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.
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.
Supporting the understanding of cardinal number knowledge in preschoolers: Evidence from instructional practices based on finger patterns
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.