Math talk by mothers, fathers, and toddlers: Differences across materials and associations with children's math understanding.

Learning words for numbers, shapes, spatial relations, and magnitudes-"math talk"-relies on input from caregivers. Language interactions between caregivers and children are situated in activity contexts and likely affected by available materials. Here, we examined how play materials influence the math talk directed to and produced by young children. We video-recorded parents (mothers and fathers; English- and/or Spanish-speaking) and their 24- to 36-month-olds during play with four sets of materials, transcribed and coded types of parent and toddler math words/phrases, and assessed toddlers' understanding of number, shape, and spatial relations terms. Categories of math words varied by materials. Numeracy talk (e.g., "one," "two," "first," "second") was more frequent during interactions with a picture book and toy grocery shopping set than with a shape sorter or magnet board; the reverse held for spatial talk (e.g., "out," "bottom," "up," "circle"). Parent math talk predicted toddler math talk, and both parent and toddler math talk predicted toddlers' understanding of spatial and number words. Different materials provide unique opportunities for toddlers to learn abstract math words during interactions with caregivers, and such interactions support early math cognition.

(Dis)similarities between non-symbolic and symbolic number representations: Insights from vector space models.

Empirical evidence in support of a shared system for non-symbolic and symbolic number processing has been inconclusive. The current study aims to address this question in a novel way, specifically by testing whether the efficient coding principle based on co-occurrence of number symbols in natural language holds for both non-symbolic and symbolic number processing. The efficient coding principle postulates that perception is optimized when stimuli frequently co-occur in a natural environment. We hypothesized that both numerical ratios and co-occurrence frequencies of symbolic numbers would significantly influence participants' performance on a non-symbolic and symbolic number comparison task. To test this hypothesis, we employed latent semantic analysis on a TASA corpus to quantify number co-occurrence in natural language and calculate language similarity estimates. We engaged 73 native English speakers (mean age = 19.36, standard deviation = 1.83) with normal or corrected vision and no learning disorders in a number comparison task involving non-symbolic (dot arrays) and symbolic stimuli (Arabic numerals and English number words). Results showed that numerical ratios significantly predicted participants' performances across all number formats (ps < 0.001). Language similarity estimates derived from everyday language also predicted performance on the non-symbolic task and the symbolic task involving number words (ps < 0.007). Our results highlight the complex nature of numerical processing, pointing to the co-occurrence of number symbols in natural language as an auxiliary factor in understanding the shared characteristics between non-symbolic and symbolic number representations. Given that our study focused on a limited number range (5 to 16) and a specific task type, future studies should explore a wider range of tasks and numbers to further test the role of the efficient coding principle in number processing.

Examining Profiles of U.S. Children's Screen Time and Associations with Academic Skills.

Children's screen time (ST) increased in recent years, but investigations of the content and context (e.g., parental presence, and device type) of ST in predicting early academic skills remains understudied. In this study of 127 four- and five-year-olds, we examined whether the educational content and contextual information about children's ST from time diary interviews at age 4 predicted direct assessments of academic skills at age five. Cluster analyses detected three unique groups: Cluster One was "lowest ST and highest non-educational TV, with little parental presence," Cluster Two was "moderate ST and highest educational mobile devices, with moderate parental presence," and Cluster Three was "highest total ST and moderate educational ST and high parental presence." Children in Cluster Two scored significantly higher in literacy skills at age five than peers in Cluster One and Cluster Three. Children in Cluster One scored significantly higher in spatial skills compared to those in Cluster Three. No significant associations were detected between children's ST and number skills. Findings suggest that educational content and contextual features of ST combine in meaningful ways and appear to better predict children's literacy and spatial skills compared to variable-centered approaches. Methodological implications of this research and future directions are discussed.

Assessing the association between parents' math talk and children's math performance: A preregistered meta-analysis.

