Number Sense Growth in Kindergarten: A Longitudinal Investigation of Children at Risk for Mathematics Difficulties

Children's arithmetic strategy use trajectories: Exploring the roles of executive functions and sociodemographic characteristics

Although young children often use counting to solve arithmetic problems, over time they move toward more efficient strategies such as direct retrieval and decomposition. Strategy selection has longitudinal associations with children's math achievement. Existing research indicates that children's executive functions (EFs) support inhibiting unnecessary strategies and adaptively switching between strategies. Moreover, research has documented gender differences in strategy use, but prior literature does not account for the contributions of socioeconomic factors in children's strategy trajectories. The current study examined the unique roles of preschoolers' EFs, gender, household income, and maternal education for the trajectories of strategy use on arithmetic problems across early elementary school. Preschoolers' EFs were assessed at 5 years 3 months of age, and children completed addition and subtraction problems in first, second, and third grades. Children's strategies were categorized as retrieval, counting, decomposition, and sign flipping. Results indicated that children with higher EFs were more likely to use retrieval and sign flipping in first grade compared with children with lower EFs, and this advantage was maintained into third grade. Boys used more retrieval and decomposition, whereas girls used more counting strategies, in first grade, and this pattern held longitudinally. Finally, children whose mothers had more years of education were likely to use decomposition and sign flipping in first grade, with an advantage through third grade. Overall, the current study sheds light on how cognitive and sociodemographic factors differentially contribute to children's accurate strategy use, with implications for how to best target early interventions to support children's math achievement.

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.

From whole numbers to fractions to word problems: Hierarchical relations in mathematics knowledge for Chinese Grade 6 students

It is well established in the literature that fraction knowledge is important for learning more advanced mathematics, but the hierarchical relations among whole number arithmetic, fraction knowledge, and mathematics word problem-solving are not well understood. In the current study, Chinese Grade 6 students (N = 1160; 465 girls; Mage = 12.1 years, SD = 0.6) completed whole number arithmetic (addition, subtraction, multiplication, and division), fraction (mapping, equivalence, comparison, and arithmetic), and mathematics word problem-solving assessments. They also completed two control measures: number writing speed and nonverbal intelligence. Structural equation modeling was used to investigate the hierarchical relations among these assessments. Among the four fraction tasks, the correlations were low to moderate, suggesting that each task may tap into a unique aspect of fraction understanding. In the model, whole number arithmetic was directly related to all four fraction tasks, but was only indirectly related to mathematics word problem-solving, through fraction arithmetic. Only fraction arithmetic, the most advanced fraction skill, directly predicted mathematics word problem-solving. These findings are consistent with the view that students need to build these associations into their mathematics hierarchy to advance their mathematical competence.

The inferior fronto-occipital fasciculus correlates with early precursors of mathematics and reading before the start of formal schooling

Diffusion-weighted imaging studies in preschoolers have almost exclusively been done in the field of reading. As a result, virtually nothing is known about white matter tracts associated with individual differences in mathematics at this age. Studying the preschoolers' brain is crucial because it allows us to identify individual differences in brain anatomy without influences of formal mathematics and reading instruction. To fill this gap, we investigated for the first time before the start of formal school entry the associations between white matter tracts and precursors of mathematics and reading simultaneously. We also investigated whether these associations were specific to mathematics and to reading, or not. We focused on four bilateral white matter tracts (arcuate fasciculus (direct, anterior), inferior fronto-occipital fasciculus, inferior longitudinal fasciculus), which have been previously correlated with mathematical performance in older children and with reading performance in children of a similar age as the current study. Participants were 56 5-year-old children (Mage = 67 months; SD = 1.8), none of which received formal instruction. Our results showed an association between the bilateral inferior fronto-occipital fasciculus and precursors of mathematics (numerical ordering, numeral knowledge) and reading (phonological awareness, letter knowledge). Follow-up regression analyses revealed that the associations found with the inferior fronto-occipital fasciculus were neither specific to mathematics nor specific to reading. These findings suggest that, already before the start of formal schooling, the inferior fronto-occipital fasciculus might be related to the neural overlap between mathematics and reading. This overlap potentially reflects one of their many shared mechanisms, such as the reliance on phonological codes or the processing of visual symbols, and these mechanisms should be exploited in future studies.

