The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation.

Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.

Math learning disability (MLD) or developmental dyscalculia is a highly prevalent and persistent difficulty in learning arithmetic that may be explained by different cognitive mechanisms. The accuracy of the number sense has been implicated by some evidence as a core deficit in MLD. However, research on this topic has been mainly conducted in demographically selected samples, using arbitrary cut-off scores to characterize MLD. The clinical relevance of the association between number sense and MLD remains to be investigated. In this study, we aimed at assessing the stability of a number sense accuracy measure (w) across five experimental sessions, in two clinically defined cases of MLD. Stable measures of number sense accuracy estimate are required to clinically characterize subtypes of MLD and to make theoretical inferences regarding the underlying cognitive mechanisms. G. A. was a 10-year-old boy with MLD in the context of dyslexia and phonological processing impairment and his performance remained steadily in the typical scores range. The performance of H. V., a 9-year-old girl with MLD associated with number sense inaccuracy, remained consistently impaired across measurements, with a nonsignificant tendency to worsen. Qualitatively, H. V.'s performance was also characterized by greater variability across sessions. Concomitant clinical observations suggested that H. V.'s difficulties could be aggravated by developing symptoms of mathematics anxiety. Results in these two cases are in line with the hypotheses that at least two reliable patterns of cognitive impairment may underlie math learning difficulties in MLD, one related to number sense inaccuracy and the other to phonological processing impairment. Additionally, it indicates the need for more translational research in order to examine the usefulness and validity of theoretical advances in numerical cognition to the clinical neuropsychological practice with MLD.

ResumoO progresso tecnológico e econômico de um país associa-se a melhorias na qualidade de vida à custa de uma demanda crescente do desempenho cognitivo e acadêmico da população. As dificuldades de aprendizagem da matemática (DAM) representam um risco, diminuindo potencialmente o capital cognitivo de uma sociedade. Os diagnósticos e intervenções neuropsicológicos melhoram potencialmente o funcionamento cognitivo e o bem-estar dos indivíduos. Pesquisas são necessárias para um planejamento efetivo e equitativo de políticas públicas. Os critérios diagnósticos atuais das dificuldades de aprendizagem são estatísticos e arbitrários, resultando em uma heterogeneidade clínica e em um alto índice de comorbidades. Neste artigo, foram analisados, através de uma revisão de literatura, os possíveis mecanismos cognitivos envolvidos nas DAM e em outros distúrbios relacionados. Conclui-se que o processamento fonológico, a memória de trabalho, o processamento visoespacial e o senso numérico são domínios potencialmente subjacentes às DAM. Mais estudos longitudinais e integrativos que avaliem simultaneamente a contribuição destes fatores são necessários. Palavras-chave:Dificuldades de aprendizagem da matemática; senso numérico; memória de trabalho; habilidades visoespaciais; revisão. AbstractTechnological and economic progress is associated to higher living standards at the expense of growing demands on cognitive/academic performance. Mathematical learning difficulties (MLD) represent a risk factor, potentially diminishing a society's cognitive capital. Neuropsychological diagnosis and interventions potentially improve cognitive functioning and well-being. Research data are required to plan effective and equitable public policies. Current diagnostic criteria for learning difficulties are statistical and arbitrary, resulting in clinical heterogeneity and high comorbidity rates. In this paper, we discuss possible cognitive mechanisms involved in MLD and their relationship to other disorders through a literature review. It is concluded that phonological processing, working memory, visuospatial processing and number sense are domains potentially underlying MLD. More longitudinal and integrative studies, simultaneously assessing the contribution of these several factors are required.

Although important for the acquisition of later math skills, fractions are notoriously difficult. Previous studies have shown that higher math anxiety (MA) is associated with lower performance in symbolic fraction tasks in adults and have suggested that MA may negatively impact the acquisition of fractions in children. However, the effects of MA on fraction skills in school‐aged children remain underexplored. We, therefore, investigated the impact of MA on the performance of younger (second and third graders) and older (fifth and sixth graders) children in math fluency (MF), written calculation, fraction knowledge (FK), and symbolic fraction and nonsymbolic ratio processing. On the basis of our prior work suggesting a perceptual foundation for fraction processing, we predicted that symbolic, but not nonsymbolic, math skills (especially fractions) would be impaired by MA. As predicted, higher MA was associated with lower performance in general mathematics achievement and symbolic fraction tasks, but nonsymbolic ratio processing was not affected by MA in either age group. Furthermore, working memory capacity partially mediated the effects of MA on general mathematics achievement, FK, and symbolic fraction processing. These results suggest that understanding the bidirectional interactions between MA and fractions may be important for helping children acquire these critical skills.

During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals' mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between (i) basic numeracy, (ii) COVID-19 health numeracy, and (iii) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) ( n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 health-related attitudes and behaviours (e.g. follow experts’ recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one's understanding of data about COVID-19, better numeracy alone is not enough to influence a population's health-related attitudes about disease severity and to increase the likelihood of following public health advice.

Math performance is negatively related to math anxiety (MA), though MA may impact certain math skills more than others. We investigated whether the relation between MA and math performance is affected by task features, such as number type (e.g., fractions, whole numbers, percentages), number format (symbolic vs. nonsymbolic), and ratio component size (small vs. large). Across two large-scale studies (combined n = 3,822), the MA-performance relation was strongest for large whole numbers and fractions, and stronger for symbolic than nonsymbolic fractions. The MA-performance relation was also stronger for smaller relative to larger components, and MA relating to specific number types may be a better predictor of performance than general MA for certain tasks. The relation between MA and estimation performance changes depending on task features, which suggests that MA may relate to certain math skills more than others, which may have implications for how people reason with numerical information and may inform future interventions.

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