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).

Corrigendum: Moving beyond dosage and adherence: a protocol for capturing dimensions of active child engagement as a measure of fidelity for social-emotional learning interventions.

[This corrects the article DOI: 10.3389/fpsyg.2022.1014713.].

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.

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.

Conceptualizing the factor structure of parents' math anxiety and associations with children's mathematics skills.

There is a growing literature examining the association between parents' math anxiety and children's mathematics skills. Previous research has considered parents' math anxiety as a unidimensional construct that primarily focused on parents' experiences doing mathematics themselves. However, this research did not account for parents' experiences when doing mathematics with their children. Thus, there were two goals of the present study: (1) to identify the structure of parents' math anxiety when considering context-dependent situations, and (2) to determine whether parental math anxiety was related to children's early numeracy skills. We conducted a series of confirmatory factor analyses using a sample of 155 preschool children (Mage  = 4.20 years, SD = 0.71; 51% female). The best fitting model of parents' math anxiety was a bifactor model, suggesting that parents' math anxiety was best conceptualized as a multidimensional construct. However, structural equation models showed parent math anxiety was not a significant predictor of children's numeracy performance. These findings provide a foundation for understanding parents' math anxiety as multidimensional and raise questions about potential mechanisms that may explain prior work finding mixed relations between math anxiety and children's numeracy performance.

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.

Examining Associations Between Food Insecurity, Inhibitory Control, and Body Mass Index in Preschoolers.

OBJECTIVE: This study examines relations between food insecurity, inhibitory control, and body mass index (BMI) in early childhood. METHOD: The sample comes from an evaluation of a state-funded prekindergarten program and includes 126 children (mean age = 4.73 yrs, female = 42%) from families with low incomes. Parents reported on their child's food insecurity. Child inhibitory control was assessed using a performance-based task, and children's height and weight were objectively collected at the same time as the inhibitory control assessment. A regression model was used to test whether inhibitory control moderated the association between food insecurity and BMI. The model included a large battery of covariates and adjusted for clustering at the classroom level. Ad hoc analyses were conducted to examine the robustness of findings to different conceptualizations of food insecurity based on the US Department of Agriculture's categories for severity. RESULTS: A significant interaction revealed that inhibitory control moderated the association between food insecurity and children's BMI percentile. Investigation of the simple slopes suggested that greater food insecurity was related to a higher BMI percentile among children who demonstrated stronger inhibitory control. In addition, results from ad hoc analyses examining categories of food insecurity indicated that experiencing very low food security was also related to a higher BMI among children with average and strong inhibitory control. CONCLUSION: This study makes a unique contribution to the existing literature by examining relations among food insecurity, inhibitory control, and BMI during a critical period in children's physical and brain development. Findings have implications for public health efforts to address childhood obesity among populations with low incomes.

Moving beyond dosage and adherence: A protocol for capturing dimensions of active child engagement as a measure of fidelity for social-emotional learning interventions.

Social-emotional competencies are important for school-readiness and can be supported through social-emotional learning (SEL) interventions in the preschool years. However, past research has demonstrated mixed efficacy of early SEL interventions across varied samples, highlighting a need to unpack the black box of which early interventions work, under what conditions, and for whom. In the present article we discuss the critical implementation component of active child engagement in an intervention as a potential point of disconnect between the intervention as designed and as implemented. Children who are physically present but unengaged during an intervention may lead to decreased average impacts of an intervention. Furthermore, measuring young children's active engagement with an intervention may help to guide iterative intervention development. We propose a four-step protocol for capturing the multi-dimensional and varied construct of active child engagement in a SEL intervention. To illustrate the utility of the protocol, we apply it to data from a pilot study of a researcher-implemented, semi-structured block play intervention focused on supporting the development of SEL and math skills in preschoolers. We then present future directions for the integration of active participant engagement into the measurement of implementation of SEL interventions for young children.

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.

Examining transactional relations between behavioral self-regulation and social-emotional functioning during the transition to kindergarten.

The present study examined longitudinal associations between behavioral self-regulation and social-emotional functioning across four waves of measurement during the transition from preschool to kindergarten in a low-income sample. Participants included two cohorts of children (N = 558; 51% male). Children in both cohorts were 4 years old (Cohort 1: M = 4.82 years, SD = .31; Cohort 2: M = 4.80 years, SD = .31). Forty-four percent of children were Black, 32% were White, 13% were Latino, 10% were Multiracial, and 1% were Asian. Monthly income ranged from $0-5,539 (M = $1,508.18, SD = $892.92). Two statistical methods were used to examine relations among constructs. The cross-lagged panel model revealed a mixed pattern of relations between behavioral self-regulation and two indicators of social-emotional functioning (social skills and behavior problems) over time. There were no significant relations among behavioral self-regulation and social-emotional functioning during the preschool year; however, evidence for bidirectional associations were found between the spring of preschool and the fall of kindergarten. There were no significant relations among behavioral self-regulation and behavior problems at any time point. Finally, there were bidirectional relations among social skills and behavior problems in preschool, but directional relations emerged after this time point. A second model that included random intercepts was also run with the cross-lagged paths. Results from this model indicated that the random intercepts between behavioral self-regulation, social skills, and behavior problems were significantly related. Implications for future research are discussed. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Examining Additive and Synergistic Relations Between Preschool Self-Regulation and Executive Function Skills: Predictions to Academic Outcomes.

