Mapping skills between symbols and quantities in preschoolers: The role of finger patterns.

Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4-year-olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence. RESEARCH HIGHLIGHTS: Children are more accurate in mapping between finger patterns and symbols (number words and Arabic digits) than in mapping finger patterns and quantities, indicating that fingers are processed holistically as symbolic codes. Children can map finger patterns to symbols above their corresponding cardinality level even in subset-knowers. Finger patterns may play a role in the process by which children learn to map symbols to quantities. Fingers patterns' use in the classroom context may be an adequate instructional and diagnostic tool.

The roles of mathematical language and emergent literacy skills in the longitudinal prediction of specific early numeracy skills.

Mathematical language (i.e., content-specific language used in mathematics) and emergent literacy skills predict children's broad numeracy development. However, little work has examined whether these domains predict development of individual numeracy skills (e.g., cardinality, number order). Thus, the aim of the current study was to examine longitudinal relations among mathematical language, emergent literacy skills, and specific early numeracy skills. Participants included 114 preschool children aged 3.12 to 5.26 years (M = 4.17 years, SD = 0.59). Specifically, this study examined whether mathematical language and three emergent literacy skills (print knowledge, phonological awareness, and general vocabulary) in the fall of preschool predicted 12 individual early numeracy skills in the spring, controlling for age, sex, rapid automatized naming, parent education, and autoregressors. Results indicated that mathematical language predicted development of most of the early numeracy skills (e.g., set comparison, numeral comparison, numeral identification), but findings for emergent literacy skills were not robust. Among the three emergent literacy skills, only print knowledge was a significant predictor of development in some specific numeracy skills, including verbal counting, number order, and story problems. Results highlight the important role of mathematical language in children's numeracy development and provide the foundation for future work in designing interventions to improve early numeracy skills.

New measures of number line estimation performance reveal children's ordinal understanding of numbers.

Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance.

Pivoting Training and Coaching for an Early Numeracy Intervention During COVID-19.

Early numeracy skills are vital for kindergarten students because they provide the foundation for acquiring mathematics skills in both kindergarten and subsequent years. Teacher support to intervene with kindergarteners at risk for poor mathematics learning outcomes is a promising approach to addressing this achievement gap. The current study replicates previous work on an established early numeracy intervention, ROOTS. In this instance, ROOTS uses remote professional development as a novel format for interventionist training support during the COVID-19 pandemic. Findings indicate that interventionists receiving remote support for implementing ROOTS found training and coaching acceptable and feasible. Remote training and coaching supported strong levels of implementation fidelity. Furthermore, children who received the ROOTS intervention outperformed their control group peers on post-test measures of mathematics achievement within a randomized controlled trial research design. Outcomes and implications for using remote professional development as a format for supporting educators in their use of early numeracy intervention programs are discussed within a pandemic-response context.

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.

Number line development of Chilean children from preschool to the end of kindergarten.

Children's performance on number line tasks reflects their developing number system knowledge. Before 5 years of age, most children perform poorly on even the simplest number lines (i.e., 0-10). Our goal was to understand how number line skills develop before formal schooling. Chilean preschoolers attempted a 0-10 number line task three times over 2 years: at the beginning of pre-kindergarten (M = 4:7 [years;months]; Time 1), at the end of pre-kindergarten (M = 5:0; Time 2), and at the end of kindergarten (M = 5:10; Time 3). We used latent class analysis to group children according to their patterns of performance across number targets. At Time 1, 86% of children had error patterns indicating that they randomly placed estimates on the line. At Time 2, 56% of children continued to respond randomly. At Time 3, 56% of children showed competent performance across the number line, 23% were accurate only near the endpoints, and 21% were accurate only for low target numbers near the origin. Latent transition analyses showed that the transition from less to more proficient estimation classes was predicted by children's number identification skills. Thus, number line performance changed dramatically from 4 to 6 years of age as children began to develop the cognitive and numerical skills necessary to accurately estimate numbers on a number line.

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

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

A probabilistic approach for quantifying children's subitizing span.

