The nature of the association between number line and mathematical performance: An international twin study

The number line estimation task is a valid tool for assessing mathematical achievement: A population-level study with 6484 Luxembourgish ninth-graders

The number line estimation task is an often-used measure of numerical magnitude understanding. The task also correlates substantially with broader measures of mathematical achievement. This raises the question of whether the task would be a useful component of mathematical achievement tests and instruments to diagnose dyscalculia or mathematical giftedness and whether a stand-alone version of the task can serve as a short screener for mathematical achievement. Previous studies on the relation between number line estimation accuracy and broader mathematical achievement were limited in that they used relatively small nonrepresentative samples and usually did not account for potentially confounding variables. To close this research gap, we report findings from a population-level study with nearly all Luxembourgish ninth-graders (N = 6484). We used multilevel regressions to test how a standardized mathematical achievement test relates to the accuracy in number line estimation on bounded number lines with whole numbers and fractions. We also investigated how these relations were moderated by classroom characteristics, person characteristics, and trial characteristics. Mathematical achievement and number line estimation accuracy were associated even after controlling for potentially confounding variables. Subpopulations of students showed meaningful differences in estimation accuracy, which can serve as benchmarks in future studies. Compared with the number line estimation task with whole numbers, the number line estimation task with fractions was more strongly related to mathematical achievement in students across the entire mathematical achievement spectrum. These results show that the number line estimation task is a valid and useful tool for diagnosing and monitoring mathematical achievement.

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.