Munez, David

This study investigates how the approximate number system (ANS) and young children’s symbolic skills jointly develop and interact. Specifically, the study aims at disentangling the directionality of the association between ANS acuity and a wide range of symbolic skills that reflect 4- to 5-year-olds’ symbolic quantitative knowledge (enumeration skills, knowledge of the verbal count sequence, symbolic comparison skills, and single-digit arithmetic). After accounting for individual differences in several domain-general skills (visuospatial working memory, non-verbal reasoning, and phonological processing), path models on longitudinal data collected from 4-year-old childen in Spain (N = 62) over one year revealed that earlier single-digit arithmetic and symbolic magnitude comparison skills predicted changes in ANS acuity over time. No contribution from earlier ANS to improvements in symbolic skills was found. Notably, the strength of the effect of visuospatial working memory on improvements in ANS acuity over time was like that of the auto-regressor – the correlation between measures of ANS acuity across time points. Implications for extant theories on the nature of the associations between ANS and young children’s symbolic skills are drawn.

The nature of the arithmetic word problems found in maths textbooks influences the way students develop their ability to solve them, as teachers use the books in their classes quite frequently. Given that students are better able to reason through and solve authentic problems that are contextualized in situations familiar to them, and that different international assessments have shown the students in Singapore to be more skilled at problem-solving than their Spanish counterparts, this study compares the level of authenticity of the problems included in the primary school textbooks from the most frequently used publishers in both countries. The results show that the books from Singapore contain problems with a higher degree of authenticity than the Spanish textbooks at all school levels, thus providing students with better opportunities to learn how to solve problems through reasoning.

In this study (n = 1000, M_{age at K1entry} = 53.4 months, SD = 3.4; 53% females), we investigated the contributions of the family socioeconomic status (SES; maternal education and an income-related measure) and number and age of siblings to the development of children's math, reading, and working memory (WM) updating skills over the kindergarten years. Results from a multivariate multilevel growth curve model showed that children from more disadvantaged SES backgrounds already had a multifaceted developmental lag at kindergarten entry. Maternal education was the aspect of SES that more clearly affected the child's cognitive development; the mother's education predicted children's math, reading, and WM-updating skills at kindergarten entry as well as the rate of development of reading skills over the kindergarten years. Independently of SES status, children with more siblings also showed poorer reading and math skills than those in one-child families at kindergarten entry. We also found that both older and younger siblings affected, negatively, children's reading skills before they attended kindergarten—which suggests that the development of reading skills is more responsive to environmental factors during the first years than other aspects of the child development. The findings underscore the independent role of siblings upon entry to kindergarten, and the enduring role of maternal education even after children are exposed to formal schooling.

Although it is thought that young children focus on the magnitude of the target dimension across ratio sets during binary comparison of ratios, it is unknown whether this is the default approach to ratio reasoning, or if such approach varies across representation formats (discrete entities and continuous amounts) that naturally afford different opportunities to process the dimensions in each ratio set. In the current study, 132 kindergarteners (Mage = 68 months, SD = 3.5, range = 62–75 months) performed binary comparisons of ratios with discrete and continuous representations. Results from a linear mixed model revealed that children followed an additive strategy to ratio reasoning—i.e., they focused on the magnitude of the target dimension across ratio sets as well as on the absolute magnitude of the ratio set. This approach did not vary substantially across representation formats. Results also showed an association between ratio reasoning and children’s math problem-solving abilities; children with better math abilities performed better on ratio reasoning tasks and processed additional dimensions across ratio sets. Findings are discussed in terms of the processes that underlie ratio reasoning and add to the extant debate on whether true ratio reasoning is observed in young children.

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.

This study recruited 428 Singaporean children at risk of math learning difficulties (MLD; M_age = 83.9 months, SD_age = 4.35 months; 41% female). Using a factor mixture model that considered both quantitative and qualitative differences in math ability, two qualitatively different groups were identified: one with generalized difficulties across different math skills and the other with more focal difficulties in arithmetic fluency. Reading, working memory capacity, and numeracy (number line estimation skills and numerical discrimination) uniquely explained group membership. Children within each group differed in the extent of difficulties they exhibited, with numeracy variables differentially contributing to math ability in each group. Findings speak against a dimensional view of MLD and underscore the conceptual limitations of using basic numeracy performance to profile learning difficulties.

Recent years have witnessed an increase in research on how numeral ordering skills relate to children’s and adults’ mathematics achievement both cross-sectionally and longitudinally. Nonetheless, it remains unknown which core competency numeral ordering tasks measure, which cognitive mechanisms underlie performance on these tasks, and why numeral ordering skills relate to arithmetic and math achievement. In the current study, we focused on the processes underlying decision-making in the numeral order judgement task with triplets to investigate these questions. A drift-diffusion model for two-choice decisions was fit to data from 97 undergraduates. Findings aligned with the hypothesis that numeral ordering skills reflected the operationalization of the numerical system, where small numbers provide more evidence of an ordered response than large numbers. Furthermore, the pattern of findings suggested that arithmetic achievement was associated with the accuracy of the ordinal representations of numbers.

Growing evidence suggests that parents’ practices contribute to their children's cognitive development and that such practices may reflect SES disparities. This study investigated longitudinal interrelations between home mathematics environment (HME), children's math achievement, and two facets of SES (mother's educational attainment and household income—subsidy status) during the first year in kindergarten (n = 500 children; M_{age at T1} = 57.3 months, SD = 3.8). Results revealed that these facets of SES operated through different mechanisms in kindergarten—the association between mothers’ education and math growth at the end of K1 is fully mediated by HME and children's baseline math knowledge. Furthermore, only home math activities that explicitly supported the understanding of addition and subtraction contributed to children's math growth independently of SES background. The pattern of longitudinal associations suggests that the provision of home math activities may reflect children's mathematical abilities rather than SES disparities.