The development of enumeration skills over childhood is thought to reflect improvements in both subitizing (for small sets) and serial counting (for larger sets). However, investigations into the contribution of subitizing to advancing mathematics ability are limited by challenges in measuring subitizing capacity across developmental populations. Subitizing capacity in adults is traditionally assessed by calculating the bilinear inflection point for reaction times or accuracy across set sizes, but in children greater variability and dramatic improvements in counting ability introduce problems with this approach. This study demonstrates this limitation in a sample of elementary school children and proposes a novel probabilistic approach to measuring subitizing capacity. This metric captures well-established trends in the development of children's subitizing. Furthermore, the proposed metric predicts unique variance in symbolic arithmetic ability, corroborating previous research that suggests a foundational role for subitizing in the development of numerical cognition. Findings demonstrate the advantages of a probabilistic approach to determining subitizing capacity in young children and suggest that it may be practically and theoretically well-suited for investigating subitizing and its role in mathematics development.

Facilitating young children's numeracy talk in play: The role of parent prompts.

Previous research has demonstrated the contribution of parents' number language to children's own engagement with numbers and later mathematical achievement. Although there is evidence that both the quantity and complexity of parent number talk contribute to children's math learning, it is unclear whether different forms of parents' number talk-statements versus prompts-offer unique contributions to how children engage in math. We examined parent number talk among 50 dyads of parents and 2- to 4-year-olds during pretend play, coding parents' provisions of informative number statements and prompts inviting children to engage in number talk. The total amount (tokens) and diversity (types) of children's number words were analyzed separately. Parents' number utterances, particularly prompts about number, were infrequent. Both parents' number statements and their prompts were uniquely related to children's number word tokens. Only prompts were associated with children's number word types. Follow-up analyses indicated that prompts were associated with lengthier parent-child conversations about number than parent statements and that children used larger number words when responding to parent prompts than when they themselves initiated number talk. These findings highlight the importance of parents' prompts for enhancing the quality of parent-child math exchanges by providing opportunities for children to advance their current use of numerical language. Consequently, parents' use of number-related prompts may play an important role in children's early math engagement.

When do preschoolers learn specific mathematics skills? Mapping the development of early numeracy knowledge.

Children's mathematics skills undergo extensive development during the preschool years. Opportunities for engaging in mathematics in the preschool classroom, however, are limited, and activities and instruction are often targeted below children's skill levels. Although researchers have developed general learning trajectories of children's mathematics skills, no fine-grained trajectories across a broad range of mathematics skills exist. Such a fine-grained trajectory of when specific numeracy skills develop would allow preschool and kindergarten instruction to more appropriately match and scaffold children's mathematics capabilities. The current study examined preschool children's item-level performance on eight numeracy subtests at half-year age points throughout the preschool period. Data were compiled across six studies, and participants comprised 801 preschool children (age range = 3.12-5.99 years, M = 4.63, SD = 0.68). Children were grouped into six age categories (3, 3.5, 4, 4.5, 5, and 5.5 years). Linear regression analyses were used to investigate the number of children who correctly answered each item of a specific subtest within a particular age group. Findings provide clear trajectories of children's early mathematics skills that can be used to inform preschool classroom practices and facilitate the design of intervention studies.

Preschoolers' selective sustained attention and numeracy skills and knowledge.

This brief report addresses preschoolers' selective sustained attention (SSA) and early numeracy skills and knowledge. Past research indicates that children's attention and early numeracy are positively associated, yet some concerns have emerged about the age appropriateness of tools used to measure preschoolers' SSA. This study used a new measure-the Track-It Task-that demonstrates strong psychometric properties. In total, 31 at-risk preschoolers (Mage = 46.6 months) participated and were assessed on SSA, nonsymbolic quantity discrimination, and symbolic quantitative skills and knowledge. The ability to sustain attention in the face of distractions was positively correlated with preschoolers' verbal counting and one-to-one correspondence, Arabic numeral recognition, and cardinal principle knowledge. SSA was not significantly associated with child age or performance on a memory task. This study provides preliminary evidence that SSA may facilitate the process whereby young children become reliable counters and learn that the symbol system of numbers represents specific quantities.

Basic numerical competences in large-scale assessment data: Structure and long-term relevance.

Basic numerical competences are seen as building blocks for later numerical and mathematical achievement. The current study aimed at investigating the structure of early numeracy reflected by different basic numerical competences in kindergarten and its predictive value for mathematical achievement 6 years later using data from large-scale assessment. This allowed analyses based on considerably large sample sizes (N > 1700). A confirmatory factor analysis indicated that a model differentiating five basic numerical competences at the end of kindergarten fitted the data better than a one-factor model of early numeracy representing a comprehensive number sense. In addition, these basic numerical competences were observed to reliably predict performance in a curricular mathematics test in Grade 6 even after controlling for influences of general cognitive ability. Thus, our results indicated a differentiated view on early numeracy considering basic numerical competences in kindergarten reflected in large-scale assessment data. Consideration of different basic numerical competences allows for evaluating their specific predictive value for later mathematical achievement but also mathematical learning difficulties.