Early numeracy profiles in young children with intellectual disabilities: The role of cognitive functions

Exploring individual differences and looking beyond averaged parameters of early numeracy in young children with mild intellectual disabilities has become an area of interest to many researchers worldwide. This study aimed to identify the different profiles of early numeracy skills in young children with mild intellectual disabilities. For this purpose, we assessed early numeracy through Utrecht early numeracy test and learning aptitude through Detroit Test, in a sample of 135 children diagnosed with intellectual disabilities. The mean of their mental age was 5:09 (years:months). Two-step cluster analysis identified four homogenous groups of children with distinct early numeracy profiles as follows:C1 were fluent in relational and numerical skills up to 20, C2 were fluent in relational skills and numerical skills up to 10, C3 had basic knowledge of relational skills and inconsistent numerical skills up to 10 and C4 had inconsistent relational skills and numerical skills. Results are discussed with reference to their educational implications.

The Longitudinal Contributions of Preschool Executive Functions and Early Math Abilities to Arithmetic Skills in Elementary School

Executive functions (EFs) are linked to children's overall math performance, although few studies have considered the joint role of prior math abilities for specific math subskills, such as arithmetic. The current study examined the longitudinal contributions of preschool EFs and early math abilities to children's accuracy and reaction time on arithmetic problems. Two hundred and eighty-three children completed EF and numeracy assessments at 5.25 years old. Children completed an arithmetic problem task in first (Mage = 7.14), second (Mage = 8.09), and third grade (Mage = 9.08). Results indicated that preschool EFs and math abilities are uniquely linked to children's accuracy and reaction time at age 7, whereas preschool EFs alone continue to predict accuracy at age 8 and reaction time at age 9, even after accounting for intervening arithmetic performance. The study highlights the sustained, unique importance of early EFs for children's arithmetic acquisition.

Mothers’ and fathers’ engagement in math activities with their toddler sons and daughters: The moderating role of parental math beliefs

Parents’ beliefs about the importance of math predicts their math engagement with their children. However, most work focuses on mothers’ math engagement with preschool- and school-aged children, leaving gaps in knowledge about fathers and the experiences of toddlers. We examined differences in mothers’ and fathers’ (N = 94) engagement in math- and non-math activities with their two-year-old girls and boys. Parents reported their beliefs about the importance of math and literacy for young children and their frequency of home learning activities. Parents of sons did not differ in their engagement in math activities from parents of daughters. Mothers reported engaging more frequently in math activities with their toddlers than fathers did, but the difference reduced when parents endorsed stronger beliefs about the importance of math for children. Even at very early ages, children experience vastly different opportunities to learn math in the home, with math-related experiences being shaped by both parent gender and parents’ beliefs.

The role of executive function in shaping the longitudinal stability of math achievement during early elementary grades

There is substantial rank-order stability in children's mathematical skills throughout development. Research has shown that children who enter school with relatively low math skills are unlikely to catch up to peers who begin kindergarten with more developed math skills. Emerging evidence suggests that children's executive function skills might play an important role in shaping the rate and stability of mathematical skill development during early development. Therefore in the present study, we used data from the Early Childhood Longitudinal Study-Kindergarten Cohort 2010-11-a prospective sample of over 18,000 children in the United States-to examine executive function as an antecedent to characteristics of growth in math skills and to test whether executive function moderates the longitudinal stability of math achievement from kindergarten through second grade. Latent growth curve models reveal that executive function is related to not only the level of math skills at school entry but also to the rate of growth in early elementary years. Moreover, we found that executive function moderated the stability of math achievement from kindergarten to second grade, suggesting that early executive function skills can serve as a compensatory mechanism for children who enter school with lower levels of mathematical skills. These findings might have important implications for narrowing gaps in math achievement during early elementary school.

