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

Number sense-arithmetic link in Grade 1 and Grade 2: A case of fluency

BACKGROUND

Recent research suggested fluent processing as an explanation on why number sense contributes to simple arithmetic tasks-'Fluency hypothesis'.

AIMS

The current study investigates whether number sense contributes to such arithmetic tasks when other cognitive factors are controlled for (including those that mediate the link); and whether this contribution varies as a function of participants' individual maths fluency levels.

SAMPLE

Four hundred and thirty-seven Chinese schoolchildren (186 females; Mage = 83.49 months) completed a range of cognitive measures in Grade 1 (no previous classroom training) and in Grade 2 (a year later).

METHODS

Number sense, arithmetic (addition and subtraction), spatial ability, visuo-spatial working memory, perception, reaction time, character reading and general intelligence were measured.

RESULTS

Our data showed that the link between number sense and arithmetic was weaker in Grade 1 (Beta = .15 for addition and .06 (ns) for subtraction) compared to Grade 2 (.23-.28), but still persisted in children with no previous maths training. Further, math's performance in Grade 1 did not affect the link between number sense and maths performance in Grade 2.

CONCLUSION

Our data extended previous findings by showing that number sense is linked with simple maths task performance even after controlling for multiple cognitive factors. Our results brought some evidence that number sense-arithmetic link is somewhat sensitive to previous formal maths education. Further research is needed, as the differences in effects between grades were quite small, and arithmetic in Grade 1 did not moderate the link at question in Grade 2.

The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study

Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; Mage = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns.

Developmental changes of the impact of visual cues on ANS acuity across grades 1-5: Different patterns of visual cues on numerosity processing

Numerous studies have consistently demonstrated the presence of the approximate number system (ANS) throughout development. Research has also revealed that visual cues may influence the ANS acuity, which may change with age. However, most studies have drawn conclusions based on performance differences between incongruent and congruent trials, which may be confounded by an individual's ability to inhibit interference. Therefore, to examine the developmental changes of the impact of visual cues on ANS acuity, we utilized congruent trials with varying visual cues. Our sample comprised Chinese children from grade one to grade five. We manipulated the salience of numerical cues (numerical ratio) and visual cues (dot size) in a non-symbolic numerosity comparison task. The results revealed a discernible leap in development from first to third grade and first to fifth grade; however, this upward trajectory did not persist into the transition from third to fifth grade, where no appreciable advancement was observed. Moreover, we observed different effects of visual cues on the dot-comparison task depending on the numerical cues and age. Specifically, visual cues (i.e., dot size) only facilitated ANS acuity in older school-aged children when numerical cues were weakened. The results indicate the presence of two distinct magnitude representational systems-one for the numerical dimension and another for the non-numerical dimension-during development.

Large-scale study of the precision of the approximate number system: Differences between formats, heterogeneity and congruency effects

The study used a large sample of elementary schoolchildren in Russia (N = 3,448, 51.6% were girls, with a mean age of 8.70 years, ranging 6-11 years) to investigate the congruency, format and heterogeneity effects in a nonsymbolic comparison test and between-individual differences in these effects with generalized linear mixed effects models (GLMMs). The participants were asked to compare two arrays of figures of different colours in spatially separated or spatially intermixed formats. In addition, the figures could be similar or different for the two arrays. The results revealed that congruency (difference between congruent and incongruent items), format (difference between mixed and separated formats) and heterogeneity (difference between homogeneous and heterogeneous conditions) interacted. The heterogeneity effect was higher in the separated format, while the format effect was higher for the homogeneous condition. The separated format produced a greater congruency effect than the mixed format. In addition, the congruency effect was lower in the heterogeneous condition than in the homogeneous condition. Analysis of between-individual differences revealed that there was significant between-individual variance in the format and congruency effects. Analysis of between-grade differences revealed that accuracy improved from grade 1 to grade 4 only for congruent trials in separated formats. Consequently, the congruency effect increased in separated/homogeneous and separated/heterogeneous conditions. In general, the study demonstrated that the test format and heterogeneity affected accuracy and that this effect varied for congruent and incongruent items.

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.

Cross-cultural Analysis of Models of the Relationship between the Cognitive Abilities and Academic Achievement in Primary School Education

Background

The cognitive predictors of academic achievement are associated both with basic cognitive abilities such as the information processing speed, number sense and visuospatial working memory, as well as with general ability including nonverbal intelligence. However, the ratio between cognitive development and school achievement can depend on sociocultural conditions.

Objective

The results of a cross-cultural analysis of the relationship between cognitive development and academic achievement during primary education are presented. The analysis was conducted sampling schoolchildren from Russia and Kyrgyzstan, two countries that have a similar organization of the national education system but differ in the level of socioeconomic development.

Design

The study involved 732 schoolchildren aged 7.7 to 11.8 years studying in Russia and Kyrgyzstan. Information processing speed, visuospatial working memory, and number sense were assessed using each of "Choice Reaction Time," "Corsi Block-Tapping Test," and "Number Sense" computerized tests.

Results

According to the results, empirical data in both samples show that a model where in information processing speed signifies basic cognitive ability is a key predictor of nonverbal intelligence, working memory, and number sense, and each of these may contribute to individual differences in academic achievement. Notwithstanding the universality of this model, cross-cultural differences were seen to engender a reduction of schoolchildren's academic achievements, given possible impacts of less favorable educational conditions.

Conclusion

In the relationship between cognitive abilities and academic success at the primary school education, there are both similarities and differences between schoolchildren studying in Russia and Kyrgyzstan.

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.

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

The relationship between cognitive abilities and academic achievement across schooling from the first to the eleventh grade was analyzed. Information processing speed, visuospatial working memory, number sense, and fluid intelligence were considered predictors of general academic achievement, which was derived from grades in mathematics, language, and biology. This cross-sectional study involved 1560 pupils who were in grades 1-11 at general education schools and were aged from 6.8 to 19.1 years (50.4% were boys). Information processing speed, visuospatial working memory, and number sense were measured using the Choice Reaction Time, Corsi Block-Tapping, and Number Sense computerized tests, respectively. Fluid intelligence was measured using the paper-and-pencil version of the Standard Progressive Matrices test. Correlation analysis and structural equation modeling were carried out. It was shown that it is possible to describe the structure of the relationship between cognitive abilities and academic achievement for all levels of schooling with a single model. In this model, information processing speed is the key predictor of fluid intelligence, working memory, and number sense, which in turn contribute to individual differences in academic success. Additionally, the specificity of the relationship between individual indicators of cognitive abilities and academic achievement at each level of schooling was revealed.