The home literacy and numeracy environment in preschool: Cross-domain relations of parent-child practices and child outcomes.

There is a growing body of evidence indicating that home literacy and numeracy environments are predictive of children's literacy and numeracy skills within their respective domains. However, there is limited research on the relations between the home literacy environment and numeracy outcomes and between the home numeracy environment and literacy outcomes. Specifically, there is limited information on relations between the home numeracy environment and specific literacy outcomes (e.g., vocabulary). The purpose of the current study was to investigate the relations of the home literacy and numeracy environments to children's literacy and numeracy outcomes both within and across domains. Participants were 114 preschool children and their parents. Children ranged in age from 3.01 to 5.17 years (M = 4.09 years) and were 54% female and 72% Caucasian. Parents reported the frequency of parent-child literacy (code-related practices and storybook reading) and numeracy practices. Children were assessed in the fall and spring of their preschool year on their literacy (definitional vocabulary, phonological awareness, and print knowledge) and numeracy skills. Four mixed-effects regression analyses were conducted to predict each of the child outcomes. Results indicate that although code-related literacy practices and storybook reading were not broadly predictive of children's literacy and numeracy outcomes, the home numeracy environment was predictive of numeracy and definitional vocabulary outcomes. These findings demonstrate a relation between the home numeracy environment and children's language development and contribute to the growing body of research indicating the important relations between early numeracy and language development.

Remedial early numeracy education: can children identified as having a language deficiency benefit?

BACKGROUND: Growing attention has been paid to the possibility of supporting early numeracy in at-risk kindergartners. Furthermore, it is assumed that language proficiency is an important prerequisite in early maths skills. AIMS: To examine whether remedial early numeracy education in kindergarten, which has been proven to be effective in general, is also beneficial for children with a language deficiency. METHODS & PROCEDURES: Based on intensive selection, four different conditions were included: two groups received remedial education, one consisting of children being language proficient (N = 86) and one of children with a language deficiency (N = 26), and two groups followed the regular curriculum, one consisting of children being language proficient (N = 51) and one of children with a language deficiency (N = 24). Remedial education was for 1.5 school years (90 sessions, 30 min per session, twice per week), following the programme 'The Road to Mathematics'. During this period, the children receiving remedial education did not attend the regular maths lessons in the classroom, which were offered for at least 1 h per week. Effects were assessed for early numeracy and mathematical skills (operationalized as basic calculation fluency) in kindergarten and first grade. OUTCOMES & RESULTS: Three analyses of covariance (ANCOVAs) revealed that, when accounting for achievement at pre-test, children with a language deficiency who received remedial numeracy education performed better on early numeracy skills in kindergarten and first grade than kindergartners with a language deficiency that followed the regular curriculum. Furthermore, they were able to catch up with their language proficient peers in early numeracy. However, children with a language deficiency who received remedial numeracy education did not differ from children who followed the regular curriculum on mathematical skills, suggesting that benefits for numeracy did not generalize to more advanced skills of addition and subtraction. CONCLUSIONS & IMPLICATIONS: Since, in general, it can be concluded that early numeracy education is indeed effective for kindergartners with a language deficiency, this study finds evidence that intensive support is desirable for children with delayed or impaired language development.

Training counting skills and working memory in preschool.

Previous studies have shown that early numeracy skills predict later mathematics learning and that they can be improved by training. Cognitive abilities, especially working memory (WM), play an important role in early numeracy, as well. Several studies have shown that working memory is related to early numeracy. So far, existing literature offers a good few examples of studies in which WM training has led to improvements in early numerical performance as well. In this study, we aim at investigating the effects of two different training conditions: (1) counting training; and (2) simultaneous training of WM and counting on five- to six-year-old preschoolers' (N = 61) counting skills. The results show that domain-specific training in mathematical skills is more effective in improving early numerical performance than WM and counting training combined. Based on our results, preschool-aged children do not seem to benefit from short period group training of WM skills. However, because of several intervening factors, one should not conclude that young children's WM training is ineffectual. Instead, future studies should be conducted to further investigate the issue.

