Children's Acquisition of the Mappings Among the Number Representations

To understand mathematics, children need to learn how the verbal and written number symbols are related to each other and how they are used to represent quantity. How are these mapping skills acquired? Across three studies I examined the relationship between children’s mapping skills and their quantitative and symbolic precursor skills. I also assessed whether children’s mapping skills were related to more advanced numerical skills such as symbolic number comparison (Study 1, 2), and whether the mapping skills improved with training (Study 3). The Pathways Model of early numeracy development (LeFevre, Fast et al., 2010) was extended to include children’s mapping skills as mediators between early quantitative and symbolic number knowledge and symbolic number comparison. The model was assessed in two samples of Canadian children (Study 1, n = 62; Study 2, n= 45) and a sample of Mexican children (Study 2, n = 57). Results from both studies show that verbal counting, identification of symbolic number, and understanding of cardinality were important predictors of children’s mapping abilities. Children’s ability to associate Arabic digits to the corresponding quantity representation was predictive of their symbolic number comparison skills. Children first learned to associate number words to digits, then number words to quantities, and finally digits to quantities. Study 3 was an intervention study in which the goal was to assess whether enhancing children’s cardinality skills would result in an improvement to their symbol-quantity mappings. No significant effects of the training procedure were found. Children in this study had relatively strong early numeracy skills and thus the lack of learning may have reflected the lack of variability in their existing knowledge. Finally, Canadian and Mexican preschool children’s early numeracy skills were assessed in relation to the home learning environment. Significant relationships between reported frequency of home numeracy practices and numeracy skills were found for the Canadian but not for the Mexican children, whereas maternal education was found to be a significant predictor of numeracy skills in both countries. In conclusion, the three studies included in the present research provide insight into how mathematical skills unfold from the earliest symbolic and quantitative skills.