The home math environment has gained considerable attention as a potential cause of variation in children's math performance, and recent research has suggested positive associations between parents' math talk and children's mathematical performance. However, the extent to which associations reflect robust causal effects is difficult to test. In a preregistered meta-analysis, we assess the association between parents' math talk and children's math performance. Our initial search identified 24,291 potential articles. After screening, we identified 22 studies that were included in analyses (k = 280 effect sizes, n = 35,917 participants). A multilevel random effects meta-analysis was employed, finding that parents' math talk is significantly associated with children's math performance (b = 0.10, SE = 0.03, p = .002). We tested whether associations differ as a function of sample characteristics, observation context, observation length, type of math talk and math performance measured, and modeling approaches to math talk variable analysis. In addition, we tested whether associations are robust to the inclusion of strong baseline covariates and found that effects attenuated when children's domain-general and/or prior math abilities are included. We discuss plausible bounds of the effects of parents' math talk on children's mathematical performance to inform power analyses and experimental work on the impact of parents' math language on children's math learning.

The benefits of math activities depend on the skills children bring to the table.

Playing board games and other math activities can provide young children with opportunities to develop their math skills. However, it is critical to understand for whom these activities may be most beneficial. In two studies, we examine the extent to which foundational cognitive skills moderate the effects of playing math games on math skills. In Study 1, we look cross-sectionally at the association between parents' frequency of math activities with their 3- to 4-year-old children (N = 124) and children's math achievement, examining the extent to which children's skills moderate this relation. We find that frequent math activities are only associated with better math performance for children with better number knowledge. In Study 2, we test this experimentally by randomly assigning parents and children (N = 76) to play with a number-related board game, an active control board game, or a business-as-usual control group. Controlling for number knowledge, inhibitory control, and vocabulary at pretest, no differences in math skills at posttest were observed between the training groups. However, a significant interaction emerged between training group assignment and number knowledge, such that children with higher pretest number knowledge had higher posttest math scores when assigned to the number board game condition compared to the two control conditions, but no differences among conditions were seen for children with lower number knowledge. Collectively, these findings suggest that math activities may be most beneficial for math skills when children have stronger number knowledge and underscore the need for tailoring activities to children's current skill level. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Diversity of spatial activities and parents' spatial talk complexity predict preschoolers' gains in spatial skills.

Children's spatial activities and parental spatial talk were measured to examine their associations with variability in preschoolers' spatial skills (N = 113, Mage = 4 years, 4 months; 51% female; 80% White, 11% Black, and 9% other). Parents who reported more diversity in daily spatial activities and used longer spatial talk utterances during a spatial activity had children with greater gains in spatial skills from ages 4 to 5 (ß = .17 and ß = .40, respectively). Importantly, this study is the first to move beyond frequency counts of spatial input and investigate the links among the diversity of children's daily spatial activities, as well as the complexity of parents' spatial language across different contexts, and preschoolers' gains in spatial skills, an important predictor of later STEM success.

Unpacking the Home Numeracy Environment: Examining Dimensions of Number Activities in Early Childhood.

A growing body of research has examined parents' practices to support their young children's number learning at home, i.e., the home numeracy environment. Many of these studies focus on formal and informal domains of numeracy activities, which are inconsistently defined and related to children's math learning. In this study, we explore dimensions of the home numeracy environment and examine their relations with children's math skills among a sample of four-year-old children and their parents over the course of one year. Parents reported on the frequency of 21 numeracy activities when children were four and five. Exploratory and confirmatory factor analyses revealed a two-factors solution: number-related play activities and use of educational materials with numbers. Frequency of play with numbers was positively related to children's ability to solve applied math problems at age five, controlling for prior number skills, child age, and socioeconomic status. In contrast, neither measure of the home numeracy environment predicted symbolic number knowledge or non-symbolic number sense when controlling for covariates. These findings underscore the need to differentiate between factors of the home numeracy environment and to develop clear theoretical definitions of these factors.

Investigating associations between parent engagement and toddlers' mathematics performance.

