Maternal education and siblings: Agents of cognitive development in kindergarten
In this study (n = 1000, Mage at K1entry = 53.4 months, SD = 3.4; 53% females), we investigated the contributions of the family socioeconomic status (SES; maternal education and an income-related measure) and number and age of siblings to the development of children's math, reading, and working memory (WM) updating skills over the kindergarten years. Results from a multivariate multilevel growth curve model showed that children from more disadvantaged SES backgrounds already had a multifaceted developmental lag at kindergarten entry. Maternal education was the aspect of SES that more clearly affected the child's cognitive development; the mother's education predicted children's math, reading, and WM-updating skills at kindergarten entry as well as the rate of development of reading skills over the kindergarten years. Independently of SES status, children with more siblings also showed poorer reading and math skills than those in one-child families at kindergarten entry. We also found that both older and younger siblings affected, negatively, children's reading skills before they attended kindergarten—which suggests that the development of reading skills is more responsive to environmental factors during the first years than other aspects of the child development. The findings underscore the independent role of siblings upon entry to kindergarten, and the enduring role of maternal education even after children are exposed to formal schooling.
Socioeconomic status, home mathematics environment and math achievement in kindergarten: A mediation analysis
Growing evidence suggests that parents’ practices contribute to their children's cognitive development and that such practices may reflect SES disparities. This study investigated longitudinal interrelations between home mathematics environment (HME), children's math achievement, and two facets of SES (mother's educational attainment and household income—subsidy status) during the first year in kindergarten (n = 500 children; Mage at T1 = 57.3 months, SD = 3.8). Results revealed that these facets of SES operated through different mechanisms in kindergarten—the association between mothers’ education and math growth at the end of K1 is fully mediated by HME and children's baseline math knowledge. Furthermore, only home math activities that explicitly supported the understanding of addition and subtraction contributed to children's math growth independently of SES background. The pattern of longitudinal associations suggests that the provision of home math activities may reflect children's mathematical abilities rather than SES disparities.
Cross- and within-domain associations of early reading and mathematical skills: Changes across the preschool years
Existing research has mainly examined the role of cognitive correlates of early reading and mathematics from a stationary perspective that does not consider how these skills unfold and interact over time. This approach constraints the interpretation of cross-domain associations and the specificity of domain-specific covariates. In this study, we disentangle the role of these predictors and investigate cross-domain associations between reading, math, and two related domain-specific predictors (phonological awareness and fluency with number sets) over the kindergarten years (n = 512, Mage = 54 months, SDage = 3.5, 52% females). Results reveal that the overlap between reading and math skills changes over development. Reciprocal associations between reading and math abilities are observed at earlier stages; then, reading abilities become the lead force. Findings also show that phonological awareness and fluency with number sets are domain-specific predictors that do not contribute to cross-domain gains in academic skills. Indeed, there is a trend for domain-specific skills to be more strongly related to achievement at the beginning of formal education than at the beginning of kindergarten, which suggests an increasing differentiation of domains over the kindergarten years. Such findings have implications for the timing and nature of interventions that aim to support children's reading and mathematical development.
Mapping skills between symbols and quantities in preschoolers: The role of finger patterns
Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4-year-olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence.
Interrelations between acuity of the approximate number system and symbolic skills in preschool children
This study investigates how the approximate number system (ANS) and young children’s symbolic skills jointly develop and interact. Specifically, the study aims at disentangling the directionality of the association between ANS acuity and a wide range of symbolic skills that reflect 4- to 5-year-olds’ symbolic quantitative knowledge (enumeration skills, knowledge of the verbal count sequence, symbolic comparison skills, and single-digit arithmetic). After accounting for individual differences in several domain-general skills (visuospatial working memory, non-verbal reasoning, and phonological processing), path models on longitudinal data collected from 4-year-old childen in Spain (N = 62) over one year revealed that earlier single-digit arithmetic and symbolic magnitude comparison skills predicted changes in ANS acuity over time. No contribution from earlier ANS to improvements in symbolic skills was found. Notably, the strength of the effect of visuospatial working memory on improvements in ANS acuity over time was like that of the auto-regressor – the correlation between measures of ANS acuity across time points. Implications for extant theories on the nature of the associations between ANS and young children’s symbolic skills are drawn.
