Mathematics Clusters Reveal Strengths and Weaknesses in Adolescents' Mathematical Competencies, Spatial Abilities, and Mathematics Attitudes

The relation between number line performance and mathematics outcomes: Two meta-analyses

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (β = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains.

Development of early numeracy skills in children with moderate intellectual disability

This study assessed the effectiveness of a program aimed at improving the early numeracy skills of students with moderate intellectual disability. The persistence of the acquired skills and the program's impact on learning were monitored. Feedback from the students and their mothers was also gathered. Using a multiple-probe design across subjects, the results were visually presented through graphical analysis. Three male students aged 8-9 years participated. After obtaining high-reliability findings from reliability analyses, results showed the program effectively increased students' number skills with a high effect size. These skills persisted post-intervention, and both students and mothers expressed positive views of the intervention.

Sex Differences and Similarities in Relations Between Mathematics Achievement, Attitudes, and Anxiety: A Seventh-to-Ninth Grade Longitudinal Study

There are consistent correlations between mathematics achievement, attitudes, and anxiety, but the longitudinal relations among these constructs are not well understood nor are sex differences in these relations. To address this gap, mathematics achievement, attitudes, and anxiety were longitudinally assessed for 342 (169 boys) adolescents from 7th to 9th grade, inclusive, and Latent Growth Curve Models were used to assess the relations among these traits and developmental change in them. Spatial abilities (7th, 8th grade) and trait anxiety (8th, 9th grade) were also assessed and used for control for sex differences in these traits. Overall, boys had stronger spatial abilities and more positive mathematics attitudes and were less anxious than girls, but there were no sex differences in mathematics achievement. Across grades, mathematics achievement improved, attitudes became less positive, and anxiety increased for both boys and girls. Higher than average cross-grade growth in mathematics achievement mitigated boys' developmental declines in mathematics attitudes and increases in anxiety. Girls with strong spatial abilities had lower mathematics anxiety, but girls overall maintained higher mathematics anxiety and less positive mathematics attitudes relative to boys, even when they showed strong cross-grade gains in mathematics achievement. The study demonstrated that longitudinal gains in mathematics are associated with cross-grade changes in attitudes and anxiety but with several different developmental patterns for boys and girls.

The Relationship between Working Memory and Arithmetic in Primary School Children: A Meta-Analysis

Working memory (WM) plays a crucial role in the development of arithmetic ability. However, research findings related to which factors influence the relationship between WM and arithmetic skills are inconsistent. The present meta-analysis aimed to examine the links between WM and arithmetic in primary school children and investigate whether this is dependent on WM domains (i.e., verbal, visual, spatial), child age, arithmetic operation type, and arithmetic task type. A total of 11,224 participants with an age range of 6- to 12 years, from 55 independent samples were included in the meta-analysis. Analysis of 46 studies with 187 effect sizes revealed an overall significant and medium correlation between WM and arithmetic. Heterogeneity analyses indicated that verbal WM showed a stronger correlation with arithmetic than visuospatial WM, and that correlations between verbal WM and arithmetic declined with age, whereas correlations between spatial-sequential, and spatial-simultaneous WM and arithmetic remained stable throughout development. Addition and subtraction were more involved in verbal WM than multiplication and division. Moreover, mental and written arithmetic showed comparable correlations with WM in all domains. These findings suggest moderation effects of WM domains, age, and operation types in the WM-arithmetic relationship and highlight the significant role of verbal WM in arithmetic ability in primary school children.