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Background: Number line accuracy (NL accuracy) shows improvement over the course of a school education. However, there are practically no cross-country longitudinal studies of NL accuracy over the whole course of elementary school. Aims: This study investigated the developmental trajectories of NL accuracy and its types across the elementary school years in two countries--Russia and Kyrgyzstan. Sample(s): The analyses were carried out on the data collected from the sample of 508 schoolchildren at Grades 1, 2, 3 and 4 (aged 6.4-11.9 years) from Russia and Kyrgyzstan, who were surveyed as part of the 'Cross-cultural Longitudinal Analysis of Student Success' project. Methods: The participants were administered the 'Number Line' computerized test task and a paper-and-pencil 'Standard Progressive Matrices' test at the end of each academic year. Results: During the course of the elementary school education, NL accuracy increases nonlinearly in both samples from Grade 1 to Grade 4, with a pronounced increase in the rate of improvement from the first to the second year. Cross-country differences in NL accuracy were observed during each year of schooling as well as in the growth of NL accuracy. The development of NL accuracy is described by a model with two developmental types: (1) 'high start and growth' (93% of the pooled sample) and (2) 'low start and no growth' (7%). Conclusions: Both NL accuracy and the rate of its growth during elementary school depend on educational conditions. Cross-country differences in the distribution of schoolchildren by these two developmental types were statistically insignificant.

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.