The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study
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.
Finger configurations and kindergarteners’ mathematical abilities
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.
Mapping skills between symbols and quantities in preschoolers: The role of finger patterns
Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4-year-olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence.
Interrelations between acuity of the approximate number system and symbolic skills in preschool 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.
Rasch modeling of the test of early mathematics ability: Third edition with a sample of K1 children in Singapore
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.
Numeral order and the operationalization of the numerical system
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.
Arithmetic word problem solving. Analysis of Singaporean and Spanish textbooks
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.
Preschool teachers’ engagement in professional development: Frequency, perceived usefulness, and relationship with self-efficacy beliefs
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.
Cross- and within-domain associations of early reading and mathematical skills: Changes across the preschool years
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.
Working memory and numeracy training for children with math learning difficulties: Evidence from a large-scale implementation in the classroom
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.