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.

Ambiente matemático de niños y niñas chilenos: Factores que explican las actividades matemáticas en el hogar / Home math environment of Chilean boys and girls: Factors that explain home math activities

Resumen Introducción: el estudio analizó (a) las diferencias entre madres y padres en sus actividades matemáticas en el hogar y en otros factores del ambiente matemático (actitudes, ansiedad, creencias y expectativas matemáticas) y (b) la asociación entre los factores del ambiente matemático y las actividades matemáticas en el hogar. Método: participaron 266 familias de niños y niñas chilenos de primer a tercer grado de primaria (edad promedio = 93.35 meses, DE = 11.45 meses). Ambos padres contestaron un cuestionario sobre matemáticas en el hogar. Resultados: las madres reportaron realizar actividades matemáticas con mayor frecuencia que los padres. Análisis de ecuaciones estructurales mostraron que las actividades matemáticas realizadas por los padres se relacionaron con sus creencias, actitudes y expectativas matemáticas; mientras que las de las madres se relacionaron con sus creencias, actitudes y género de los niños. Conclusiones: los hallazgos aportan a la comprensión del ambiente matemático en el hogar.

Abstract Introduction: The study analyzes (a) the differences between mothers and fathers in their home math activities and home math environment factors (math attitudes, anxiety, beliefs, and expectations) and (b) the associations among the home math environment factors and home math activities of Chilean families. Method: Participants were 266 families of boys and girls attending grades 1-3 (mean age = 93.35 months, DS = 11.45 months). Both parents of each child independently answered a home math questionnaire. Results: Mothers reported doing more math activities with their children than fathers. The structural equation model analyses showed that the frequency with which fathers engage in home math activities was related to their math beliefs, attitudes, and expectations, whereas maternal home math activities were related to their beliefs, attitudes, and the gender of the child. Conclusions: The findings contribute to the understanding of the home math environment.

Walking another pathway: The inclusion of patterning in the pathways to mathematics model.

According to the Pathways to Mathematics model [LeFevre et al. (2010), Child Development, Vol. 81, pp. 1753-1767], children's cognitive skills in three domains-linguistic, attentional, and quantitative-predict concurrent and future mathematics achievement. We extended this model to include an additional cognitive skill, patterning, as measured by a non-numeric repeating patterning task. Chilean children who attended schools of low or high socioeconomic status (N = 98; 54% girls) completed cognitive measures in kindergarten (Mage = 71 months) and numeracy and mathematics outcomes 1 year later in Grade 1. Patterning and the original three pathways were correlated with the outcomes. Using Bayesian regressions, after including the original pathways and mother's education, we found that patterning skills predicted additional variability in applied problem solving and arithmetic fluency, but not number ordering, in Grade 1. Similarly, patterning skills were included in the best model for applied problem solving and arithmetic fluency, but not for number ordering, in Grade 1. In accord with the hypotheses of the original Pathways to Mathematics model, patterning varied in its unique and relative contributions to later mathematical performance, depending on the demands of the tasks. We conclude that patterning is a useful addition to the Pathways to Mathematics model, providing further insights into the range of cognitive precursors that are related to children's mathematical development.

Socioeconomic Variations in the Frequency of Parent Number Talk: A Meta-Analysis.

Using data from 12 studies, we meta-analyze correlations between parent number talk during interactions with their young children (mean sample age ranging from 22 to 79 months) and two aspects of family socioeconomics, parent education, and family income. Potential variations in correlation sizes as a function of study characteristics were explored. Statistically significant positive correlations were found between the amount of number talk in parent-child interactions and both parent education and family income (i.e., r = 0.12 for education and 0.14 for income). Exploratory moderator analyses provided some preliminary evidence that child age, as well as the average level of and variability in socioeconomic status, may moderate effect sizes. The implications of these findings are discussed with special attention to interpreting the practical importance of the effect sizes in light of family strengths and debate surrounding "word gaps".

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.

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.

Home Learning Environments of Children in Mexico in Relation to Socioeconomic Status.

