Cognitive Abilities and Mathematical Competencies at School Entry

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.

The role of executive function in shaping the longitudinal stability of math achievement during early elementary grades

There is substantial rank-order stability in children's mathematical skills throughout development. Research has shown that children who enter school with relatively low math skills are unlikely to catch up to peers who begin kindergarten with more developed math skills. Emerging evidence suggests that children's executive function skills might play an important role in shaping the rate and stability of mathematical skill development during early development. Therefore in the present study, we used data from the Early Childhood Longitudinal Study-Kindergarten Cohort 2010-11-a prospective sample of over 18,000 children in the United States-to examine executive function as an antecedent to characteristics of growth in math skills and to test whether executive function moderates the longitudinal stability of math achievement from kindergarten through second grade. Latent growth curve models reveal that executive function is related to not only the level of math skills at school entry but also to the rate of growth in early elementary years. Moreover, we found that executive function moderated the stability of math achievement from kindergarten to second grade, suggesting that early executive function skills can serve as a compensatory mechanism for children who enter school with lower levels of mathematical skills. These findings might have important implications for narrowing gaps in math achievement during early elementary school.

Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling

Background

The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children.

Methods

The current study recruited 6- and 7-year-old children (N_total = 505, n_6yrs = 238, and n_7yrs = 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses.

Results

The current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.

Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach

Previous research repeatedly found basic numerical abilities (e.g., magnitude understanding, arithmetic fact knowledge, etc.) to predict young students' current and later arithmetic achievement as assessed by achievement tests - even when controlling for the influence of domain-general abilities (e.g., intelligence, working memory). However, to the best of our knowledge, previous studies hardly addressed this issue in secondary school students. Additionally, they primarily assessed basic numerical abilities in a between-task approach (i.e., using different tasks for different abilities). Finally, their relevance for real-life academic outcomes such as mathematics grades has only rarely been investigated. The present study therefore pursued an approach using one and the same task (i.e., a within-task approach) to reduce confounding effects driven by between-task differences. In particular, we evaluated the relevance of i) number magnitude understanding, ii) arithmetic fact knowledge, and iii) conceptual and procedural knowledge for the mathematics grades of 81 students aged between ten and thirteen (i.e., in Grades 5 and 6) employing the number bisection task. Results indicated that number magnitude understanding, arithmetic fact knowledge, and conceptual and procedural knowledge contributed to explaining mathematics grades even when controlling for domain-general cognitive abilities. Methodological and practical implications of the results are discussed.

The Multifactorial Nature of Early Numeracy and Its Stability

Early numeracy is a robust predictor of later mathematical abilities. So far, early numeracy has typically been presented as a unitary or two-factorial construct. Nevertheless, there is recent evidence suggesting that it may also be reflected by more basic numerical competences. However, the structure and stability of such a multifactorial model of early numeracy over time has not been investigated yet. In the present study, we used data from a large, longitudinal sample (N = 1292) in the United States with assessments of math ability in prekindergarten and kindergarten to evaluate both the factorial structure of early numeracy and its stability over time. Confirmatory factor analysis identified four distinct basic numerical competences making up early numeracy in prekindergarten: patterning/geometry, number sense, arithmetic, and data analysis/statistics. Stability as tested by means of measurement invariance indicated configural invariance of these four factors from prekindergarten to kindergarten. This reflected that early numeracy in kindergarten was made up by the same four basic numerical competences as in prekindergarten and thus seemed rather stable over the course of preschool. These findings may not only have implications for research on numerical cognition but particularly for diagnostic processes or the development of interventions in educational practice.

Executive functions form a single construct and are associated with schooling: Evidence from three low- and middle- income countries

Measuring executive function (EF) among adults is important, as the cognitive processes involved in EF are critical to academic achievement, job success and mental health. Current evidence on measurement and structure of EF largely come from Western, Educated, Industrialized, Rich and Democratic (WEIRD) countries. However, measuring EF in low-and-middle-income countries (LMICs) is challenging, because of the dearth of EF measures validated across LMICs, particularly measures that do not require extensive training, expensive equipment, or professional administration. This paper uses data from three LMIC cohorts to test the feasibility, validity and reliability of EF assessment in adults using three sub-tests (representing key components of EF) of the NIH Toolbox Cognitive battery. For each cohort, all three EF measures (inhibition, flexibility and working memory) loaded well onto a unidimensional latent factor of EF. Factor scores related well to measures of fluid intelligence, processing speed and schooling. All measures showed good test-retest reliability across countries. This study provides evidence for a set of sound measures of EF that could be used across different cultural, language and socio-economic backgrounds in future LMIC research. Furthermore, our findings extend conclusions on the structure of EF beyond those drawn from WEIRD countries.

Executive Functions and Fine Motor Skills in Kindergarten as Predictors of Arithmetic Skills in Elementary School

The present longitudinal study focused on domain-general predictors of arithmetics in elementary school. The role of executive functions (EFs) and fine motor skills for the prediction of arithmetic skills in 1st/2nd grade was examined. Data from N = 173 kindergarten children were included. Age, socioeconomic status, fluid intelligence, and processing speed were controlled. Regression analyses revealed that fine motor skills predicted arithmetic skills. When EFs were added, fine motor skills did not contribute to the prediction of arithmetic skills. Visuospatial working memory and interference control were significant predictors. Findings indicate an important role of EF as predictors of arithmetic skills.