Association between motor and math skills in preschool children with typical development: Systematic review

Mathematics has been the subject in which many school-age children have revealed many difficulties. Research carried out in an attempt to understand the causes of failure in this area pointed to a positive association between mathematical performance and motor performance. Given the importance of math development in future school outcomes, knowing which specific motor components are most associated with math performance can help educators define better strategies for teaching mathematics. In this sense, the present systematic review study aimed to identify the components of motor skills most positively associated with mathematical performance in children with typical development who attend preschool. The PRISMA methodology (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) was used in this study. The databases searched were ERIC, PubMED, SciELO, Scopus and Web of Science. A total of 2,909 articles were identified, of which 18 were included in this systematic review. The main results showed positive associations between fine motor skills, namely fine motor coordination and visuomotor integration, and mathematical performance. The math skill of numerical counting was the most associated with FMS. The main characteristics of the instruments used showed that the tasks of copying figures or drawings are the most used to assess visuomotor integration and the tasks of handling objects with pinch-like movements are the most used to assess fine motor coordination. Given the importance of mathematical performance in future school results, identifying early children with difficulties in fine motor skills will help educators to design better strategies for teaching mathematical skills. In this sense, the need to identify instruments to assess fine motor skills in preschool children with characteristics that facilitate their administration by the educator in the classroom context, i.e., requiring little administration time, not requiring much experience or training, the possibility of being administered to the group/class, few material resources, and the results can be easily interpreted, classified, and associated with mathematical performance.

The influence of home environmental factors on kindergarten children's addition strategy use

Young children vary widely in their levels of math knowledge, their abilities to solve math problems, and the strategies they use to solve math problems. As much of later math builds on children's early understanding of basic math facts and problem-solving strategies, understanding influences on children's early problem solving is important. Few studies, however, have examined the home environment in relation to children's strategy use during arithmetic problems. We examined how both structural characteristics of children's home environments, such as socioeconomic status (SES), as well as the learning environment, such as engagement in math and literacy activities at home, related to their use of problem-solving strategies for numerical addition problems. Kindergarten children from diverse backgrounds completed a measure of addition problem solving and strategy use, including simple and complex numerical problems. Strategies were coded based on a combination of accuracy and strategy sophistication, with higher scores indicating problems solved correctly with more sophisticated strategies. Parents completed a home activities questionnaire, reporting the frequency with which they and their child had engaged in math and literacy activities at home over the past month. An exploratory factor analysis identified three components of the home activities - a basic activities factor, an advanced math activities factor, and a literacy activities factor. Findings indicated that SES related to children's strategy sophistication, and frequency of engaging in advanced math and literacy activities at home predicted strategy sophistication, however, engaging in activities at home did not moderate the relations between SES and strategy sophistication. This suggests that family engagement in activities at home may promote early arithmetic skills, and that the role of home environmental characteristics should be considered in children's arithmetic strategy use and performance over development.

Executive functions and mathematical competence in Chinese preschool children: A meta-analysis and review

Numerous studies have been conducted on the correlation between preschool children’s executive functions and mathematical competence, the findings of those studies are inconsistent. This study used meta-analysis to investigate the correlation between executive functions and mathematical competence of preschool children in China, and then explored the moderating effects of age, gender, and instruments. The researchers conducted an extensive search of CNKI, Web of Science, Google Scholar and used screening criteria to identify 22 studies of Chinese preschoolers aged 3–7 years from 2007 to 2021. The findings indicated that there was a positive correlation between Chinese preschool children’s executive functions and mathematical competence (r = 0496), of which the effect size between mathematical competence and inhibition control was 0.347, and the effect size for working memory was 0.432, with an effect size of 0.370 for cognitive flexibility. Furthermore, Moderation analysis suggests that the preschoolers’ age, gender, and instruments affected the association between the executive functions and mathematical competence. The implications of these findings for theory and practice deserve further discussion.

Developing mental number line games to improve young children's number knowledge and basic arithmetic skills

The learning of number knowledge in childhood may directly influence children's mathematics learning ability in subsequent periods. Previous studies also show that the difficulties in mathematics learning faced by schoolchildren are mainly rooted in the lack of number knowledge in early childhood. Focusing on the development of numerical knowledge and basic arithmetic skills in early childhood, this study designed a linear number line game based on the theory of the mental number line. Accordingly, this study examined the effectiveness of the linear number line game in children's learning of number concepts and arithmetic skills and compared the effectiveness of the linear number line game with that of two other games (a nonlinear number line game and a non-number-line game). This study adopted a quasi-experimental research design. A total of 140 young children from remote areas of eastern Taiwan participated and were divided into three experimental groups and one control group, and a pretest-posttest experiment was conducted. The experimental results showed that the linear number line game could help children to acquire numerical knowledge effectively, especially in number line estimation compared with other experimental groups. In terms of the learning effectiveness of basic arithmetic skills (e.g., addition, subtraction), the two number line games (linear and nonlinear number line games) are significantly superior to the non-number-line game (traditional number decomposition and synthesis game). This study recommends that preschool teachers use linear number line games to improve children's numerical knowledge and arithmetic skills.

