Children’s Non-symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability

Abstract

Most empirical evidence supports the view that non-symbolic and symbolic representations are foundations for advanced mathematical ability. However, the detailed development trajectories of these two types of representations in childhood are not very clear, nor are the different effects of non-symbolic and symbolic representations on the development of mathematical ability. We assessed 253 4- to 8-year-old children’s non-symbolic and symbolic numerical representations, mapping skills, and mathematical ability, aiming to investigate the developmental trajectories and associations between these skills. Our results showed non-symbolic numerical representation emerged earlier than the symbolic one. Four-year-olds were capable of non-symbolic comparisons but not symbolic comparisons; five-year-olds performed better at non-symbolic comparisons than symbolic comparisons. This performance difference disappeared at age 6. Children at age 6 or older were able to map between symbolic and non-symbolic quantities. However, as children learn more about the symbolic representation system, their advantage in non-symbolic representation disappeared. Path analyses revealed that a direct effect of children’s symbolic numerical skills on their math performance, and an indirect effect of non-symbolic numerical skills on math performance via symbolic skills. These results suggest that symbolic numerical skills are a predominant factor affecting math performance in early childhood. However, the influences of symbolic and non-symbolic numerical skills on mathematical performance both declines with age.

Variation in early number skills and mathematics achievement: Implications from cognitive profiles of children with or without Turner syndrome

“…Among both matched peer participant groups in our study, we found that MC N and TEMA-3 partial correlations (.29 or .56 in our verbal-or MC N -matched peers, respectively) were similar to effect sizes reported among other samples of young children~.28 [31] to .52 [33]. In contrast, the partial correlation between MC N and the TEMA-3 observed in girls with TS (.20) did not meet our significance threshold, and a smaller effect size compared to the of MC N and TEMA-3 correlations reported in other studies of mathematics skills in early childhood (e.g., [31,33,68,69]). On the one hand, these findings may suggest that there is nothing unique about the MC N and TEMA-3 correlation in TS, because a correlation of .20 approaches those earlier reported levels; on the other hand, these correlations among girls with TS were weaker relative to the other groups, did not reach statistical significance when correcting for multiple comparisons, and thus may be suggestive of a disparate trend in the TS group compared to peers.…”

Effects of Gender on Basic Numerical and Arithmetic Skills: Pilot Data From Third to Ninth Grade for a Large-Scale Online Dyscalculia Screener

“…It has been shown repeatedly that basic number skills form the foundations for learning more complex mathematical skills (Butterworth, 2005;Jordan et al, 2009;Li et al, 2018), and early numerical skills predict later achievement in mathematics (Zhang et al, 2017;Blume et al, 2021).…”

Patterns of symbolic numerical magnitude processing and working memory as predictors of early mathematics performance

“…Several cross-sectional and longitudinal studies have looked at numerical magnitude processing (NMP) and working memory (WM) as possible domain-specific and domain-general cognitive precursors of children's mathematics performance and development (e.g. Alloway & Alloway, 2010;De Smedt et al, 2013;Friso-van den Bos et al, 2013;Kroesbergen & van Dijk, 2015;Li et al, 2018;Toll et al, 2016). Both NMP and WM have been…”