Early mathematics skills relate to later mathematics achievement and educational attainment, which in turn predict career choice, income, health and financial decision-making. Critically, large differences exist among children in early mathematics performance, with parental mathematics engagement being a key predictor. However, most prior work has examined mothers' mathematics engagement with their preschool- and school-aged children. In this Registered Report, we tested concurrent associations between mothers' and fathers' engagement in mathematics activities with their 2- to 3-year-old toddlers and children's mathematics performance. Mothers and fathers did not differ in their engagement in mathematics activities, and both parents' mathematics engagement related to toddlers' mathematics skills. Fathers' mathematics engagement was associated with toddlers' number and mathematics language skills, but not their spatial skills. Mothers' mathematics engagement was only associated with toddlers' mathematics language skills. Critically, associations may be domain-specific, as parents' literacy engagement did not relate to measures of mathematics performance above their mathematics engagement. Mothers' and fathers' mathematics activities uniquely relate to toddlers' developing mathematics skills, and future work on the nuances of these associations is needed.

Exploring the role of "in the moment" and global caregiver and child factors in caregiver questioning during shared book viewing.

Questions of high (vs. low) cognitive demand (CD), which encourage children to engage in abstract or critical thinking (e.g., problem solve, reason about cause-and-effect relations, make inferences), may drive relations between children's language exposure and early skills. The present study adopted a micro-analytic approach to examine caregivers' high-CD questioning with their preschool-aged children while viewing a wordless picture book (n = 121) and "in the moment" (e.g., interaction time, child responses) and global factors (e.g., caregiver education). The probability of caregivers' high-CD questioning increased with interaction time and caregiver education. Post-hoc exploratory analyses revealed that the relation between children's responses and caregivers' high-CD questioning depended on caregivers' perceptions of children's vocabulary skills. Specifically, the probability of caregivers' subsequent high-CD questioning was greater if their child did not respond previously and if caregivers perceived them to have high vocabulary skills. In contrast, caregivers' questioning remained relatively constant for responsive children across different vocabulary skills. Thus, caregivers may employ certain types of input during brief, informal learning interactions with their children by considering their own and their child's propensities and micro-level changes that occur during their conversations.

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain.

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Mothers' and fathers' engagement in math activities with their toddler sons and daughters: The moderating role of parental math beliefs.

Parents' beliefs about the importance of math predicts their math engagement with their children. However, most work focuses on mothers' math engagement with preschool- and school-aged children, leaving gaps in knowledge about fathers and the experiences of toddlers. We examined differences in mothers' and fathers' (N = 94) engagement in math- and non-math activities with their two-year-old girls and boys. Parents reported their beliefs about the importance of math and literacy for young children and their frequency of home learning activities. Parents of sons did not differ in their engagement in math activities from parents of daughters. Mothers reported engaging more frequently in math activities with their toddlers than fathers did, but the difference reduced when parents endorsed stronger beliefs about the importance of math for children. Even at very early ages, children experience vastly different opportunities to learn math in the home, with math-related experiences being shaped by both parent gender and parents' beliefs.

Toddler home math environment: Triangulating multi-method assessments in a U.S. Sample.

Introduction: Current research has documented the home math environment (HME) of preschoolers and kindergarteners. Very few studies, however, have explored the number and spatial activities in which parents engage with children during their toddler years. Methods: This study examined the HME of 157 toddlers using several methodologies, including surveys, time diaries, and observations of math talk. Further, it examined correlations within and across data sources to identify areas of convergence and triangulation, and correlated HME measures with measures of toddlers' number and spatial skills. Results: Findings showed that, in general, uses of different types of math activities, including both number and spatial, were intercorrelated within method. Across methods, there was high intercorrelation between the frequency of math activities reported on parent surveys and the diversity of types of math activities endorsed in time diary interviews. Parent math talk gleaned from semi-structured interviews functioned as a separate aspect of the HME; different types of math talk shared few intercorrelations with engagement in math activities as reported in either surveys or time diaries. Finally, several HME measures positively correlated with toddlers' math skills. Discussion: Given extant research demonstrating that both math activities and math talk predict children's math skills, our results stress the need for multimethod studies that differentiate among these HME opportunities.

Representations within the Intraparietal Sulcus Distinguish Numerical Tasks and Formats.