Explaining numeracy development in weak performing kindergartners.

Gaining better insight into precursors of early numeracy in young children is important, especially in those with inadequate numeracy skills. Therefore, in the current study, visual and verbal working memory, non-symbolic and symbolic comparison skills, and specific math-related language were used to explain early numeracy performance and development of weak performing children throughout kindergarten. The early numeracy ability of both weak performers and typical performers was measured at four time points during 2 years of kindergarten to compare growth rates. Results show a significant faster development of early numeracy in the weak performers. The development of weak performers' numeracy was influenced by verbal working memory, symbolic comparison skills, and math language, whereas only math language was positively related to the slope of typical performers' numeracy. In the weak performers, visual working memory, non-symbolic comparison skills, and math language showed an effect on the initial early numeracy level of these children. The intercept of the typical performers was predicted by five covariates, all except non-symbolic comparison.

Formal and informal home learning activities in relation to children's early numeracy and literacy skills: the development of a home numeracy model.

The purpose of this study was to propose and test a model of children's home numeracy experience based on Sénéchal and LeFevre's home literacy model (Child Development, 73 (2002) 445-460). Parents of 183 children starting kindergarten in the fall (median child age=58 months) completed an early home learning experiences questionnaire. Most of the children whose parents completed the questionnaire were recruited for numeracy and literacy testing 1 year later (along with 32 children from the inner city). Confirmatory factor analyses were used to reduce survey items, and hierarchical regression analyses were used to predict the relation among parents' attitudes, academic expectations for their children, reports of formal and informal numeracy, and literacy home practices on children's test scores. Parental reports of formal home numeracy practices (e.g., practicing simple sums) predicted children's symbolic number system knowledge, whereas reports of informal exposure to games with numerical content (measured indirectly through parents' knowledge of children's games) predicted children's non-symbolic arithmetic, as did numeracy attitudes (e.g., parents' enjoyment of numeracy). The home literacy results replicated past findings; parental reports of formal literacy practices (e.g., helping their children to read words) predicted children's word reading, whereas reports of informal experiences (i.e., frequency of shared reading measured indirectly through parents' storybook knowledge) predicted children's vocabulary. These findings support a multifaceted model of children's early numeracy environment, with different types of early home experiences (formal and informal) predicting different numeracy outcomes.

Developmental associations of fundamental motor skills and executive functions in preschoolers - The role of the physical activity and the effects on early numeracy.

BACKGROUND: Physical activity, fundamental motor skills, executive functions and early numeracy have shown to be related, but very little is known about the developmental relations of these factors. PROCEDURE: We followed 317 children (3-6 years) over two years. Fundamental motor skills and executive functions (inhibition+switching, updating) were measured at all time points (T1, T2, T3) and physical activity at T1 and early numeracy at T3. MAIN FINDINGS: Children with better fundamental motor skills at T1 developed slower in inhibition and switching. Fundamental motor skills developed faster in children who had better initial inhibition and switching ability. Vigorous physical activity at T1 was associated with a weaker initial inhibition and switching. The initial level and the developmental rate of updating were related to better early numeracy skills. CONCLUSIONS: Findings indicate that fundamental motor skills and executive functions are developmentally related, and updating is an important predictor for early numeracy in preschoolers.

Intervention effects on low performing preschoolers' early mathematical skills: Adding fundamental motor skill practice as a supporting method.

BACKGROUND: This study examined the effects of (1) combined early numeracy and fundamental motor skills (MovEN), (2) early numeracy, and (3) fundamental motor skills intervention programs on children's early mathematical and fundamental motor skills, and how individual background variables affect the effectiveness of these interventions. PROCEDURE: Together 50 preschoolers participated in the interventions (16 × 45 min sessions). Children's early numeracy, mathematical problem-solving, and fundamental motor skills were measured once before and twice after the interventions. MAIN FINDINGS: The results showed that the MovEN and early numeracy -interventions were effective in improving children's early numeracy, and mathematical problem-solving. Whereas the MovEN and fundamental motor skills interventions improved children's fundamental motor skills. From individual factors, only updating ability predicted the intervention's effectiveness over and above prior performance. CONCLUSION: The results suggest that children's early mathematical and fundamental motor skills can be supported effectively at the same time with the MovEN -intervention.

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

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