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.

Contributions of preschool behavioral self-regulation and social skills to growth in different domains of early math knowledge.

The current study explored the relative contribution of individual differences in children's behavioral self-regulation and social skills (often referred to as learning-related skills) in the fall of preschool to children's rate of growth in different domains of early math knowledge through the spring of kindergarten. Participants were 684 children (Mage = 57.6 months, SD = 3.8, at Time 1 [fall of preschool]; 48% female; 43% Black, 32% White, 13% Latine, 11% multiracial, and 1% Asian). All children were from families with low incomes and lived in the midwestern United States. The math domains of informal numeracy, formal numeracy, and math language were assessed at four time points: fall and spring of preschool and fall and spring of kindergarten. Contrary to expectations, we did not find that either learning-related skill positively predicted rate of growth in math knowledge or observe differential relations by math domain. Rather, the relative contribution of behavioral self-regulation and social skills in the fall of preschool to rate of growth in math knowledge followed similar patterns across all math domains: an early advantage for children with higher initial social skills that stayed consistent over time (i.e., a nonsignificant slope effect) and an early advantage for children with higher initial behavioral self-regulation that diminished over time (i.e., a negative slope effect).

The home numeracy environment and children's math skills: The moderating role of parents' math anxiety.

Evidence suggests that parents' math anxiety moderates the association between parents' help in mathematics homework and first graders' mathematics skills. Understanding whether similar associations are evident in younger children, in regard to the home numeracy environment (HNE) is essential, given that early math skills are strong predictors of later academic outcomes, and children's skills prior to kindergarten are fostered principally by their parents. Thus, the purpose of this study was to examine the association and interaction between the HNE and parents' math anxiety related to preschool children's numeracy performance. Participants were 121 parent-child dyads. Results from hierarchical multiple regression models demonstrated that parents' math anxiety and the HNE, included as separate predictors of children's math skills, were not statistically significant. However, the interaction between HNE and parents' math anxiety was statistically significant, such that the positive association between HNE and children's numeracy skills emerged when parents felt less anxious about math. These findings highlight the importance of accounting for parents' math anxiety when exploring the home influences on children's numeracy skills.

Home science interactions and their relation to children's science core knowledge in preschool.

A limited body of work has examined the nature and scope of young children's science-related activities outside of the school context, and thus there is little understanding or consensus regarding what comprises the home science environment (HSE; e.g., interactions, activities, resources) and how specific factors of the HSE relate to children's science performance. The two primary goals of this study were to (a) examine the factor structure of a parent-report measure of home science interactions and (b) evaluate how these factors relate to the science core knowledge of young children from families with low incomes. A total of 125 families with children aged 3 to 5 years (52 girls) participated in the study. Children were assessed on a measure of science core knowledge, and parents completed a brief questionnaire on their home science interactions that included questions pertaining to both home science disciplinary core idea (DCI) engagement and home science and engineering practice (SEP) engagement. Findings revealed that although separating home science interactions into distinct DCI and SEP factors represented the data well, the best overall representation of home science interactions was a one-factor model that included only home DCI engagement items. In addition, home DCI engagement was significantly predictive of children's science core knowledge over and above a large group of covariates, including children's age, race/ethnicity, sex, and performance on math, executive function, and vocabulary tasks as well as their parents' education.

Why do early mathematics skills predict later mathematics and reading achievement? The role of executive function.

A robust association between young children's early mathematical proficiency and later academic achievement is well established. Less is known about the mechanisms through which early mathematics skills may contribute to later mathematics and especially reading achievement. Using a parallel multiple mediator model, the current study investigated whether executive function (integration of working memory, inhibition, and cognitive flexibility) can explain the relations between early mathematics skills and elementary school mathematics and reading achievement. Data in this longitudinal study were collected from 243 children during the last year of early childhood education and care (kindergarten ages 5 and 6 years), 1 year later in first grade, and 5 years later when the children were in fifth grade. Background variables (maternal education, age, sex, and immigrant status), kindergarten baseline skills, and mediating effects of first-grade mathematics, phonological awareness, vocabulary, and possible omitted variables were controlled. Results showed that first-grade executive function mediated the effects of kindergarten mathematics on fifth-grade mathematics and on reading achievement. These findings suggest that executive function may work as a mechanism that may help to explain the frequently found strong association between children's early mathematics skills and later mathematics and reading achievement.

Parents' math anxiety and mathematics performance of pre-kindergarten children.

Prior research demonstrates that individuals' math anxiety may be negatively related to their mathematics performance. However, little research has examined how caregivers' math anxiety is associated with children's mathematics performance prior to kindergarten. The purpose of this study was to investigate the relation between parents' math anxiety and the change in children's mathematics performance during the preschool year. Participants were 310 preschool-age children (155 female; 4.12-5.78 years of age, M = 5.20 years, SD = 0.29). Structural equation modeling results demonstrated that parents' math anxiety was significantly negatively related to change in children's mathematics performance during the pre-kindergarten year when controlling for fall mathematics performance and demographics. Moreover, multigroup path analyses revealed that this association did not differ for male versus female children.