How does our brain understand the number five when it is written as an Arabic numeral, and when presented as five fingers held up? Four facets have been implicated in adult numerical processing: semantic, visual, manual, and phonological/verbal. Here, we ask how the brain represents each, using a combination of tasks and stimuli. We collected fMRI data from adult participants while they completed our novel "four number code" paradigm. In this paradigm, participants viewed one of two stimulus types to tap into the visual and manual number codes, respectively. Concurrently, they completed one of two tasks to tap into the semantic and phonological/verbal number codes, respectively. Classification analyses revealed that neural codes representing distinctions between the number comparison and phonological tasks were generalizable across format (e.g., Arabic numerals to hands) within intraparietal sulcus (IPS), angular gyrus, and precentral gyrus. Neural codes representing distinctions between formats were generalizable across tasks within visual areas such as fusiform gyrus and calcarine sulcus, as well as within IPS. Our results identify the neural facets of numerical processing within a single paradigm and suggest that IPS is sensitive to distinctions between semantic and phonological/verbal, as well as visual and manual, facets of number representations.

Exploring effects of an early math intervention: The importance of parent-child interaction.

We explore whether training parents' math skills or playing number games improves children's mathematical skills. Participants were 162 parent-child dyads; 88.3% were white and children (79 female) were 4 years (M = 46.88 months). Dyads were assigned to a number game, shape game, parent-only approximate number system training, parent-only general trivia, or a no-training control condition and asked to play twice weekly for 8 weeks. Children in the number game condition gained over 15% SD on an assessment of mathematical skill than did those in the no-training control. After 8 additional weeks without training, effects diminished; however, children of parents in the ANS condition underperformed those in the no-treatment control, which was partially explained by changes in the home numeracy environment.

Environmental influences on mathematics performance in early childhood.

Math skills relate to lifelong career, health, and financial outcomes. Individuals' own cognitive abilities predict math performance and there is growing recognition that environmental influences including differences in culture and variability in math engagement also impact math skills. In this Review, we summarize evidence indicating that differences between languages, exposure to math-focused language, socioeconomic status, attitudes and beliefs about math, and engagement with math activities influence young children's math performance. These influences play out at the community and individual level. However, research on the role of these environmental influences for foundational number skills, including understanding of number words, is limited. Future research is needed to understand individual differences in the development of early emerging math skills such as number word skills, examining to what extent different types of environmental input are necessary and how children's cognitive abilities shape the impact of environmental input.

Self-regulation in toddlers and the emergence of pre-academic disparities.

A growing body of research has examined how children's self-regulation during early and middle childhood mediates SES disparities in academic achievement. Evidence suggests that these self-regulation skills begin developing even earlier, during the toddler years, but more work is needed examining how different measures of self-regulation relate to key constructs such as socioeconomic status (SES) and toddlers' pre-academic skills. In this online study, we examine multiple approaches to measuring self-regulation using confirmatory factor analyses and assess the extent to which self-regulatory skills help explain SES differences in early math and language skills among a sample of 158 two- and three-year-old children. Self-regulation was assessed through a battery of parent- and examiner-ratings. Children's counting, cardinality, and vocabulary skills were measured online through direct assessments and parent surveys. Two self-regulation factors emerged representing parent-reported and observational measures, and only observational measures of self-regulation mediated associations between SES and children's math and language skills. Parent-reported self-regulation was not uniquely related to SES or children's pre-academic skills, underscoring the need for careful consideration of how self-regulation is measured among toddlers when examining its associations with pre-academic skills.

Parental math input is not uniformly beneficial for young children: The moderating role of inhibitory control.

Recent work has stressed the importance of considering child-level propensities and environmental opportunities when studying early math achievement; however, few studies investigate the interaction between these factors. This study examined whether children's inhibitory control moderates the association between parental math input and children's math performance. Parental math input via number talk and parent-reported frequencies of math activities were measured in 123 children (M age = 3.9 years) and one of their parents. High levels of parent number talk were associated with higher math achievement among children with higher inhibitory control. This association was not seen in children with lower inhibitory control, for children's vocabulary as the outcome measure, or for parents' overall talk or parent-reported math activities as the opportunity measures. Thus, children may differentially benefit from parental math input depending on their cognitive abilities and this association is specific to parental number talk and children's math abilities.

