Does It Count? Pre-School Children’s Spontaneous Focusing on Numerosity and Their Development of Arithmetical Skills at School

Abstract

Background: Children’s spontaneous focusing on numerosity (SFON) is related to numerical skills. This study aimed to examine (1) the developmental trajectory of SFON and (2) the interrelations between SFON and early numerical skills at pre-school as well as their influence on arithmetical skills at school. Method: Overall, 1868 German pre-school children were repeatedly assessed until second grade. Nonverbal intelligence, visual attention, visuospatial working memory, SFON and numerical skills were assessed at age five (M = 63 months, Time 1) and age six (M = 72 months, Time 2), and arithmetic was assessed at second grade (M = 95 months, Time 3). Results: SFON increased significantly during pre-school. Path analyses revealed interrelations between SFON and several numerical skills, except number knowledge. Magnitude estimation and basic calculation skills (Time 1 and Time 2), and to a small degree number knowledge (Time 2), contributed directly to arithmetic in second grade. The connection between SFON and arithmetic was fully mediated by magnitude estimation and calculation skills at pre-school. Conclusion: Our results indicate that SFON first and foremost influences deeper understanding of numerical concepts at pre-school and—in contrast to previous findings –affects only indirectly children’s arithmetical development at school.

Taking a Closer Look: The Relationship between Pre-School Domain General Cognition and School Mathematics Achievement When Controlling for Intelligence

“…However, previously acquired mathematical skills and thus domain-specific predictors are even more relevant. This is in line with previous longitudinal studies highlighting the importance of early numerical skills for the development of arithmetical skills in school (e.g., Aunio and Niemivirta 2010;Fritz et al 2013Fritz et al , 2018Gallit et al 2018;Poltz et al 2022;Toll et al 2016).…”

“…The domain Magnitude Estimation/Calculation describes the child's ability to grasp quantities quickly and to compare them with one another. The task descriptions, the number of items and the maximum score of each subtest as well as results of confirmational factor analysis were described by Poltz et al (2022). The T-values of the three math-related domains Counting, Number Knowledge and Magnitude Estimation/Calculation were added, standardized and transformed into T-values.…”

“…In particular, visual attention in kindergarten was found to be a good predictor of later mathematical ability. Results of Poltz et al (2022) show that domain-general cognitive abilities (nonverbal intelligence, visuospatial working memory and visual attention) explain a small but significant proportion of children's tendencies to spontaneously focus on numerosity.…”

Challenges in Understanding Numerical Learning: Editorial for Brain Sciences Special Issue “Neurocognitive Signatures of Math (Learning) across the Lifespan and Their Interrelation with Other Aspects of Cognition and Emotion”

“…Moreover, the numerical training had transfer effects to cardinality understanding, while knowledge of the number line was unaffected. Poltz and colleagues [ 5 ] investigated the developmental trajectories of spontaneous focusing on numerosity (SFON) in preschool to second-grade school children. While SFON was found to facilitate numerical concepts in pre-school-age children, it had—contrary to previous findings—only indirect effects on children’s arithmetical development in the first and second grade.…”

Mathematical knowledge and skills as longitudinal predictors of fraction learning among sixth-grade students.

“…Whole number line estimation (WNLE), spontaneous focusing on numerosity tendency (SFoN), and spontaneous focusing on relations tendency (SFoR) are examples of such constructs. Their effects on a range of later mathematics skills have been reported in the literature (e.g., Batchelor et al, 2015: arithmetic skills including addition; Lepola & Hannula-Sormunen, 2019: arithmetic skills including addition, subtraction, multiplication, division; Poltz et al, 2022: arithmetic skills including addition, subtraction, division). Since these later skills include some of the prerequisites of fraction learning mentioned above, the indirect effects of the earlier skills on fraction knowledge are plausible.…”