The Interaction between Congruency and Numerical Ratio Effects in the Nonsymbolic Comparison Test.

The nonsymbolic comparison task is used to investigate the precision of the Approximate Number Sense, the ability to process discrete numerosity without counting and symbols. There is an ongoing debate regarding the extent to which the ANS is influenced by the processing of non-numerical visual cues. To address this question, we assessed the congruency effect in a nonsymbolic comparison task, examining its variability across different stimulus presentation formats and numerical proportions. Additionally, we examined the variability of the numerical ratio effect with the format and congruency. Utilizing generalized linear mixed-effects models with a sample of 290 students (89% female, mean age 19.33 years), we estimated the congruency effect and numerical ratio effect for separated and intermixed formats of stimulus presentation, and for small and large numerical proportions. The findings indicated that the congruency effect increased in large numerical proportion conditions, but this pattern was observed only in the separated format. In the intermixed format, the congruency effect was insignificant for both types of numerical proportion. Notably, the numerical ratio effect varied for congruent and incongruent trials in different formats. The results may suggest that the processing of visual non-numerical parameters may be crucial when numerosity processing becomes noisier, specifically when numerical proportion becomes larger. The implications of these findings for refining the ANS theory are discussed.

Processing Speed throughout Primary School Education: Evidence from a Cross-Country Longitudinal Study.

This cross-country four-year longitudinal study investigated the development of processing speed throughout primary school education. The analyses were conducted on data accumulated from 441 pupils in grades from 1 to 4 (aged 6.42 to 11.85 years) in Kyrgyzstan and Russia. Mixed effects growth modeling was applied to estimate average and individual growth trajectories for processing speed in two cross-country samples. Latent class growth modeling was conducted to describe various types of growth trajectories for processing speed and to compare the distribution of the types within the analyzed samples. According to the results, processing speed significantly increases across primary school years. The trajectory is described by nonlinear changes with most dynamic growth between grades 1 and 2, which slows down until grade 4. No significant cross-country differences were found in the initial score of processing speed or developmental changes in processing speed across primary school years. The development of processing speed is described by a model including three quadratic growth types but this minimally differs. It is concluded that in both samples, the development of processing speed may be characterized by homogeneity, with the most intensive growth from grade 1 to grade 2 and subsequent linear improvement until grade 4.

The development of number line accuracy in elementary school children: A cross-country longitudinal study.

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.

The effect of visual parameters on nonsymbolic numerosity estimation varies depending on the format of stimulus presentation.

The extent to which the approximate number sense is based on the estimation of continuous visual properties has been widely discussed. Some investigators have hypothesized that humans are able to estimate numerosity directly and independently of visual cues. Other investigators have posited that numerosity can be processed only via the estimation of non-numeric visual properties. The latter theory is confirmed by the existence of the congruency effect, that is, greater accuracy in congruent trials where visual properties were positively correlated with numerosity compared with that in incongruent trials. In this study, we tested the assumption that the congruency effect, reflecting the bias in numerosity estimation due to the estimation of visual cues, varies depending on the format of the stimulus presentation and object heterogeneity. The study involved a sample of pupils in Grades 5-9 from Kyrgyzstan (N = 764; 48% girls; mean age = 13.06 years), whereby participants performed a nonsymbolic comparison test in four formats of stimulus presentation: paired/homogeneous, paired/heterogeneous, mixed/homogeneous, and mixed/heterogeneous. Compared arrays of figures might be congruent or incongruent for one visual parameter (convex hull or cumulative area), whereas another visual parameter was held constant for two arrays. The results of generalized linear mixed-effect models demonstrated that the largest congruency effect occurred in a paired format with homogeneous figures. The congruency effect was insignificant in the mixed/heterogeneous format. The results also revealed that the effects of the convex hull and cumulative area varied in different formats of stimulus presentations.

Developmental Changes in ANS Precision Across Grades 1-9: Different Patterns of Accuracy and Reaction Time.

The main aim of this study was to analyze the patterns of changes in Approximate Number Sense (ANS) precision from grade 1 (mean age: 7.84 years) to grade 9 (mean age: 15.82 years) in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1-5 (elementary school education plus the first year of secondary education), and the second cohort was assessed at grades 5-9 (secondary school education). ANS precision was assessed by accuracy and reaction time (RT) in a non-symbolic comparison test ("blue-yellow dots" test). The patterns of change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3 (7-9 years old). The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9 (13-15 years old), while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7 (7-13 years old), and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system.

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

In this study, we aimed to compare developmental changes in nonsymbolic and symbolic magnitude representations across the elementary school years. For this aim, we used a four-wave longitudinal study with a one-year interval in schoolchildren in grades 1-4 in Russia and Kyrgyzstan (N = 490, mean age was 7.65 years at grade 1). The results of mixed-effects growth models revealed that growth in the precision of symbolic representation was larger than in the nonsymbolic representation. Moreover, growth in nonsymbolic representation was fully explained by growth in fluid intelligence (FI), visuospatial working memory (VSWM) and processing speed (PS). The analysis demonstrated that growth in nonsymbolic magnitude representation was significant only for pupils with a high level of FI and PS, whereas growth in precision of symbolic representation did not significantly vary across pupils with different levels of FI or VSWM.

The Relationship Between Non-symbolic and Symbolic Numerosity Representations in Elementary School: The Role of Intelligence.

This study aimed to estimate the extent to which the development of symbolic numerosity representations relies on pre-existing non-symbolic numerosity representations that refer to the Approximate Number System. To achieve this aim, we estimated the longitudinal relationships between accuracy in the Number Line (NL) test and "blue-yellow dots" test across elementary school children. Data from a four-wave longitudinal study involving schoolchildren in grades 1-4 in Russia and Kyrgyzstan (N = 490, mean age 7.65 years in grade 1) were analyzed. We applied structural equation modeling and tested several competing models. The results revealed that at the start of schooling, the accuracy in the NL test predicted subsequent accuracy in the "blue-yellow dots" test, whereas subsequently, non-symbolic representation in grades 2 and 3 predicted subsequent symbolic representation. These results indicate that the effect of non-symbolic representation on symbolic representation emerges after a child masters the basics of symbolic number knowledge, such as counting in the range of twenty and simple arithmetic. We also examined the extent to which the relationships between non-symbolic and symbolic representations might be explained by fluid intelligence, which was measured by Raven's Standard Progressive Matrices test. The results revealed that the effect of symbolic representation on non-symbolic representation was explained by fluid intelligence, whereas at the end of elementary school, non-symbolic representation predicted subsequent symbolic representation independently of fluid intelligence.

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.