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.

Prekindergarten classroom language environments and children's vocabulary skills.

The number of adult words children hear and conversational turns they experience are key aspects of their language environments. The current study examined variability in language environments throughout 2 prekindergarten days and variability within and between classrooms for 44 children (Mage = 4.77 years) in 11 classrooms in the United States. In addition, the study examined to what extent prekindergarten language environments are associated with children's vocabulary skills. Language environments varied considerably throughout the prekindergarten day and between classrooms, although children within the same prekindergarten classrooms had generally similar experiences. Conversational turns were more robustly associated with children's vocabulary skills than were adult words heard even when only examining within-classroom variability. Implications for understanding prekindergarten classroom language experiences and their associations with vocabulary skills are discussed.

Language Clearly Matters; Methods Matter Too.

Over two decades ago, the "30-million-word" gap rose to prominence after work by Hart & Risley (1995) suggested that children from families with low socioeconomic status (SES) heard fewer words than their peers from families with higher SES during their first 4 years of life. Recent research challenges the magnitude and even existence of this gap. However, due to methodological limitations, we know very little about the presence, magnitude, and settings in which there may be a word gap. Moreover, causal evidence is also limited. I highlight why it is critical for the field to have a more precise understanding of the nature of the word gap (or lack thereof) and potential avenues for better evaluating this phenomenon.

Predictive links among vocabulary, mathematical language, and executive functioning in preschoolers.

The primary aim of the current study was to identify the predictive relations of both vocabulary and mathematical language to executive functioning (EF) development using a sample of 558 preschool children (Mage = 57.75 months, SD = 3.71). Monthly family income ranged from $0 to $5539 (M = $1508.18, SD = $892.92). Among the sample, 44% of the children were African American, 32% were Caucasian, 12% were Hispanic, 11% were multiracial, and 1% were Asian. Although the primary study goal was to examine the extent to which language predicted EF development, a secondary aim was to explore whether EF also predicted vocabulary and mathematical language development. Regression analyses accounting for classroom-level variance and key covariates revealed that vocabulary was a significant predictor of EF at the end of preschool after accounting for fall EF. When mathematical language was added into the models, it was a significant predictor of EF, but vocabulary was no longer significant. Furthermore, EF predicted vocabulary and mathematical language. These findings suggest that young children's mathematical language skills are related to the acquisition of higher levels of EF during the preschool year and that there may be bidirectional associations between EF and mathematical language in preschool. Implications for future research are discussed.

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.

Relations between preschoolers' mathematical language understanding and specific numeracy skills.

Understanding of mathematical language is critical for numeracy skill development. However, prior research has focused exclusively on relations between mathematical language and numeracy skills, broadly measured. Thus, the aim of the current study was to explore more targeted relations between preschoolers' mathematical language and specific numeracy skills (e.g., cardinality, numeral comparison). The participants were 124 preschoolers aged 3.52 to 6.03 years (M = 4.78 years, SD = 0.53). Children were assessed on a battery of early numeracy skills and mathematical language as well as expressive vocabulary. Mixed-effects regression models were conducted, with school as a random effect and age, gender, and parental education as fixed effects covariates. Results indicated that mathematical language was significantly related to most numeracy skills, including verbal counting, one-to-one correspondence, numeral identification, cardinality, comparisons of sets and/or numerals, ordering numerals, and story problems. As hypothesized, mathematical language was not significantly related to either subitizing or formal addition because these skills are independent of general language ability. Importantly, mathematical language was generally more proximal to each of these numeracy skills than was general language. These results provide direction for future research, in particular for the development of more precise measures to identify children at risk for mathematics difficulties as well as the incorporation of focused mathematical language instruction within early mathematics interventions.

Foundations of mathematics and literacy: The role of executive functioning components.

The current study investigated the relations between the three cognitive processes that comprise executive functioning (EF)-response inhibition, working memory, and cognitive flexibility-and individual components of mathematics and literacy skills in preschool children. Participants were 125 preschool children ranging in age from 3.12 to 5.26years (M=4.17years, SD=0.58). Approximately 53.2% were female, and the sample was predominantly Caucasian (69.8%). Results suggest that the components of EF may be differentially related to the specific components of early mathematics and literacy. For mathematics, response inhibition was broadly related to most components. Working memory was related to more advanced mathematics skills that involve comparison or combination of numbers and quantities. Cognitive flexibility was related to more conceptual or abstract mathematics skills. For early literacy, response inhibition and cognitive flexibility were related to print knowledge, and working memory was related only to phonological awareness. None of the EF components was related to vocabulary. These findings provide initial evidence for better understanding the ways in which EF components and academic skills are related and measured. Furthermore, the findings provide a foundation for further study of the components of each domain using a broader and more diverse array of measures.

Early Numeracy Assessment: The Development of the Preschool Numeracy Scales.

