. Nevertheless, empirical evidence remains elusive on the unique role of the different forms of memory and their specific mechanisms as predictors of mathematics development. Therefore, in this study, the role of visuospatial short-term memory, visuospatial working memory, verbal short-term memory, and verbal long-term memory was investigated at three key stages of the development of mathematics (5-6 years, 6-7 years, 7-8 years), as well as their interactions across development. The relation between the different memory types and informal and formal mathematics was also studied. The findings of this study provide empirical support for a shift in the relation between different memory types and mathematics achievement over development with: 1) visuospatial short-term memory predicting informal mathematics achievement at the age of 5-6 years; 2) visuospatial working memory predicting informal and formal mathematics achievement at the age of 6-7 years; and 3) verbal short-term memory predicting formal mathematics achievement at the age of 7-8 years. These shifts clearly appear consistent with children's mathematics curriculum content over time and the requirements of mathematics acquisition at specific stages in development. With these findings, the unique role of various forms of memory in the development of mathematics and the timeframe in which they play a crucial part is highlighted, which should be taken into consideration for future research and possible intervention studies in children's mathematics achievement.

The relevance of basic numerical skills for fraction processing: Evidence from cross-sectional data

Recent research indicated that fraction understanding is an important predictor of later mathematical achievement. In the current study we investigated associations between basic numerical skills and students' fraction processing. We analyzed data of 939 German secondary school students (age range = 11.92 to 18.00 years) and evaluated the determinants of fraction processing considering basic numerical skills as predictors (i.e., number line estimation, basic arithmetic operations, non-symbolic magnitude comparison, etc.). Additionally, we controlled for general cognitive ability, grade level, and sex. We found that multiplication, subtraction, conceptual knowledge, number line estimation, and basic geometry were significantly associated with fraction processing beyond significant associations of general cognitive ability and sex. Moreover, relative weight analysis revealed that addition and approximate arithmetic should also be considered as relevant predictors for fraction processing. The current results provide food for thought that further research should focus on investigating whether recapitulating basic numerical content in secondary school mathematics education can be beneficial for acquiring more complex mathematical concepts such as fractions.

The number line estimation task is a valid tool for assessing mathematical achievement: A population-level study with 6484 Luxembourgish ninth-graders

The number line estimation task is an often-used measure of numerical magnitude understanding. The task also correlates substantially with broader measures of mathematical achievement. This raises the question of whether the task would be a useful component of mathematical achievement tests and instruments to diagnose dyscalculia or mathematical giftedness and whether a stand-alone version of the task can serve as a short screener for mathematical achievement. Previous studies on the relation between number line estimation accuracy and broader mathematical achievement were limited in that they used relatively small nonrepresentative samples and usually did not account for potentially confounding variables. To close this research gap, we report findings from a population-level study with nearly all Luxembourgish ninth-graders (N = 6484). We used multilevel regressions to test how a standardized mathematical achievement test relates to the accuracy in number line estimation on bounded number lines with whole numbers and fractions. We also investigated how these relations were moderated by classroom characteristics, person characteristics, and trial characteristics. Mathematical achievement and number line estimation accuracy were associated even after controlling for potentially confounding variables. Subpopulations of students showed meaningful differences in estimation accuracy, which can serve as benchmarks in future studies. Compared with the number line estimation task with whole numbers, the number line estimation task with fractions was more strongly related to mathematical achievement in students across the entire mathematical achievement spectrum. These results show that the number line estimation task is a valid and useful tool for diagnosing and monitoring mathematical achievement.

Ordinality and Verbal Framing Influence Preschoolers' Memory for Spatial Structure

During the preschool years, children are simultaneously undergoing a reshaping of their mental number line and becoming increasingly sensitive to the social norms expressed by those around them. In the current study, 4- and 5-year-old American and Israeli children were given a task in which an experimenter laid out chips with numbers (1-5), letters (A-E), or colors (Red-Blue, the first colors of the rainbow), and presented them with a specific order (initial through final) and direction (Left-to-right or Right-to-left). The experimenter either did not demonstrate the laying out of the chips (Control), emphasized the process of the left-to-right or right-to-left spatial layout (Process), or used general goal language (Generic). Children were then asked to recreate each sequence after a short delay. Children also completed a short numeracy task. The results indicate that attention to the spatial structuring of the environment was influenced by conventional framing; children exhibited better recall when the manner of layout was emphasized than when it was not. Both American and Israeli children were better able to recall numerical information relative to non-numerical information. Although children did not show an overall benefit for better recall of information related to the culture's dominant spatial direction, American children's tendency to recall numerical direction information predicted their early numeracy ability.

Teacher perceptions of working memory and executive function improvements following school-day cognitive training

Considerable research has documented the impact of teacher perceptions on students’ academic-related outcomes (e.g., classroom performance). This body of literature clearly shows that teacher perceptions (resulting from direct interactions with students) can have both positive and negative effects with respect to student behaviors and experiences in the classroom. What remains unclear is whether teachers perceive changes that result from interventions administered outside of their classrooms. The purpose of this study was to examine changes in teacher perceptions of working memory and executive function concerns (two important predictors of academic success) among students who participated in a computerized cognitive training program designed to enhance working memory skills. The current results indicate that teachers perceived fewer concerns following students’ participation in the training; this outcome was supplemented with significant improvements in the students’ working memory capabilities following the training program. These findings have important implications given the literature highlighting the relation between teacher perceptions and student outcomes as a function of a school-based computerized cognitive training intervention.

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.

What children's number naming errors tell us about early understanding of multidigit numbers

This investigation examined the nature and development of a foundational symbolic numeric skill-number identification-focusing on children's emerging knowledge of multidigit numbers. Two studies were conducted with Russian preschoolers. Study 1 (N = 350; 51-77 months of age) investigated age-related changes in the accuracy of number naming and in the types of errors children produced. The errors fell into distinct categories: syntactic (structural errors such as naming each digit separately without using place-value markers) and lexical (nonstructural errors such as replacing the name of a digit with the name of another digit). Number reading accuracy improved with age, primarily due to a decreased frequency of syntactic errors. Boys made fewer syntactic errors than girls. Study 2 (N = 110; 61-74 months of age) showed that accuracy of naming double-digit numbers was related to conceptual understanding of the base-10 numeric structure. The frequency of syntactic errors in number naming was negatively associated with the use of base-10 representations, whereas lexical errors were not related to children's ability to represent base-10 number structure. Implications for understanding children's mathematics trajectories are discussed.

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

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

Contributions of Executive Function to Spatial Thinking in Young Children

Identifying factors that contribute to spatial thinking is of great interest given links between spatial thinking and success in STEM. Working memory has been found to be predictive of spatial thinking but little research has explored other components of executive function (i.e., inhibition, shifting) in relation to spatial thinking. A total of 131 four- to six-year-olds (M age = 5.06; 53.4% male; 56% Latinx, 18% White, 12% Mixed Race, 5% Asian, and 5% other) were assessed using spatial, executive function, and intelligence tasks. Results show that inhibition, shifting, and working memory are all associated with intrinsic and extrinsic spatial task scores. These results advance developmental theory on spatial thinking and offer a promising route for future interventions in improving spatial ability.