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

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.