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.

Kindergarten predictors of formal understanding of mathematical equivalence in second grade.

A longitudinal study was conducted to identify unique sources of individual differences in later understanding of the equal sign as a relational symbol of equivalence (i.e., formal understanding of mathematical equivalence). The sample included 141 children from a mid-sized city in the Midwestern United States (Mage = 6 years, 2 months in kindergarten; 88 boys, 53 girls; 71% white, 8% Hispanic or Latine, 7% Black, 3% Asian, 11% multiracial or other race/ethnicity; 42% qualified for free/reduced lunch). Children were assessed on three categories of skills in kindergarten including number knowledge, relational thinking, and executive functioning. These skills were hypothesized to provide a foundation for a formal understanding of mathematical equivalence (assessed in second grade) by preventing a specific, narrow misunderstanding of the equal sign that hinders learning. Results showed that kindergarten relational thinking, particularly tasks assessing nonsymbolic equivalence understanding, uniquely and positively predicted formal understanding of mathematical equivalence and negatively predicted the specific misunderstanding of the equal sign in second grade, controlling for IQ, gender, and free/reduced lunch status. Exploratory analyses unpacking the categories of skills into individual tasks also indicated specific areas of kindergarten instructional focus that may help children construct understanding of mathematical equivalence in future years. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

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.

Consequences of Individual Differences in Children's Formal Understanding of Mathematical Equivalence.

Experts claim that individual differences in children's formal understanding of mathematical equivalence have consequences for mathematics achievement; however, evidence is lacking. A prospective, longitudinal study was conducted with a diverse sample of 112 children from a midsized city in the Midwestern United States (Mage [second grade] = 8:1). As hypothesized, understanding of mathematical equivalence in second grade predicted mathematics achievement in third grade, even after controlling for second-grade mathematics achievement, IQ, gender, and socioeconomic status. Most children exhibited poor understanding of mathematical equivalence, but results provide clues about which children are on the path to constructing an understanding and which may need extra support to overcome their misconceptions. Findings suggest that mathematical equivalence may deserve more attention from educators.

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.

Comparing Meta-analysis and Individual Person Data Analysis Using Raw Data on Children's Understanding of Equivalence.

A prevailing theory of mathematical problem solving predicts that children will be less accurate solving a + b = c + __ problems versus a + b = __ + c. However, this has never been tested directly. Because of low base rates, information combined from multiple studies can help improve estimation accuracy and precision. This study compared meta-analysis and individual person data (IPD) analysis using raw data from 14 studies (N = 1,414; ns = 30-232; Mage reported = 8;7). Substantive results challenge the prevailing theory. Methodological results demonstrate the advantages of using meta-analysis and IPD over single-study analysis. Moreover, IPD can be more powerful than meta-regression for detecting between-study moderation effects.

An integrative data analysis of gender differences in children's understanding of mathematical equivalence.

This study examined gender as a potential source of variation in children's formal understanding of mathematical equivalence. The hypothesis was that girls would perform more poorly than boys. An integrative data analysis was conducted with 960 second and third graders across 14 previously conducted studies of children's understanding of mathematical equivalence. Measures included problem solving, problem encoding, and equal sign definition. Overall, children performed poorly on all measures. As predicted, girls were less likely than boys to solve mathematical equivalence problems correctly, even though there were no gender differences in calculation accuracy. In addition, girls were more likely than boys to use the "add-all" strategy, an incorrect strategy that has been shown to be more resistant to change than other incorrect strategies. There were not statistically significant differences for encoding or defining the equal sign, suggesting that deficits may reflect girls' tendency to follow taught algorithms.

Specific early number skills mediate the association between executive functioning skills and mathematics achievement.

A growing literature reports significant associations between children's executive functioning skills and their mathematics achievement. The purpose of this study was to examine if specific early number skills, such as quantity discrimination, number line estimation, number sets identification, fast counting, and number word comprehension, mediate this association. In 141 kindergarteners, cross-sectional analyses controlling for IQ revealed that number sets identification (but not the other early number skills) mediated the association between executive functioning skills and mathematics achievement. A longitudinal analysis showed that higher executive functioning skills predicted higher number sets identification in kindergarten, which in turn predicted growth in mathematics achievement from kindergarten to second grade. Results suggest that executive functioning skills may help children quickly and accurately identify number sets as wholes instead of getting distracted by the individual components of the sets, and this focus on sets, in turn, may help children learn more advanced mathematics concepts in the early elementary grades. (PsycINFO Database Record