Environmental influences on mathematics performance in early childhood

Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.

Parental math input is not uniformly beneficial for young children: The moderating role of inhibitory control

Recent work has stressed the importance of considering child-level propensities and environmental opportunities when studying early math achievement; however, few studies investigate the interaction between these factors. This study examined whether children's inhibitory control moderates the association between parental math input and children's math performance. Parental math input via number talk and parent-reported frequencies of math activities were measured in 123 children (M age = 3.9 years) and one of their parents. High levels of parent number talk were associated with higher math achievement among children with higher inhibitory control. This association was not seen in children with lower inhibitory control, for children's vocabulary as the outcome measure, or for parents' overall talk or parent-reported math activities as the opportunity measures. Thus, children may differentially benefit from parental math input depending on their cognitive abilities and this association is specific to parental number talk and children's math abilities.

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

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

Associations Between Children’s Numeracy Competencies, Mothers’ and Fathers’ Mathematical Beliefs, and Numeracy Activities at Home

Children’s numeracy competencies are not only relevant for their academic achievement, but also later in life. The development of early numeracy competencies is influenced by children’s learning environment. Here, the home numeracy environment (HNE) and parent’s own beliefs about mathematics play an important role for children’s numeracy competencies. However, only a few studies explicitly tested these associations separately for mothers and fathers. In our study, we assessed mothers’ and fathers’ mathematical gender stereotypes, self-efficacy and their beliefs on the importance of mathematical activities at home, and tested their associations with parents’ numeracy activities and children’s numeracy competencies in a sample of N = 160 children (n = 80 girls) with an average age of M = 59.15 months (SD = 4.05). Both, fathers and mothers regarded boys as being more competent in mathematics than girls. Fathers when compared to mothers reported a greater mathematical self-efficacy. Further, only mothers’ self-efficacy was associated with the frequency of numeracy activities with the study child. In contrast, only fathers’ beliefs on the importance of mathematics was associated with their numeracy activities which, in turn, predicted children’s numeracy competencies. However, the non-invariant constructs and varying results lead to the question whether a revision of existing scales assessing parental beliefs and home numeracy activities is needed to investigate differences of mothers and fathers and their potential associations with children’s numeracy outcomes.

Get in touch with numbers - an approximate number comparison task in the haptic modality

The Approximate Number System (ANS) is conceptualized as an innate cognitive system that allows humans to perceive numbers of objects or events (>4) in a fuzzy, imprecise manner. The representation of numbers is assumed to be abstract and not bound to a particular sense. In the present study, we test the assumption of a shared cross-sensory system. We investigated approximate number processing in the haptic modality and compared performance to that of the visual modality. We used a dot comparison task (DCT), in which participants compare two dot arrays and decide which one contains more dots. In the haptic DCT, 67 participants had to compare two simultaneously presented dot arrays with the palms of their hands; in the visual DCT, participants inspected and compared dot arrays on a screen. Tested ratios ranged from 2.0 (larger/smaller number) to 1.1. As expected, in both the haptic and the visual DCT responses similarly depended on the ratio of the numbers of dots in the two arrays. However, on an individual level, we found evidence against medium or stronger positive correlations between “ANS acuity” in the visual and haptic DCTs. A regression model furthermore revealed that besides number, spacing-related features of dot patterns (e.g., the pattern’s convex hull) contribute to the percept of numerosity in both modalities. Our results contradict the strong theory of the ANS solely processing number and being independent of a modality. According to our regression and response prediction model, our results rather point towards a modality-specific integration of number and number-related features.

