Development of approximate number sense across the elementary school years: A cross‐cultural longitudinal study

Abstract

In recent years, there has been growing interest among researchers in exploring approximate number sense (ANS)—the ability to estimate and discriminate quantities without the use of symbols. Despite the growing number of studies on ANS, there have been no cross‐cultural longitudinal studies to estimate both the development of ANS and the cross‐cultural differences in ANS growth trajectories. In this study, we aimed to estimate the developmental trajectories of ANS from the beginning of formal education to the end of elementary school in two countries, Russia and Kyrgyzstan, which have similar organization of their educational systems but differences in socioeconomic status (SES) and in the results of large‐scale educational assessments. To assess the developmental trajectories of ANS, we used a four‐wave longitudinal study with 416 participants from two countries and applied the mixed effect growth approach and the latent class growth approach. Our analysis revealed that the rate of growth in ANS accuracy was higher for the Russian sample than for the Kyrgyz sample and that this difference remained significant even after controlling for fluid intelligence. We identified two latent classes of growth trajectories: the first class had a significant growth in ANS, whereas the second class had no growth. Comparing the distribution of latent classes within the two countries revealed that there was a significantly larger proportion of schoolchildren from the second class in Kyrgyzstan than in Russia.

Domain-general cognitive functions fully explained growth in nonsymbolic magnitude representation but not in symbolic representation in elementary school children

“…Our sample consisted of pupils from Russia and Kyrgyzstan. An estimation of cross-country differences in growth of ANS revealed that the rate growth was significantly lower in the Kyrgyz sample [24]. These differences might be partly explained by certain characteristics of educational processes in elementary school in the Kyrgyz sample Particularly, the class size was larger in the school in Kyrgyzstan than in Russia.…”

“…21]. Growing precision of the ANS manifested as a decrease in Weber fraction (w) [21][22][23] or an increasing proportion of correct answers in nonsymbolic comparison tasks [24,25]. The peak of precision in ANS and smallest w occur near 30 years of age [21].…”

“…It was also shown that the precision of nonsymbolic representation may increase after training and feedback [30,31]. However, some studies demonstrated that experience with formal math was not always associated with growth in ANS precision [24,27,32].…”

Predicting Academic Achievement with Cognitive Abilities: Cross-Sectional Study across School Education

“…Studies have shown that academic achievement is largely related to the individual characteristics of basic cognitive processes, i.e., information processing speed, visuospatial working memory, and number sense [ 2 , 5 , 6 , 7 , 8 ], as well as higher-order cognitive processes, such as primarily fluid intelligence [ 1 , 3 , 5 , 9 , 10 ].…”

“…In general, basic cognitive traits, along with intelligence, explain up to 60% of the dispersion of academic success [ 5 ]. Additionally, studies report that the indicators of cognitive abilities are age-related and have unique developmental trajectories across schooling [ 6 , 27 , 28 ]. Thus, the trajectory of the development of information processing speed in childhood and adolescence is best described by quadratic dependency, showing an increase in the information processing speed indicators between the ages of 5 and 18, with periods of sharp increases and periods of relative stability [ 29 , 30 ].…”