Early Math Development Research Articles

A Window into Early Math Development: An Observational Study of Skills and Strategies

A Window into Early Math Development: An Observational Study of Skills and Strategies

Foundations for future math achievement: Early numeracy, home learning environment, and the absence of math anxiety

BackgroundMathematics achievement is pivotal in shaping children's future prospects. Cognitive skills (numeracy), feelings (anxiety), and the social environment (home learning environment) influence early math development. MethodA longitudinal study involved 85 children (mean age T1 = 6.4 years; T2 = 7.9) to explore these predictors holistically. Data were collected on early numeracy skills, home learning environment, math anxiety, and their impact on various aspects of math. ResultsThe study found that early numeracy skills, home learning environment, and math anxiety significantly influenced math school achievement. However, they affected written computation, sequences, and comparisons differently. Early numeracy skills strongly predicted overall achievement and comparison subtest performance. ConclusionThese findings underscore the substantial role of math anxiety and home learning environment in children's math achievement. The study emphasizes the need to consider the selective impacts of these factors in future research, shedding light on the multifaceted nature of mathematics achievement determinants.

Lessons from a preschool intervention study carried out during the Covid-19 pandemic

The article describes how a series of adaptions enabled us to carry out a controlled intervention study in 15 preschools, with 420 children and about 40 preschool teachers, during the Covid‑19 pandemic restrictions. The original overarching aim of the study was to develop and evaluate an early math intervention supporting children from low-SES environments to develop basic mathematical skills. The two main research questions addressed preschool children’s early math development using a digital play-&-learn game (anonymized), and the pedagogical impact of an integrated teacher resources package. Four guiding principles complemented the research questions: accumulation of new knowledge, collaboration & participatory design, experimental control & ecological validity, and real-world applicability. The focus of this article is on how data collections methods and analyses were adapted to handle the constraints induced by Covid‑19 without deviating from the original research questions and the four guiding principles. The adaptions clearly entailed methodological limitations. Yet the study demonstrates the possibility to conduct a remotely controlled effect study encompassing both ecological validity and real-world applicability

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.

Engaging girls in math: The unequal effects of text messaging to help parents support early math development

This study assesses the effects of two text messaging programs for parents that aim to support the development of math skills in prekindergarten students. One program focuses purely on math, while the other takes an identical approach but focuses on a combination of math, literacy, and social-emotional skills. We find no evidence that the math-only program benefits children's math development. However, the combination program shows greater promise, particularly for girls. Quantile regressions indicate that the effects are concentrated in the lower half of the outcome distribution. We discuss and provide evidence for various hypotheses that could explain these differences.

Spatial language during a household task with bilingual Latine families

Children's exposure to everyday math talk contributes positively to their early math development, yet little is known about family everyday math in culturally and linguistically diverse communities. The present study described the spatial language used by 75 low-income, bilingual, Latine caregivers as they taught their preschoolers to set a table for a birthday party. Forty percent of caregivers' content-rich utterances contained math references, half of which were spatial terms. “Where” spatial references were the most frequent and used to provide instructions. Analyses comparing Spanish and English interactions showed variations in spatial language types and manners of use, as well as in the relation between adult and child math talk. Results underscore the need to build foundational knowledge in early math with culturally and linguistically diverse families, and to encompass a wide range of everyday adult-child interactions, in an effort to forge equitable STEM initiatives and practices.

Parent and child spontaneous focus on number, mathematical abilities, and mathematical talk during play activities

The mathematical talk that parents use when engaging with their children is important for children’s early math development. However, parents vary in the amount and type of mathematical input they provide. Because early math knowledge is predictive of later achievement, understanding contributors to this variation has implications for children’s math development. The current study examined how individual parent and child cognitive factors, including math ability and spontaneous focus on number (SFON), relate and contribute to math talk during parent-child play. Findings indicate that SFON relates to math ability for both parents and children. SFON was not a significant predictor of math talk, but parent and child math ability related to talk about advanced math concepts and numbers in context. These results suggest that the relation of SFON and math ability is consistent in adulthood, and that more research is needed to understand factors that contribute to variation in math talk.