In the present study, we examined the extent to which teacher-rated self-regulation and directly assessed executive function skills were independently, additively, or synergistically related to academic achievement during the transition to kindergarten. The sample included 126 children (42% female; M age = 4.73 years) from families with low incomes who participated in a larger evaluation of state-funded preschool. Regression models with children nested in their respective preschool classrooms investigated main effects and moderated effects of teacher-rated self-regulation skills manifested in preschool classroom behaviors and cognitive executive function skills assessed through direct assessments on math, literacy, and vocabulary in the spring of preschool and in the fall of kindergarten. Results revealed independent but not additive relations between executive function and math in the spring of preschool and self-regulation and literacy in the fall of kindergarten. One significant interaction emerged providing evidence for synergistic relations between teacher-rated self-regulation and directly assessed executive function for literacy at both timepoints across the transition to kindergarten. Implications for policy and practice are discussed.

Next Directions in Measurement of the Home Mathematics Environment: An International and Interdisciplinary Perspective.

This article synthesizes findings from an international virtual conference, funded by the National Science Foundation (NSF), focused on the home mathematics environment (HME). In light of inconsistencies and gaps in research investigating relations between the HME and children's outcomes, the purpose of the conference was to discuss actionable steps and considerations for future work. The conference was composed of international researchers with a wide range of expertise and backgrounds. Presentations and discussions during the conference centered broadly on the need to better operationalize and measure the HME as a construct - focusing on issues related to child, family, and community factors, country and cultural factors, and the cognitive and affective characteristics of caregivers and children. Results of the conference and a subsequent writing workshop include a synthesis of core questions and key considerations for the field of research on the HME. Findings highlight the need for the field at large to use multi-method measurement approaches to capture nuances in the HME, and to do so with increased international and interdisciplinary collaboration, open science practices, and communication among scholars.

Examining the Factor Structure of the Home Mathematics Environment to Delineate Its Role in Predicting Preschool Numeracy, Mathematical Language, and Spatial Skills.

A growing body of evidence suggests that the ways in which parents and preschool children interact in terms of home-based mathematics activities (i.e., the home mathematics environment; HME) is related to children's mathematics development (e.g., primarily numeracy skills and spatial skills); however, this body of evidence is mixed with some research supporting the relation and others finding null effects. Importantly, few studies have explicitly examined the factor structure of the HME and contrasted multiple hypothesized models. To develop more precise models of how the HME supports children's mathematics development, the structure of the HME needs to be examined and linked to mathematics performance. The purpose of this study was to extend prior work by replicating the factor structure of the HME (as one general HME factor and three specific factors of direct numeracy, indirect numeracy, and spatial) and using those factors to predict direct assessments of children's numeracy, mathematical language, and spatial skills. It was hypothesized that the general HME factor would be related to each direct assessment, the direct numeracy factor would be related to both numeracy and mathematical language, and the spatial factor would be related to spatial skills. Using a sample of 129 preschool children (M age = 4.71 years, SD = 0.55; 46.5% female), a series of confirmatory factor analyses were conducted. Results diverged somewhat from prior work as the best fitting model was a bifactor model with a general HME factor and two specific factors (one that combined direct and indirect numeracy activities and another of spatial activities) rather than three specific factors as had previously been found. Further, structural equation modeling analyses suggested that, in contrast to expectations, only the direct + indirect numeracy factor was a significant predictor of direct child assessments when accounting for age, sex, and parental education. These findings provide evidence that a bifactor model is important in understanding the structure of the HME, but only one specific factor is related to children's outcomes. Delineating the structure of the HME, and how specific facets of the HME relate to children's mathematics skills, provides a strong foundation for understanding and enhancing the mechanisms that support mathematics development.

Construct-Specific and Timing-Specific Aspects of the Home Environment for Children's School Readiness.

Prior evidence supports that the home environment is related to children's development of school readiness skills. However, it remains unclear how construct- and timing-specific aspects of the home environment are related to children's school readiness skills, unique from overall, stable aspects of home quality. Unpacking associations due to specific constructs and timing of the home environment may provide insights on the theoretical processes that connect the home environment to school readiness. Using data from the NICHD Study of Early Child Care and Youth Development (N = 1,364), the current study examines how timing (36 and 54 months) and constructs (educational stimulation and socio-emotional responsivity) of the home environment, relative to overall levels across time, relate to children's language skills, math skills, and externalizing behaviors. The overall, stable aspects of the home environment were significantly associated with children's language skills and externalizing problems. Additionally, there were significant paths from the stimulation construct at 54 months to math skills, language skills, and externalizing problems. These findings provide evidence that although the overall home environment is predictive of school readiness, the stimulation construct of the home environment at 54 months has additional concurrent relations to children's school readiness. Implications for the role of the home environment and children's school readiness are discussed.

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.