Abstract
Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.
Highlights
The ability to understand and perform basic operations with numbers, or numeracy, begins before most children enter school [1,2,3]
The analyses showed that children trained on numerical comparisons with symbolic aids made larger gains on two of the four outcome measures, one-to-one correspondence (F(1,158) = 7.851, p = .006, partial eta squared = .047) and arithmetic (F(1,170) = 6.260, p = .013, partial eta squared = .036), compared to children who participated in non-symbolic numerical comparison training (Fig 3)
There were no differences when counting proficiency was coded as a knower-level. (F(1,201) = 0.003, p = .955, partial eta squared < .001). These results show that numerical comparison training with symbolic aids leads to greater increases in several important aspects of numeracy compared to non-symbolic numerical comparison training alone
Summary
The ability to understand and perform basic operations with numbers, or numeracy, begins before most children enter school [1,2,3]. Correlations between preschool numeracy and later mathematics achievement suggest that difficulties may originate before children enter school [7, 8]. Preschool numeracy interventions show promise for promoting shorter and longer-term enhancements in children’s readiness for learning school mathematics and for lowering the risk of dyscalculia [9,10,11,12,13,14,15]. To maximize the effectiveness of preschool interventions, we need to better understand the precise factors that promote the growth of numeracy
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