Rasch modeling of the test of early mathematics ability: Third edition with a sample of K1 children in Singapore
The Test of Early Mathematics Ability – Third Edition (TEMA-3) is a commonly used measure of early mathematics knowledge for children aged 3 years to 8 years 11 months. In spite of its wide use, research on the psychometric properties of TEMA-3 remains limited. This study applied the Rasch model to investigate the psychometric properties of TEMA-3 from three aspects: technical qualities, internal structure, and convergent evidence. Data were collected from 971 K1 children in Singapore. Item fit statistics suggested a reasonable model-data fit. The TEMA-3 items were found to demonstrate generally good technical qualities, interpretable internal structure, and reasonable convergent evidence. Implications for test development, test use, and future research are further discussed.
Supporting the understanding of cardinal number knowledge in preschoolers: Evidence from instructional practices based on finger patterns
The acquisition of cardinal numbers represents a crucial milestone in the development of early numerical skills and more advanced math abilities. However, relatively few studies have investigated how children's grasping of the cardinality principle can be supported. It has been suggested that the richness of number inputs children receive influences the acquisition of cardinal numbers. The present study was designed to investigate whether canonical finger patterns representing numbers may contribute to this acquisition. Fifty-one 3-year-olds were randomly assigned to 1 of 2 training conditions: (a) a condition that involved counting and labeling, which has shown efficacy to support the acquisition of cardinality, and (b) a condition in which counting and labeling were enriched with finger patterns. Crucially, we aimed at providing evidence of both training programs in a real-life learning environment where teachers incorporated the training as a group-based activity into their regular schedule of daily activities. Children assigned to the finger-based condition outperformed those who received the counting-and-label training. Findings suggest that finger patterns may have a role in children's cardinality understanding. Furthermore, our study shows that instructional approaches for improving cardinality understanding can be easily and successfully implemented into real-life learning settings.
Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks
The success or failure of education systems in promoting student problem-solving skills depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from high-achieving countries show better problem-solving ability in international assessments. In the current study, we delved into this question and compared the frequency and characteristics of arithmetic word problems (AWPs) contained in primary school math textbooks in two countries with different levels of performance in international assessments—Singapore and Spain. In our analyses, we focused on (1) the quantity of arithmetic word problems, (2) the variety of problems in terms of their additive or multiplicative structures and semantic-mathematical substructures, and (3) the quantity and nature of illustrations that were presented together with arithmetic word problems. Although a larger proportion of AWP activities was found in Singaporean textbooks, the results showed a similar variety of AWPs in both Singaporean and Spanish math textbooks. Furthermore, in both countries, math textbooks emphasized the structures classified as (additive) combine 1 and (multiplication) simple rate in AWPs. Notably, the Singaporean textbook contained a larger percentage of illustrations that reflected the semantic-mathematical structures of the problems and helped students learn how to solve AWPs (e.g., bar models). The findings are discussed in light of theories that posit that textbooks constitute a fundamental part of the teaching–learning process in the classroom.
Cultural variability in finger representations / Variabilidad cultural en las representaciones con dedos
Finger representations are used to count or show quantities. How fingers are lifted to count and the type of representation that we use to communicate quantities have been the focus of studies that have aimed at providing evidence of dominant patterns across cultures. In the current study, we go beyond those studies and investigate intracultural variability. Specifically, whether finger counting habits and finger montring patterns are similar in children and adults. To this aim, a total of 3,210 Spaniard participants took part in this study (637 children and 2,573 adults). All of them were assessed regarding handedness, the way in which they counted with their fingers from 1 to 10 (finger counting) and how they show quantities with their fingers (finger montring). The results showed certain consistency; however, there was substantial variability within each group. Findings are interpreted within the context of current theories reinforcing the relevance of finger patterns to support the understanding of the meaning of numbers.
Heterogeneity in children at risk of math learning difficulties
This study recruited 428 Singaporean children at risk of math learning difficulties (MLD; Mage = 83.9 months, SDage = 4.35 months; 41% female). Using a factor mixture model that considered both quantitative and qualitative differences in math ability, two qualitatively different groups were identified: one with generalized difficulties across different math skills and the other with more focal difficulties in arithmetic fluency. Reading, working memory capacity, and numeracy (number line estimation skills and numerical discrimination) uniquely explained group membership. Children within each group differed in the extent of difficulties they exhibited, with numeracy variables differentially contributing to math ability in each group. Findings speak against a dimensional view of MLD and underscore the conceptual limitations of using basic numeracy performance to profile learning difficulties.