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.

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.

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.

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.

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.

Actions may speak louder than words: Comparing methods of assessing children's spontaneous focusing on number.

Young children vary widely in the extent to which they attend to numerical information in their everyday environments without explicit prompting. This tendency to spontaneously focus on numerosity has been linked to children's math skills in past work. However, various measures have been used to quantify children's spontaneous focusing on numerosity (SFON) in previous studies, some of which rely on children's behavioral responses and others of which rely on verbal responses. Furthermore, these measures are not consistently related to one another or to children's math skills. In this study, we compared children's SFON as demonstrated through their behaviors and verbal responses during a set of imitation tasks in a sample of 107 3- and 4-year-olds. We found that children behaviorally demonstrate SFON (e.g., stamping the same number of spikes on a dinosaur as an experimenter) more frequently than they discuss number during the same tasks, but the two indices of SFON were significantly associated when accounting for variability in children's overall speech. Furthermore, we found that children's SFON through their actions was significantly predicted by prior math skills, whereas SFON through speech was not. These findings indicate that SFON may be a multifaceted construct, although more work is needed to extend these findings to other common SFON tasks.

A rational explanation for links between the ANS and math.

The proposal by Clarke and Beck offers a new explanation for the association between the approximate number system (ANS) and math. Previous explanations have largely relied on developmental arguments, an underspecified notion of the ANS as an "error detection mechanism," or affective factors. The proposal that the ANS represents rational numbers suggests that it may directly support a broader range of math skills.

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.

Measuring Emerging Number Knowledge in Toddlers.

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children's cardinal number knowledge and understanding of exact number words but does not capture children's preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., "Which has three?"). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children's emerging number knowledge and capturing nuances in children's number-word knowledge that Give-N may miss.

Beyond the Motor Domain: Exploring the Secondary Effects of a Fundamental Motor Skill Intervention for Children With Autism Spectrum Disorder.

Early motor skill interventions have been shown to improve the motor skill proficiency of children with autism spectrum disorder; however, little is known about the secondary effects associated with these types of interventions (e.g., influence on behavior, social skills, family dynamics). The purpose of this qualitative study was to (a) investigate parents' perceptions of the child-level benefits associated with a fundamental motor skill intervention for their 4-year-olds with autism spectrum disorder and (b) explore how child-level benefits influenced the family unit. Eight parents (N = 8) were interviewed (semistructured) about their experiences with the intervention for their child(ren); the study was grounded in phenomenology. Five main child-level benefits emerged, including improvements with (a) motor skills, (b) social skills, (c) listening skills, (d) turn-taking skills, and (e) transition skills. The child-level benefits then extended to family members in a number of ways (e.g., more positive sibling interactions). These findings highlight several important secondary effects that should be investigated in future research.

When beliefs matter most: Examining children's math achievement in the context of parental math anxiety.

A growing body of research suggests that parents' beliefs about and attitudes toward math predict their young children's math skills. However, limited research has examined these factors in conjunction with one another or explored potential mechanisms underlying these associations. In a sample of 114 preschool-aged children and their parents, we examined how parents' beliefs about math and math anxiety together relate to children's math achievement and how parents' practices to support math might explain these associations. We used a range of measures of parental math input, including survey measures of the home numeracy environment as well as observations of number talk. Parents with stronger beliefs about the importance of math tended to have children with more advanced math skills, and parents with math anxiety tended to exacerbate the effects of these beliefs such that children whose math-anxious parents held strong beliefs about math's importance performed best. Furthermore, we found some evidence that parents' math practices may relate to this interaction or to children's math skills, but no single measure of math input mediated the effect of the interaction between parental math anxiety and parental math beliefs on children's math outcomes. Thus, parents' math anxiety differentially relates to children's math performance depending on parents' beliefs about math, but future research is needed to uncover the specific mechanisms through which these processes operate.

Understanding the unique contributions of home numeracy, inhibitory control, the approximate number system, and spontaneous focusing on number for children's math abilities.