Associations among socioeconomic status and preschool-aged children's, number skills, and spatial skills: The role of executive function.

Extensive literature has documented socioeconomic status (SES) disparities in young children's standardized math achievement, which primarily reflect differences in basic number and arithmetic skills. In addition, growing evidence indicates that direct assessments of executive function (EF) both predict standardized math achievement and mediate SES differences in standardized math tests. However, early spatial skills and children's approximate number system (ANS) acuity, critical components of later math competence, have been largely absent in this past research. The current study examined SES associations with multiple direct assessments of early ANS, cardinality, and spatial skills, as well as standardized math achievement, in a socioeconomically diverse sample of 4-year-old children (N = 149). Structural equation modeling revealed SES effect sizes of .21 for geometric sensitivity skills, .23 for ANS acuity, .39 for cardinality skills, and .28 for standardized math achievement. Furthermore, relations between SES and children's spatial skills, ANS acuity, cardinality, and standardized math skills were mediated by a composite measure of children's EF skills. Implications of pervasive SES disparities across multiple domains of early math development, as well as the mitigating role of EF, are discussed.

Numerical estrangement and integration between symbolic and non-symbolic numerical information: Task-dependence and its link to math abilities in adults.

Most adults have access to two different number systems to represent numerical information: an exact number system, which relies on different forms of number symbols to represent exact numerical information, and an approximate number system, which allows for approximate estimates of numerical quantities. Here we investigate the integration between the symbolic and non-symbolic numerical information (i.e., "numerical integration"), and how numerical integration relates to adults' formal math abilities. We administered two tasks to measure numerical integration. For a number comparison task with non-symbolic dot arrays and Arabic numerals, participants indicated the larger of two sequentially presented stimuli that were same-format (dot-dot or numeral-numeral), or mixed-format (dot-numeral or numeral-dot). For a number-letter discrimination task, participants identified Arabic numerals or letter pairs that co-occurred with dot arrays (matching or mismatching the quantity represented by the numeral). In the number comparison task, participants were significantly slower when comparing mixed-format stimuli, especially when Arabic numerals were presented first and dot arrays second, suggesting estrangement between symbolic and non-symbolic numerical information and an asymmetry depending on the order in which the numerical information is presented. In contrast, in the number-letter discrimination task, participants were significantly faster in number-letter discrimination for matching dot arrays and numerals, suggesting integration between symbolic and non-symbolic numerical information. Surprisingly, some measures of numerical estrangement derived from the number comparison task significantly correlated with adults' performance on a standardized math assessment. Thus, we conclude that numerical integration or estrangement is task-dependent, and adults with greater levels of symbolic estrangement tend to have higher math skills.

Teasing apart the unique contributions of cognitive and affective predictors of math performance.

Math permeates everyday life, and math skills are linked to general educational attainment, income, career choice, likelihood of full-time employment, and health and financial decision making. Thus, researchers have attempted to understand factors predicting math performance in order to identify ways of supporting math development. Work examining individual differences in math performance typically focuses on either cognitive predictors, including inhibitory control and the approximate number system (ANS; a nonsymbolic numerical comparison system), or affective predictors, like math anxiety. Studies with children suggest that these factors are interrelated, warranting examination of whether and how each uniquely and independently contributes to math performance in adulthood. Here, we examined how inhibitory control, the ANS, and math anxiety predicted college students' math performance (n = 122, mean age = 19.70 years). Using structural equation modeling, we find that although inhibitory control and the ANS were closely related to each other, they did not predict math performance above and beyond the effects of the other while also controlling for math anxiety. Instead, math anxiety was the only unique predictor of math performance. These findings contradict previous results in children and reinforce the need to consider affective factors in our discussions and interventions for supporting math performance in college students.