Extending ideas of numerical order beyond the count-list from kindergarten to first grade

Ordinal processing plays a fundamental role in both the representation and manipulation of symbolic numbers. As such, it is important to understand how children come to develop a sense of ordinality in the first place. The current study examines the role of the count-list in the development of ordinal knowledge through the investigation of two research questions: (1) Do K-1 children struggle to extend the notion of numerical order beyond the count-list, and if so (2) does this extension develop incrementally or manifest as a qualitative re-organization of how children recognize the ordinality of numerical sequences. Overall, we observed that although young children reliably identified adjacent ordered sequences (i.e., those that match the count-list; '2-3-4') as being in the correct ascending order, they performed significantly below chance on non-adjacent ordered trials (i.e., those that do not match the count-list but are in the correct order; '2-4-6') from the beginning of kindergarten to the end of first grade. Further, both qualitative and quantitative analyses supported the conclusion that the ability to extend notions of ordinality beyond the count-list emerged as a conceptual shift in ordinal understanding rather than through incremental improvements. These findings are the first to suggest that the ability to extend notions of ordinality beyond the count-list to include non-adjacent numbers is non-trivial and reflects a significant developmental hurdle that most children must overcome in order to develop a mature sense of ordinality.

Establishing Health Mentals on the Use of Number Sense on Operations with Integers

This study aimed to establish health mentals on the use of number sense on operations with integers in Indonesian elementary school level. Setting of the study was a Private Elementary School in Indonesia, Sekolah Dasar Muhammadiyah Terpadu (SDMT), class VI students. This research was a qualitative study utilizing test and interview as data collection technique. The result of the study showed that on the use of number sense on operations with integers are: numeracy skills 52.2%, numerical knowledge 30.5%, transformation skills 21.7%, estimation skills 65.5%, and numerical patterns 52.2% which is categorized a healthy mental.

Parental (STEM) Occupations, the Home Numeracy Environment, and Kindergarten Children’s Numerical Competencies

Children’s early numerical competencies are of great importance for later academic achievement. Young children gain these competencies in the context of the home numeracy environment (HNE). Additionally, child characteristics and families’ socioeconomic status (SES) are associated with children’s competencies. In this study, we investigated parents’ occupations (i.e., STEM or non-STEM occupation) as a specific aspect of the SES to understand whether parental occupations are associated with children’s numerical competencies and whether such an association may depend on the HNE. We analysed data from a sample of N = 190 children (Mage = 63.58 months; SD = 4.41) at two measurement points. Correlational analyses and crossed-lagged models were conducted to predict children’s numerical competencies by a global measure of the HNE and parental STEM vs. non-STEM occupations. We found significant associations between parents’ learned and current occupations and the HNE. Further, significant associations between parents’ learned occupations and children’s numerical competencies were observed. However, parents’ current occupations were not significantly associated with children’s numerical competencies. Consequently, more specific facets of the SES instead of a global measure seem to be associated with children’s numerical competencies. A greater focus on specific differences between family characteristics and their potential impact on children’s HNE and the development of their numerical competencies seems expedient.

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

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

Measuring Emerging Number Knowledge in Toddlers

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.

Factor structure of early numeracy: evaluation of a measurement model in greek-speaking children with intellectual disabilities

Exploring the individual differences of the longitudinal growth of early numeracy (EN) in young children with Intellectual disabilities (IDs) prerequires the critical stage of exploring and validating the potential factor structure. Despite the fact that Relational Skills (RS), Counting Skills (CS) and Operations (O) are expected to constitute distinct domains of EN, there is not sufficient evidence to support either the above position or the position that they are different means of assessing a general-informal numeracy skill construct. This study was designed to shed light in the field through the evaluation of a measurement model describing the structure of RS, CS and O domains of EN and their interrelation. The sample included N = 155 children with IDs, enrolled in special school classes, mentally aged between 5;02 (y;m) and 6;10 (M = 5.11, SD = 0.974). Confirmatory Factor Analysis indicated a "good fit" of the two-factor model (RS, CS + O) of EN in ID (RMSEA=.029 < 0.08, CFI = 0.98 ≥ 0.90 and SRMR = 0.000 < 0.08). No measurement invariance across gender was reported for the proposed two-factor model of EN. The nested EN models validated full measurement invariance across gender. Finally, educational implications are discussed.

