Munez, David

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.

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.

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.

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.

Existing research has mainly examined the role of cognitive correlates of early reading and mathematics from a stationary perspective that does not consider how these skills unfold and interact over time. This approach constraints the interpretation of cross-domain associations and the specificity of domain-specific covariates. In this study, we disentangle the role of these predictors and investigate cross-domain associations between reading, math, and two related domain-specific predictors (phonological awareness and fluency with number sets) over the kindergarten years (n = 512, Mage = 54 months, SDage = 3.5, 52% females). Results reveal that the overlap between reading and math skills changes over development. Reciprocal associations between reading and math abilities are observed at earlier stages; then, reading abilities become the lead force. Findings also show that phonological awareness and fluency with number sets are domain-specific predictors that do not contribute to cross-domain gains in academic skills. Indeed, there is a trend for domain-specific skills to be more strongly related to achievement at the beginning of formal education than at the beginning of kindergarten, which suggests an increasing differentiation of domains over the kindergarten years. Such findings have implications for the timing and nature of interventions that aim to support children's reading and mathematical development.

We explored the challenges, limitations, and potential effectiveness of a large-scale computerized working memory and numeracy intervention in the classroom with children at risk of mathematical learning disabilities (n = 428, Mage = 83.85 months, 41% female). Children were assigned to four different treatment protocols (working memory [WM], working memory plus numeracy [NWM], numeracy [NUM], and active control [AC]) that were implemented as part of normally scheduled class activities for 1 year. Wide variability in training exposure highlighted the challenges of implementing an ecologically valid large-scale classroom intervention. The NUM and NWM intervention contributed to improvements in various early numeracy skills as well as math achievement after accounting for training exposure. Some of these effects emerged once the intervention concluded. However, the intervention failed to improve WM, which was likely due to insufficient training dosage in the practical setting. Findings suggest that combining both working memory and numerical skills training is worth further investigation. The study also provides evidence of challenges related to the implementation of training programs in real-life learning environments.

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 Test of Early Mathematics Ability – Third Edition (TEMA-3) is a commonly used measure of early mathematics knowledge for children aged 3 years to 8 years 11 months. In spite of its wide use, research on the psychometric properties of TEMA-3 remains limited. This study applied the Rasch model to investigate the psychometric properties of TEMA-3 from three aspects: technical qualities, internal structure, and convergent evidence. Data were collected from 971 K1 children in Singapore. Item fit statistics suggested a reasonable model-data fit. The TEMA-3 items were found to demonstrate generally good technical qualities, interpretable internal structure, and reasonable convergent evidence. Implications for test development, test use, and future research are further discussed.

The success or failure of education systems in promoting student problem-solving skills depends on attitudinal, political, and pedagogical variables. Among these variables, the design of mathematics textbooks is thought to partially explain why students from high-achieving countries show better problem-solving ability in international assessments. In the current study, we delved into this question and compared the frequency and characteristics of arithmetic word problems (AWPs) contained in primary school math textbooks in two countries with different levels of performance in international assessments—Singapore and Spain. In our analyses, we focused on (1) the quantity of arithmetic word problems, (2) the variety of problems in terms of their additive or multiplicative structures and semantic-mathematical substructures, and (3) the quantity and nature of illustrations that were presented together with arithmetic word problems. Although a larger proportion of AWP activities was found in Singaporean textbooks, the results showed a similar variety of AWPs in both Singaporean and Spanish math textbooks. Furthermore, in both countries, math textbooks emphasized the structures classified as (additive) combine 1 and (multiplication) simple rate in AWPs. Notably, the Singaporean textbook contained a larger percentage of illustrations that reflected the semantic-mathematical structures of the problems and helped students learn how to solve AWPs (e.g., bar models). The findings are discussed in light of theories that posit that textbooks constitute a fundamental part of the teaching–learning process in the classroom.