Now showing 1 - 10 of 19
  • Publication
    Metadata only
    The development of early arithmetic skills: What, when, and how?
    Arithmetic skills – the ability to add, subtract, multiply, and divide – are the building blocks of mathematics. Poor arithmetic skills can lead to poor job prospects and life outcomes. It is thus important to investigate the development of arithmetic skills. What constitute the foundations for arithmetic skills? When do they develop? Previous studies have highlighted the importance of the toddler and preschool period as providing foundations for later math learning. In this chapter, we provide an overview of key factors across domain-specific and domain-general areas that support the development of arithmetic skills. We then draw on existing data from the Singapore Kindergarten Impact Project (SKIP) and describe the performance of basic numeracy skills at entry to kindergarten that are relevant for arithmetic learning. These skills include counting, informal arithmetic, and the reading and writing of Arabic digits. Finally, we conclude with guidelines for promoting the development of early mathematical knowledge in the classroom and at home.
      335
  • Publication
    Open Access
    Heterogeneity in children at risk of math learning difficulties
    (2023) ;
    Bull, Rebecca
    ;
    Lee, Kerry
    ;
    Ruiz, Carola
    This study recruited 428 Singaporean children at risk of math learning difficulties (MLD; Mage = 83.9 months, SDage = 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.
    Scopus© Citations 1  42  16
  • Publication
    Open Access
    Working memory and numeracy training for children with math learning difficulties: Evidence from a large-scale implementation in the classroom
    (2022) ;
    Lee, Kerry
    ;
    Bull, Rebecca
    ;
    ;
    Cheam, Fiona
    ;
    Ridzuan Abdul Rahim
    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.
    WOS© Citations 6Scopus© Citations 12  132  917
  • Publication
    Open Access
    Socioeconomic status, home mathematics environment and math achievement in kindergarten: A mediation analysis
    (2021) ;
    Bull, Rebecca
    ;
    Lee, Kerry
    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; Mage 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.
    WOS© Citations 12Scopus© Citations 17  66  176
  • Publication
    Metadata only
    Supporting the understanding of cardinal number knowledge in preschoolers: Evidence from instructional practices based on finger patterns
    (2022)
    Orrantia, Josetxu
    ;
    ;
    Sanchez, Maria Rosario
    ;
    Matilla, Laura
    The acquisition of cardinal numbers represents a crucial milestone in the development of early numerical skills and more advanced math abilities. However, relatively few studies have investigated how children's grasping of the cardinality principle can be supported. It has been suggested that the richness of number inputs children receive influences the acquisition of cardinal numbers. The present study was designed to investigate whether canonical finger patterns representing numbers may contribute to this acquisition. Fifty-one 3-year-olds were randomly assigned to 1 of 2 training conditions: (a) a condition that involved counting and labeling, which has shown efficacy to support the acquisition of cardinality, and (b) a condition in which counting and labeling were enriched with finger patterns. Crucially, we aimed at providing evidence of both training programs in a real-life learning environment where teachers incorporated the training as a group-based activity into their regular schedule of daily activities. Children assigned to the finger-based condition outperformed those who received the counting-and-label training. Findings suggest that finger patterns may have a role in children's cardinality understanding. Furthermore, our study shows that instructional approaches for improving cardinality understanding can be easily and successfully implemented into real-life learning settings.
    WOS© Citations 2Scopus© Citations 5  210
  • Publication
    Open Access
    Working memory training and math achievement evidence from a large-scale intervention in a real learning environment.
    (National Institute of Education (Singapore), 2020) ; ;
    Lee, Kerry
    ;
    Bull, Rebecca
    ;
    Cheam, Fiona
    ;
    Ridzuan Abdul Rahim
      195  197
  • Publication
    Open Access
    Non-symbolic ratio reasoning in kindergarteners: Underlying unidimensional heuristics and relations with math abilities
    (2022) ;
    Bull, Rebecca
    ;
    ;
    Orrantia, Josetxu
    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.
      89  64
  • Publication
    Open Access
    Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks
    (2022)
    Vicente, Santiago
    ;
    Verschaffel, Lieven
    ;
    Sanchez, Maria Rosario
    ;
    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.
    WOS© Citations 3Scopus© Citations 9  272  38
  • Publication
    Open Access
    Numeral order and the operationalization of the numerical system
    (2021) ;
    Orrantia, Josetxu
    ;
    Matilla, Laura
    ;
    Sanchez, Maria Rosario
    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.
    WOS© Citations 3Scopus© Citations 4  256  120
  • Publication
    Embargo
    The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study
    (Elsevier, 2024)
    Ruiz, Carola
    ;
    Kohnen, Saskia
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    ;
    Bull, Rebecca
    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.
      11  15