The importance of early numerical and executive function (EF) skills is well-established, with each skill set positively and specifically predicting later mathematics achievement, income, postsecondary education, and more. Less is known, however, about the relations between EF and numerical skills. Therefore, we examined the concurrent and predictive relations between EF and numerical skills in preschoolers to third graders (N = 205; 4.67-8.75 years of age; 43.9% female; 51.2% White non-Hispanic, 18% multiracial, 6.3% Hispanic, 12.2% Black, 2% American Indian/Alaska Native, 4.9% Asian, 1% not otherwise listed). We found positive concurrent relations between EF and all six numerical skills examined: nonsymbolic magnitude comparison, verbal counting, numerical literacy, count on, non-rote counting, and numerical problem solving. There were unidirectional predictive relations between EF and four of the six numerical skills after controlling for covariates and prior performance on the skill of interest. Bidirectional relations were found only for EF and nonsymbolic magnitude comparison. We also found that the concurrent relation between EF and count on was higher for children with typical versus persistently low mathematics achievement. All other concurrent and predictive relations were similar for children with typical and persistently low mathematics achievement. Overall, these findings show that the relations between EF and numerical skills are both pervasive and nuanced, such that they vary by timing of assessments (i.e., concurrent or predictive) and numerical skill. These results can inform future theoretical models on the role of EF in numerical development , have practical implications for designing interventions targeting these skill sets in early childhood. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training , similar technologies.

Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC -ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Relational language is thought to influence mathematical skills. This study examines the association between relational language and number relation skills-knowledge of cardinal, ordinal, and spatial principles-among 104 U.S. kindergartners (5.9 years; 44% boys; 37% White, 25% Black, 14% Asian, 24% other) in the 2017-2018 academic year. Controlling for general verbal knowledge, executive function, and counting and number identification skills, relational language predicted later number relation skills, specifically number line estimation, beta = .30. Relational language did not differentially predict number line estimation performance in children with low or high number relation skills, likely due to the restricted ranges of data within subgroups. Number relation skills, specifically number line estimation and number ordering, may be a pathway between relational language and mathematical skills.

Children's spontaneous focus on numerosity (SFON) is described as an unprompted tendency that is stable across contexts. The attention to number task (AtN), an experimental forced-choice picture-matching task designed to evaluate select aspects of children's focus on numerosity, may reveal whether task materials can implicitly prompt children to focus on numerosity. In two studies, we replicate earlier findings showing an effect of task context on children's performance on the AtN: When asked to identify one or more matches to a target picture from an array of four options, the frequency with which preschoolers and adults identify a numerosity-based match varies as a function of the features on which the remaining match options are based. We addressed a limitation of the original AtN study by including novel combinations of features as additional trials, with which we continued to demonstrate contextual effects. We also showed that adults seemed more susceptible than children to be primed to attend to numerosity on subsequent trials. Children's focus on numerosity under these experimental conditions was remarkably low. We discuss the implications of these findings for better understanding the SFON construct.

Individuals with Mathematics Learning Disabilities have persistent mathematics underperformance but vary with respect to their cognitive profiles. The present study examined mathematics ability and achievement, and associated mathematics-specific numerical skills and domain-general cognitive abilities, in young children with Turner syndrome compared to their matched peers. We utilized two independent peer groups so that group comparisons would account for verbal skills, a hypothesized strength of girls with Turner syndrome, and nonsymbolic magnitude comparison skills, a hypothesized difference of girls with Turner syndrome. This individual matching approach afforded characterization of mathematics profiles of girls with Turner syndrome and girls without Turner syndrome that share potential key features of the Turner syndrome phenotype. Results indicated differences in mathematics ability and nonsymbolic magnitude comparison tasks between girls with Turner syndrome and peers with similar levels of verbal skill. Mathematics ability and mathematics achievement scores of girls with Turner syndrome did not differ significantly from their peers with similar levels of accuracy on a nonsymbolic magnitude comparison task. Cognitive correlates of mathematics outcomes showed disparate patterns across groups. These quantitative and qualitative differences across profiles enhance our understanding of variation in mathematics ability in early childhood and inform how mathematics skills develop in young children with or without Turner syndrome.

A growing body of evidence reveals the need for research on, and consideration for, children's and students' own--self-guided--spontaneous use of mathematical reasoning and knowledge in action. Spontaneous focusing on numerosity (SFON) and quantitative relations (SFOR) have been implicated as key components of mathematical development. In this chapter, we review existing research on SFON and SFOR tendencies in the broader context of the development of mathematical skills and knowledge and examine how the state-of-the-art evidence on SFON and SFOR is relevant for the field of mathematics education. We discuss individual differences in SFON and SFOR, associations between spontaneous focus on mathematical features and mathematics achievement, the contributions of situational contexts that implicitly prompt attention to number, and ways to increase children's focus on number regardless of their baseline level tendencies. We conclude that children's and students' tendencies to focus on number and quantitative relations--spontaneous or otherwise--are key components of mathematical development and education. [For the complete volume, "Constructing Number: Merging Perspectives from Psychology and Mathematics Education. Research in Mathematics Education," see ED616587.]