We explored the home learning environments of 173 Mexican preschool children (aged 3-6 years) in relation to their numeracy performance. Parents indicated the frequency of their formal home numeracy and literacy activities, and their academic expectations for children's numeracy and literacy performance. Children completed measures of early numeracy skills. Mexican parent-child dyads from families with either high- or low-socioeconomic status (SES) participated. Low-SES parents (n = 99) reported higher numeracy expectations than high-SES parents (n = 74), but similar frequency of home numeracy activities. In contrast, high-SES parents reported higher frequency of literacy activities. Path analyses showed that operational (i.e., advanced) numeracy activities were positively related to children's numeracy skills in the high- but not in the low-SES group. These findings improve the understanding of the role of the home environment in different contexts and provide some insights into the sources of the variable patterns of relations between home learning activities and children's numeracy outcomes. They also suggest that SES is a critical factor to consider in research on children's home numeracy experiences.

Children's Home Numeracy Environment Predicts Growth of their Early Mathematical Skills in Kindergarten.

This study investigated the longitudinal associations between children's early mathematics and their home numeracy environment (HNE). Chilean children from families who varied widely in socioeconomic status were assessed at the beginning and end of prekindergarten in 2016 (N = 419, Mage  = 4:7 [years:months]), and at the end of kindergarten in 2017 (N = 368, Mage  = 5:10). Children whose parents provided frequent operational numeracy activities (e.g., learning simple sums) at prekindergarten showed better arithmetic performance and growth in nonsymbolic and symbolic number comparison at the end of kindergarten. Parents' knowledge of number-related games predicted children's arithmetic skills and growth in nonsymbolic number comparison. These findings underscore the persistent relations between the HNE and the development of children's mathematical skills.

Chilean kindergarten children's beliefs about mathematics: Family matters.

This study examines the relations among parental beliefs and practices about mathematics, children's beliefs about mathematics, participants' gender, and family socioeconomic status (SES). The study was conducted in Chile, a country with significant gender gaps in standardized test results in mathematics, with boys receiving significantly higher scores than girls. One hundred eighty Chilean kindergarteners (Mage = 5.6 years) of low and high SES completed both implicit and explicit measures of their beliefs about mathematics. Children's mothers and fathers also completed adult versions of these tests, as well as measures of home numeracy practices. This combination of child and parental assessments (both mother and father), including both implicit and explicit measures, provided a wider range of measures than in previous studies. On implicit measures of math-gender stereotypes, boys showed the math = boy stereotype significantly more strongly than girls did. Both fathers and mothers showed this stereotype on both implicit and explicit measures. Fathers also linked me = math (math self-concept) more strongly than mothers on both implicit and explicit measures. Kindergarten girls' implicit math self-concept was explained by a combination of parents' math self-concepts and SES. Taken together, these results show that by 5 years of age children are already developing beliefs about "who does math" in their culture, and that parental beliefs and practices are significantly linked to children's stereotypes and self-concepts about mathematics before they enter formal schooling. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Self-Concept Predicts Academic Achievement Across Levels of the Achievement Distribution: Domain Specificity for Math and Reading.

This study examines whether self-concept of ability in math and reading predicts later math and reading attainment across different levels of achievement. Data from three large-scale longitudinal data sets, the Avon Longitudinal Study of Parents and Children, National Institute of Child Health and Human Development-Study of Early Child Care and Youth Development, and Panel Study of Income Dynamics-Child Development Supplement, were used to answer this question by employing quantile regression analyses. After controlling for demographic variables, child characteristics, and early ability, the findings indicate that self-concept of ability in math and reading predicts later achievement in each respective domain across all quantile levels of achievement. These results were replicated across the three data sets representing different populations and provide robust evidence for the role of self-concept of ability in understanding achievement from early childhood to adolescence across the spectrum of performance (low to high).

Early predictors of high school mathematics achievement.

Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students' knowledge of fractions and of division uniquely predicts those students' knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.