Relations between parental math beliefs and emergent math skills among preschoolers from low-income households

ABSTRACT We examined how parent math attitudes and practices relate to emergent math skills in 72 preschoolers from low-income households. Specifically, we investigated parents’ views about the importance of math learning, their confidence in teaching math, their perceptions of child interest in math, and their time spent engaging their child in math activities. For comparison, we also investigated these attitudes and practices surrounding preliteracy development. Parents rated math as significantly less important than reading and perceived their children as being significantly less interested in math than reading. Reports of confidence in teaching math and perceptions of child interest in math were positively related to time spent engaging preschoolers in math activities. In turn, global reports of time spent engaging preschoolers in math activities were positively related to preschoolers’ actual math achievement. These findings strengthen the case that parental beliefs surrounding math predict practices associated with early math development.

Finding patterns in objects and numbers: Repeating patterning in pre-K predicts kindergarten mathematics knowledge

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns—predictable sequences that follow a rule—are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, focusing on development in children aged 4–6 years. The current study examined the relation between 65 preschool children’s repeating patterning knowledge (via a fast, teacher-friendly measure) and their end-of-kindergarten broad math and numeracy knowledge, controlling for verbal and visual-spatial working memory (WM) skills as well as end-of-pre-K (pre-kindergarten) broad math knowledge. Relations were also examined between repeating patterning and specific aspects of numeracy knowledge—knowledge of the count sequence to 100 and the successor principle. Children’s repeating patterning knowledge was significantly predictive of their broad math and general numeracy knowledge, as well as one specific aspect of their numeracy knowledge (counting to 100), even after controlling for verbal and visual-spatial WM skills. Further, repeating patterning knowledge remained a unique predictor of general numeracy knowledge and counting to 100 after controlling for end-of-pre-K broad math knowledge. The relation between repeating patterning and mathematics may be explained by the central role that identifying predictable sequences based on underlying rules plays in both. Theories of math development and early math instruction standards should thus give even greater attention to the role of children’s repeating patterning knowledge.

The home math environment: More than numeracy

The goal of the current study is to develop a more complete understanding of the early home math environment, encompassing both numeracy and non-numeracy aspects of that environment. Parents of preschoolers (n = 63) were surveyed about their support of three components of early mathematics knowledge (i.e., numeracy, spatial, and pattern) as well as parents’ math-related beliefs about themselves and their children. Children were administered a broad math knowledge assessment which included a numeracy subscale, and individual measures of spatial and patterning skills in the fall (concurrently). Broad math knowledge was measured again in the spring of the preschool year. Parents indicated providing some support of early math development through numeracy, spatial, and patterning activities, with a stronger emphasis on numeracy than pattern and space. Parents’ child-specific ability beliefs were related to their numeracy, pattern, and broad math support, while their parent-specific ability beliefs were related to their spatial support. Parent support was rarely linked to child skills, except that numeracy support related to concurrent numeracy knowledge. Findings suggest that although parents do support a broad range of early math skills at home, parents tend to prioritize supporting early numeracy. Parents’ beliefs, especially about their child’s academic abilities, may influence components of the early home math environment, but future research is needed to better understand the relations between parent’s academic beliefs and the home math environment they create.

The roles of patterning and spatial skills in early mathematics development

Because math knowledge begins to develop at a young age to varying degrees, it is important to identify foundational cognitive and academic skills that might contribute to its development. The current study focused on two important, but often overlooked skills that recent evidence suggests are important contributors to early math development: patterning and spatial skills. We assessed preschool children’s repeating patterning skills, spatial skills, general cognitive skills and math knowledge at the beginning of the pre-kindergarten year. We re-assessed their math knowledge near the end of the school year, with complete data for 73 children. Children’s repeating patterning and spatial skills were related and were each unique predictors of children’s math knowledge at the same time point and seven months later. Further, repeating patterning skills predicted later math knowledge even after controlling for prior math knowledge. Thus, although repeating patterning and spatial skills are related, repeating patterning skills are a unique predictor of math knowledge and growth. Both theories of early math development and early math standards should be expanded to incorporate a role for repeating patterning and spatial skills.