When one size does not fit all: A latent profile analysis of low-income preschoolers' math skills

On average, preschoolers from lower-income households perform worse on symbolic numerical tasks than preschoolers from middle- and upper-income households. Although many recent studies have developed and tested mathematics interventions for low-income preschoolers, the variability within this population has received less attention. The goal of the current study was to describe the variability in low-income children's math skills using a person-centered analysis. We conducted a latent profile analysis on six measures of preschoolers' (N = 115, mean age = 4.6 years) numerical abilities (nonsymbolic magnitude comparison, verbal counting, object counting, cardinality, numeral identification, and symbolic magnitude comparison). The results showed different patterns of strengths and weaknesses and revealed four profiles of numerical skills: (a) poor math abilities on all numerical measures (n = 13), (b) strong math abilities on all numerical measures (n = 41), (c) moderate abilities on all numerical measures (n = 35), and (d) strong counting and numeral skills but poor magnitude skills (n = 26). Children's age, working memory, and inhibitory control significantly predicted their profile membership. We found evidence of quantitative and qualitative differences between profiles, such that some profiles were higher performing across tasks than others, but the overall patterns of performance varied across the different numerical skills assessed.

Parent-based training of basic number skills in children with Down syndrome using an adaptive computer game

BACKGROUND

Numeracy is an area of difficulty for children with Down syndrome (DS). It has been demonstrated that The Number Race, a non-commercial adaptive computer game designed to foster basic mathematical abilities, represents a promising instrument to enhance these skills in children with DS when delivered by an expert in a clinical setting.

AIMS

In the present study, we assessed the efficacy of The Number Race when administered at home by properly instructed and remotely supervised parents.

METHODS AND PROCEDURES

Basic numerical skills were assessed before and after training, as well as at three-months follow-up. Performance of children with DS who worked at home with the parent (PG) was compared with that of children who received the training by an expert (EG). For both groups, the training lasted ten weeks, with two weekly sessions of 20-30 min.

OUTCOMES AND RESULTS

Results show that both groups improved across various measures of numerical proficiency, including the overall score of the numeracy assessment battery, while only the EG showed an improvement in a measure of mental calculation. The improvements were maintained three months after the end of the training.

CONCLUSIONS AND IMPLICATIONS

These findings confirm the efficacy of The Number Race and extend it to an home-based setting, whereby parents administer the training with external supervision.

Associations Between Repeating Patterning, Growing Patterning, and Numerical Ability: A Longitudinal Panel Study in 4- to 6-Year Olds

The present study aimed to analyze the direction of the associations between repeating patterning, growing patterning, and numerical ability. Participants were 410 children who were annually assessed on their repeating patterning, growing patterning, and numerical ability, at ages 4, 5, and 6 years (i.e., spring 2017, 2018, and 2019). A cross-lagged panel model identified bidirectional associations between all three abilities from ages 4 to 5 years while taking into account spatial skills. From ages 5 to 6 years, both patterning abilities predicted later numerical ability, but the reverse was no longer true. Associations between performances on both pattern types also disappeared. Results highlight the unique associations between repeating patterning, growing patterning, and numerical ability, above spatial skills.

No Association Between the Home Math Environment and Numerical and Patterning Skills in a Large and Diverse Sample of 5- to 6-year-olds

Selecting a large and diverse sample of 5–6-year-old preschool children (179 boys and 174 girls; M_age = 70.03 months, SD_age = 3.43), we aimed to extend previous findings on variability in children’s home math environment (i.e., home math activities, parental expectations, and attitudes) and its association with children’s mathematical skills. We operationalized mathematics in a broader way than in previous studies, by considering not only children’s numerical skills but also their patterning skills as integral components of early mathematical development. We investigated the effects of children’s gender and socioeconomic status (SES) on their home math environment, examined the associations between children’s home math environment and their mathematical skills, and verified whether these associations were moderated by children’s gender and/or SES. Parents of 353 children completed a home math environment questionnaire and all children completed measures of their numerical (e.g., object counting) and patterning skills (e.g., extending repeating patterns). Results indicated no effect of children’s gender on their home math environment. There was no effect of SES on the performed home math activities, but small SES differences existed in parents’ math-related expectations and their attitudes. We found no evidence for associations between children’s home math environment and their mathematical skills. Furthermore, there were no moderating effects of gender or SES on these associations. One explanation for these findings might relate to the characteristics of the general preschool system in the country of the present study (Belgium). Future studies should consider the effect of the preschool learning environment because it might explain differences between studies and countries with regard to the home math environment and its association with mathematical skills.

