Munez, David

The current study examines how kindergarten domain-general and domain-specific factors, mathematical skills at primary 1 (P1), and socioeconomic status (SES) predict high versus low (top and bottom 13th percentile) mathematical ability at primary 6 (P6). Four-hundred-and-seven P6 students had previously completed the measures. Logistic path analyses showed that SES, P1 mathematics, and fluid intelligence showed direct significant effects on P6 high achievement group membership. Visuospatial working memory, SES, reading, and P1 mathematics showed direct effects on P6 low group membership. Number sense, fine motor skills, and reading demonstrated indirect effects on both group memberships through P1 mathematics. No significant effect was found for executive functioning or verbal working memory. Findings suggest that there is a qualitative difference in mathematical ability across the performance spectrum. Assessment and instruction should be differentiated to account for predictors that are specific to either end of the ability spectrum.

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.

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.

Enhancing the quality of early childhood education is currently a central goal for many countries. There is widespread agreement that providing preschool teachers with opportunities for professional development (PD) is one of the key ingredients to achieving such a goal. Little is known, however, about the frequency with which preschool teachers engage in the different types of PD activities and about how teachers themselves perceive the usefulness of these activities. Similarly, there is limited research on how participating in PD relates to teachers' self-efficacy beliefs. The present study addresses these gaps in the literature with data collected in a Southeast Asian country: Singapore. Participants were 97 Singapore preschool teachers. A survey composing of several scales was used to collect the data. We explored the frequency and perceived usefulness of seven formal PD activities and 19 informal PD activities, both collaborative and individual. Teachers' self-efficacy was measured with the 'Teacher Sense of Efficacy Scale' (TSES). Our findings showed that: 1) Participants engaged in informal PD (both collaborative and individual) more frequently than in formal PD; 2) There were positive correlations between frequency of participation and teachers' perceived usefulness for both formal and informal PD; and 3) High engagement in collaborative informal PD activities was a strong predictor of teachers' self-efficacy beliefs. These results indicate that work-embedded PD, both collaborative and individual, is highly important to Singapore preschool teachers. In order to enhance the impact and responsiveness of PD, we suggest that formal PD should be integrated as part of the informal PD activities in which teachers regularly engage. Limitations and lines for further research are discussed.

Finger representations are used to count or show quantities. How fingers are lifted to count and the type of representation that we use to communicate quantities have been the focus of studies that have aimed at providing evidence of dominant patterns across cultures. In the current study, we go beyond those studies and investigate intracultural variability. Specifically, whether finger counting habits and finger montring patterns are similar in children and adults. To this aim, a total of 3,210 Spaniard participants took part in this study (637 children and 2,573 adults). All of them were assessed regarding handedness, the way in which they counted with their fingers from 1 to 10 (finger counting) and how they show quantities with their fingers (finger montring). The results showed certain consistency; however, there was substantial variability within each group. Findings are interpreted within the context of current theories reinforcing the relevance of finger patterns to support the understanding of the meaning of numbers.

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.

Previous research has demonstrated a link between children’s ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved. Five-year-old children in Spain (N = 143) were assessed on their ability to name canonical finger configurations and analogous representations (buildings on a hill), alongside a range of mathematical skills (counting, knowledge of the verbal count sequence, single-digit arithmetic, and subitizing). Findings indicated that five-year-olds only recognize single-hand canonical finger configurations as summary symbols, processing them holistically. However, no direct association was found between the ability to recognize these configurations and the assessed mathematical skills. Notably, only the ability to name finger configurations corresponding to larger numbers (requiring enumeration) was associated with children’s arithmetic skills, suggesting that these configurations elicit combinatorial processes that are handshape specific. The implications of these findings for cognitive development and mathematical assessment are discussed, highlighting the potential for finger configurations as a tool for fostering mathematical understanding and the need for further exploration of their cognitive underpinnings.

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.