Long-term relevance and interrelation of symbolic and non-symbolic abilities in mathematical-numerical development: evidence from large-scale assessment data

There is consistent evidence that symbolic abilities predict later mathematical achievement, whereas findings for non-symbolic abilities are more inconsistent. However, in previous research non-symbolic abilities were primarily considered as acuity of the approximate number system. In this study, we conceptualized symbolic and non-symbolic abilities as reflecting the development from operating with and mastery of concrete non-symbolic towards abstract symbolic-digital (Arabic digits) numerical presentation formats across a range of numerical tasks. We considered data from a population-based mathematical assessment (N = 3940) which followed students from grade 1 (Mage = 6;4 years) to grade 3. Confirmatory factor analysis substantiated the differentiation between symbolic and non-symbolic numerical abilities and indicated that both abilities were highly correlated, and each predicted later mathematical achievement significantly. As such, this study corroborated the long-term relevance of both numerical abilities at school-entry. Furthermore, the results extend previous experimental research by an ecologically valid developmental approach.