The Multifactorial Nature of Early Numeracy and Its Stability

Early numeracy is a robust predictor of later mathematical abilities. So far, early numeracy has typically been presented as a unitary or two-factorial construct. Nevertheless, there is recent evidence suggesting that it may also be reflected by more basic numerical competences. However, the structure and stability of such a multifactorial model of early numeracy over time has not been investigated yet. In the present study, we used data from a large, longitudinal sample (N = 1292) in the United States with assessments of math ability in prekindergarten and kindergarten to evaluate both the factorial structure of early numeracy and its stability over time. Confirmatory factor analysis identified four distinct basic numerical competences making up early numeracy in prekindergarten: patterning/geometry, number sense, arithmetic, and data analysis/statistics. Stability as tested by means of measurement invariance indicated configural invariance of these four factors from prekindergarten to kindergarten. This reflected that early numeracy in kindergarten was made up by the same four basic numerical competences as in prekindergarten and thus seemed rather stable over the course of preschool. These findings may not only have implications for research on numerical cognition but particularly for diagnostic processes or the development of interventions in educational practice.

Neural Correlate Differences in Number Sense Between Children With Low and Middle/High Socioeconomic Status

Although some cognitive studies provided reasons that children with low socioeconomic status (SES) showed poor mathematical achievements, there was no explicit evidence to directly explain the root of lagged performance in children with low SES. Therefore, the present study explored the differences in neural correlates in the process of symbolic magnitude comparison between children with different SESs by the event-related potentials (ERPs). A total of 16 second-graders from low-SES families and 16 from middle/high-SES families participated in this study. According to the results of anterior N1 (early attention) and P2 (extraction of numerical meaning) over the frontal region, the differences among children with different SESs were manifested as differences in general neural activities in terms of attention and top-down cognitive control. In the late stage of cognitive processing, there was no significant difference in the average amplitude of the late positive component (LPC) between children with different SES, indicating that low SES did not influence the information encoding and memory updating of numerical representation, which was responsible by the parietal lobe. The educational implications of this study are mentioned in the discussion.

Longitudinally adaptive assessment and instruction increase numerical skills of preschool children

Social inequality in mathematical skill is apparent at kindergarten entry and persists during elementary school. To level the playing field, we trained teachers to assess children's numerical and spatial skills every 10 wk. Each assessment provided teachers with information about a child's growth trajectory on each skill, information designed to help them evaluate their students' progress, reflect on past instruction, and strategize for the next phase of instruction. A key constraint is that teachers have limited time to assess individual students. To maximize the information provided by an assessment, we adapted the difficulty of each assessment based on each child's age and accumulated evidence about the child's skills. Children in classrooms of 24 trained teachers scored 0.29 SD higher on numerical skills at posttest than children in 25 randomly assigned control classrooms (P = 0.005). We observed no effect on spatial skills. The intervention also positively influenced children's verbal comprehension skills (0.28 SD higher at posttest, P < 0.001), but did not affect their print-literacy skills. We consider the potential contribution of this approach, in combination with similar regimes of assessment and instruction in elementary schools, to the reduction of social inequality in numerical skill and discuss possible explanations for the absence of an effect on spatial skills.

When beliefs matter most: Examining children's math achievement in the context of parental math anxiety

A growing body of research suggests that parents' beliefs about and attitudes toward math predict their young children's math skills. However, limited research has examined these factors in conjunction with one another or explored potential mechanisms underlying these associations. In a sample of 114 preschool-aged children and their parents, we examined how parents' beliefs about math and math anxiety together relate to children's math achievement and how parents' practices to support math might explain these associations. We used a range of measures of parental math input, including survey measures of the home numeracy environment as well as observations of number talk. Parents with stronger beliefs about the importance of math tended to have children with more advanced math skills, and parents with math anxiety tended to exacerbate the effects of these beliefs such that children whose math-anxious parents held strong beliefs about math's importance performed best. Furthermore, we found some evidence that parents' math practices may relate to this interaction or to children's math skills, but no single measure of math input mediated the effect of the interaction between parental math anxiety and parental math beliefs on children's math outcomes. Thus, parents' math anxiety differentially relates to children's math performance depending on parents' beliefs about math, but future research is needed to uncover the specific mechanisms through which these processes operate.