Math abilities are important predictors of both children's academic achievement and their outcomes in adulthood such as full-time employment and income. Previous work indicates that parenting factors (i.e., parental education, parent math ability, frequency of math activities) relate to children's math performance. Further, research demonstrates that both domain-general (i.e., language skills, inhibitory control) and domain-specific (i.e., approximate number system acuity, tendency to spontaneously focus on number) cognitive predictors are related to math during early childhood. However, work to date has not examined all of these factors together to identify their unique contributions for young children's math abilities. Thus, in the present study we examine whether parent-level and child-level factors uniquely explain children's math abilities. To this end, 112 four-year-old children and one of their parents completed a battery of assessments and questionnaires. Results indicate that children's math performance is uniquely predicted by the frequency of home math activities reported by the parents, as well as children's own inhibitory control, approximate number system acuity, and tendency to spontaneously focus on number. These parent- and child-level factors provide independent targets for future interventions aimed at improving early math performance.

Triangulating multi-method assessments of parental support for early math skills.

Past research has examined parental support for math during early childhood using parent-report surveys and observational measures of math talk. However, since most studies only present findings from one of these methods, the construct (parental support for early math) and the method are inextricably linked, and we know little about whether these methods provide similar or unique information about children's exposure to math concepts. This study directly addresses the mono-operation bias operating in past research by collecting and comparing multiple measures of support for number and spatial skills, including math talk during semi-structured observations of parent-child interactions, parent reports on a home math activities questionnaire, and time diaries. Findings from 128 parents of 4-year-old children reveal substantial within-measure variability across all three data sources in the frequency of number and spatial activities and the type and content of parent talk about number and spatial concepts. Convergence in parental math support measures was evident among parent reports from the questionnaire and time diaries, such that scale composites about monthly number activities were related to number activities on the previous work day, and monthly spatial activities were correlated with spatial activities the prior non-work days. However, few parent report measures from the survey or time diary were significantly correlated with observed quantity or type of math talk in the semi-structured observations. Future research implications of these findings are discussed.

Patient and caregiver engagement in research: factors that influence co-enrollment in research.

BACKGROUND: Recruitment of pediatric participants in studies is difficult due to the vulnerability of this population and the scarcity of certain conditions. Co-enrolling in multiple studies is a strategy that may help overcome this problem. Although anecdotal evidence suggests that co-enrollment may increase patient and caregiver burden, few studies have been conducted from the patient perspective. The objective of this quality improvement project was to elicit patient and caregiver opinions on co-enrolling in multiple research studies. METHODS: Patients and caregivers attending the rheumatology clinic at The Hospital for Sick Children were invited to participate in a semi-structured interview or focus group session. Participants were asked to respond to ten prompts, organized into five categories: experience in clinical research, multiple studies, study selection, study timing and other comments. Sessions were recorded, transcribed and analyzed using NVivo 10 to identify common themes. RESULTS: Overall, eighteen caregivers and two patients were included in the study. Participants felt that the level of study involvement, rather than the number of studies, was the biggest factor affecting their decision to participate. Another factor commonly identified was the competing demands of participants' work and family life. Participants indicated that they generally preferred to be informed about all study opportunities and liked to receive this information prior to their appointments. Once informed, they preferred to be approached by the research team while they were waiting for their appointment. CONCLUSION: Patients and caregivers are open to the concept of co-enrolling in multiple research studies. There are multiple factors which influence decisions to co-enroll in studies including the demands of the study and personal limitations. These findings will help guide the design and practices of future research.

Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics.

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples' ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults' accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities.

Understanding sources of individual variability in parents' number talk with young children.

Several studies suggest that parents' use of number words while talking with their children is positively related to children's understanding of certain mathematical concepts. In this study, we extended these findings and further examined several parent characteristics that could be related to individual differences in their number talk, including their subjective ratings of their math skills, preference for using math, beliefs about the importance of their children's math skills, and numerical approximation abilities, an early number skill present in children and adults. A sample of 44 5- and 6-year-old children and their parents completed a variety of laboratory-based tasks, including a 10-min free play session to assess number talk, a standardized math assessment for children, a nonsymbolic numerical comparison task for parents, and several questionnaires for parents. Parents' overall number talk was not related to children's performance on the math assessment; however, parents' use of numbers larger than 10 was positively and significantly related to children's math abilities even when controlling for parents' overall talk. Parents' large number talk was also associated with their numerical approximation abilities and subjective math ability, suggesting that math-specific characteristics of parents themselves can explain some of the individual variability in parents' use of number words, especially those larger than 10.