RESEARCH FINDINGS: The focus of this study was to construct and validate twelve brief early numeracy assessment tasks that measure the skills and concepts identified as key to early mathematics development by the National Council of Teachers of Mathematics (2006) and the National Mathematics Advisory Panel (2008)-as well as critical developmental precursors to later mathematics skill by the Common Core State Standards (CCSS; 2010). Participants were 393 preschool children ages 3 to 5 years old. Measure development and validation occurred through three analytic phases designed to ensure that the measures were brief, reliable, and valid. These measures included: one-to-one counting, cardinality, counting subsets, subitizing, number comparison, set comparison, number order, numeral identification, set-to-numerals, story problems, number combinations, and verbal counting. PRACTICE OR POLICY: Teachers have extensive demands on their time, yet, they are tasked with ensuring that all students' academic needs are met. To identify individual instructional needs and measure progress, they need to be able to efficiently assess children's numeracy skills. The measures developed in this study are not only reliable and valid, but also easy to use and can be utilized for measuring the effects of targeted instruction on individual numeracy skills.

Working memory and language: skill-specific or domain-general relations to mathematics?

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills.

Evaluating the components of an emergent literacy intervention for preschool children at risk for reading difficulties.

Many preschool children are at risk for reading problems because of inadequate emergent literacy skills. Evidence supports the effectiveness of interventions to promote these skills, but questions remain about which intervention components work and whether combining intervention components will result in larger gains. In this study, 324 preschoolers (mean age=54.32 months, SD=5.88) from low-income backgrounds (46% girls and 54% boys; 82% African American, 14% White, and 4% other) were randomized to combinations of meaning-focused (dialogic reading or shared reading) and code-focused (phonological awareness, letter knowledge, or both) interventions or a control group. Interventions had statistically significant positive impacts only on measures of their respective skill domains. Combinations of interventions did not enhance outcomes across domains, indicating instructional needs in all areas of weakness for young children at risk for later reading difficulties. Less time for each intervention in the combined phonological awareness and letter knowledge intervention conditions, however, did not result in reduced effects relative to nearly twice as much time for each intervention when children received either only the phonological awareness intervention or only the letter knowledge intervention. This finding suggests that a relatively compact code-focused intervention can address the needs of children with weaknesses in both domains.

International comparisons of the home mathematics environment and relations with children's mathematical achievement.

BACKGROUND: Home mathematics environment (HME) research has focused on parent-child interactions surrounding numerical activities as measured by the frequency of engaging in such activities. However, HME survey questions have been developed from limited perspectives (e.g., Early Childhood Research Quarterly, 27, 2012, 231; Journal of Social Issues, 64, 2008, 95; Early childhood mathematics education research: Learning trajectories for young children, Routledge, New York, 2009), by researchers from a small subset of countries (15; Psychological Bulletin, 147, 2020, 565), which may skew our interpretations. AIMS AND SAMPLE: This study broadened international representation by leveraging secondary data from the 2019 TIMSS to examine the variation of the frequency and reliability of the HME scale and its relation to children's mathematical achievement. Across 54 countries, 231,138 parents and children (Mage = 10.22 years; 51% male) participated in the larger study. METHODS: Parents completed a retrospective home environment survey and children were assessed on mathematics skills. Basic frequency descriptive statistics, Cronbach's alpha reliability coefficients, and Pearson's r correlation coefficients were used to assess variability across countries. RESULTS: Findings suggested that families in certain countries engaged in home mathematics activities more frequently than families in other countries; however, the HME scale demonstrated acceptable internal consistency across families in all countries (M α = .79; range = [.73, .89]). Further, the average relation between HME and mathematical achievement was r = .15 with a range between r = .02 to r = .41. CONCLUSION: Our results indicate substantial variation across countries in the HME-mathematical achievement association. These findings underscore the importance of international representation in advancing research on the diversity of a child's home environment.

Factor structure of school readiness skills: conceptual vs. statistical distinctions.

Introduction: School readiness skills are a broad set of abilities that children develop in early childhood that support achievement once they enter formal schooling. Three components of school readiness skills are of focus in the current study: executive function (EF), language/literacy, and mathematics. The current study examines to what extent 13 direct assessments of these skills statistically align with theoretical models for distinct construct- and timepoint-specific latent factors. Methods: The sample included 684 children (52.34% male; 42% Black/African American; Mage = 4.80 years in the fall of prekindergarten) assessed in the fall and spring of the prekindergarten year. Results: Factor analyses revealed the most statistical support for a model with a latent random intercept across timepoints and constructs, along with timepoint-specific latent factors in the fall and spring of prekindergarten (independent of the random intercept). The timepoint-specific latent factors primarily consisted of early literacy and mathematics assessments. Discussion: These findings challenge commonly held practices of creating construct-specific latent factors in early childhood research and, to a lesser extent, timepoint-specific latent factors without consideration of the substantial shared variance across different constructs and timepoints. Implications for the factor structure and developmental theory of school readiness skills are considered, as well as practical considerations for future research.