Probing the Relationship Between Home Numeracy and Children's Mathematical Skills: A Systematic Review

The concept of home numeracy has been defined as parent–child interactions with numerical content. This concept started to receive increasing attention since the last decade. Most of the studies indicated that the more parents and their children engage in numerical experiences, the better children perform in mathematical tasks. However, there are also contrasting results indicating that home numeracy does not play a role or that there is a negative association between the parent–child interactions and children's mathematics performance. To shed light on these discrepancies, a systematic review searching for available articles examining the relationship between home numeracy and mathematical skills was conducted. Thirty-seven articles were retained and a p-curve analysis showed a true positive association between home numeracy and children's mathematical skills. A more qualitative investigation of the articles revealed five common findings: (1) Advanced home numeracy interactions but not basic ones are associated with children's mathematical skills. (2) Most participants in the studies were mothers, however, when both parents participated and were compared, only mothers' reports of formal home numeracy activities (i.e., explicit numeracy teaching) were linked to children's mathematical skill. (3) Formal home numeracy activities have been investigated more commonly than informal home numeracy activities (i.e., implicit numeracy teaching). (4) The number of studies that have used questionnaires to assess home numeracy is larger compared with the ones that have used observations. (5) The majority of the studies measured children's mathematical skills with comprehensive tests that index mathematical ability with one composite score rather than with specific numerical tasks. These five common findings might explain the contradictory results regarding the relationship between home numeracy and mathematical skills. Therefore, more research is necessary to draw quantitative conclusions about these five points.

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

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

Finding patterns in objects and numbers: Repeating patterning in pre-K predicts kindergarten mathematics knowledge

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns-predictable sequences that follow a rule-are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, focusing on development in children aged 4-6 years. The current study examined the relation between 65 preschool children's repeating patterning knowledge (via a fast, teacher-friendly measure) and their end-of-kindergarten broad math and numeracy knowledge, controlling for verbal and visual-spatial working memory (WM) skills as well as end-of-pre-K (pre-kindergarten) broad math knowledge. Relations were also examined between repeating patterning and specific aspects of numeracy knowledge-knowledge of the count sequence to 100 and the successor principle. Children's repeating patterning knowledge was significantly predictive of their broad math and general numeracy knowledge, as well as one specific aspect of their numeracy knowledge (counting to 100), even after controlling for verbal and visual-spatial WM skills. Further, repeating patterning knowledge remained a unique predictor of general numeracy knowledge and counting to 100 after controlling for end-of-pre-K broad math knowledge. The relation between repeating patterning and mathematics may be explained by the central role that identifying predictable sequences based on underlying rules plays in both. Theories of math development and early math instruction standards should thus give even greater attention to the role of children's repeating patterning knowledge.

Are differences between social classes reduced by non-symbolic numerical tasks? Evidence from the ELFE cohort

BACKGROUND

Young children's mathematics abilities may be divided between symbolic and non-symbolic skills. Lower performance of SES disadvantaged versus advantaged children has already been established in symbolic math.

AIM

This study aimed to verify the effect of children's SES category on non-symbolic mathematical (numerical) performance.

SAMPLE

The main sample comprises 4,955 children from the French longitudinal study, ELFE, tested when they were in the nursery school (4- to 5-year-olds).

METHOD

The distinction between symbolic and non-symbolic math skills based on the specific math assessment items used in the present study was verified on a larger sample. The SES-related difference in non-symbolic math skills was then examined in the ELFE sample only.

RESULTS

The children's performance in non-symbolic maths is significantly and almost as strongly correlated with their family's income and their mother's level of education as their performances in symbolic maths. Linear regression mixed-effects modelling shows that the score in non-symbolic maths (out of 100) of children from families with below median income is 3.8 points lower than that of their peers from families with above median income.

CONCLUSION

Children from disadvantaged SES backgrounds perform significantly lower than those from advantaged backgrounds in non-symbolic maths. Even if non-symbolic math skills retain an educational interest, they should not reduce the importance of symbolic math skills in young children.