Relationship between single digit addition strategies and working memory reflects general reasoning sophistication

With age, children employ increasingly more sophisticated strategies to solve single-digit addition (SDA) number fact problems. Changes in SDA strategy-use are correlated with age-related changes in cognitive measures (e.g., working-memory capacity, WM); however, this correlation does not explain the basis of SDA strategy-use or change per se. Does strategy-use reflect differences in generally reasoning abilities or are they uniquely tied to SDA abilities? Answers to these questions would help clarify the nature of SDA abilities specifically and early math abilities more generally. To investigate these issues, we assessed 144 5- to 9-year-olds' SDA strategies, visuospatial working memory (VSWM), verbal WM, non-verbal IQ, basic RT, and visuospatial reasoning abilities. We focused on these abilities since recent research shows visuospatial processes support early math development. We used latent profile/class analysis to classify children's SDA strategies and visuospatial reasoning abilities, which yielded four ability subgroups in both cases, only partially related to age. Findings show SDA strategy subgroup and general reasoning subgroup memberships were related. More sophisticated subgroups had better WM, but did not differ in IQ and RT. Findings suggest SDA reasoning reflect general reasoning abilities. Implications for math skills acquisition and intervention are discussed.

Preschoolers' Dot Enumeration Abilities Are Markers of Their Arithmetic Competence

The abilities to enumerate small sets of items (e.g., dots) and to compare magnitudes are claimed to be indexes of core numerical competences that scaffold early math development. Insofar as this is correct, these abilities may be diagnostic markers of math competence in preschoolers. However, unlike magnitude comparison abilities, little research has examined preschoolers' ability to enumerate small sets, or its significance for emerging math abilities; which is surprising since dot enumeration is a marker of school-aged children's math competence. It is nevertheless possible that general cognitive functions (working memory, response inhibition in particular) are associated with preschoolers' math abilities and underlie nascent dot enumeration abilities. We investigated whether preschoolers' dot enumeration abilities predict their non-verbal arithmetic ability, over and above the influence of working memory and response inhibition. Two measures of dot enumeration ability were examined—inverse efficiency and paradigm specific (response time profiles) measures—to determine which has the better diagnostic utility as a marker of math competence. Seventy-eight 42-to-57 month-olds completed dot enumeration, working memory, response inhibition, and non-verbal addition and subtraction tasks. Dot enumeration efficiency predicted arithmetic ability over and above the influence of general cognitive functions. While dot enumeration efficiency was a better predictor of arithmetic ability than paradigm specific response time profiles; the response time profile displaying the smallest subitizing range and steepest subitizing slope, also displayed poor addition abilities, suggesting a weak subitizing profile may have diagnostic significance in preschoolers. Overall, the findings support the claim that dot enumeration abilities and general cognitive functions are markers of preschoolers' math ability.

Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence.

Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners' nonverbal number sense and domain-general abilities (i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (i.e., arithmetic, shape and space skills, and number line estimation) assessed 1 year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms.

Childcare quality and preschoolers' math development

This study examined the associations between four types of childcare quality (i.e. teacher–child closeness, frequency of math-related activities, and teacher education and experience) and preschoolers' residualised gain in math over the course of six months. Additionally, potential interactions between teacher–child closeness and other indicators of childcare quality were examined. Findings indicated that teacher–child closeness was positively associated with math gains, and the main effect was moderated by teacher experience: the association between teacher–child closeness and gains in math was weaker for children with more experienced teachers. Findings also showed that the frequency of math activities related to shapes and patterns were positively related to gains in math, while none of the other frequencies of math-related activities were significant. Lastly, teacher's experience was negatively associated with early math development. Policy implications were discussed.