Individual differences in kindergarten math achievement: The integrative roles of approximation skills and working memory

• The interrelationship between approximation, WM and math skills is unexplored.
• We examined a model on these skills' associations with 444 kindergarteners.
• Approximation comprises two separate abilities (nonsymbolic and symbolic).
• Both abilities correlate with math skills even when WM is taken into account.
• Symbolic skills mediate the association between nonsymbolic skills and math.

Kindergarteners can conduct basic computations with large nonsymbolic (e.g. dots, objects) and symbolic (i.e. Arabic numbers) numerosities in an approximate manner. These abilities are related to individual differences in mathematics achievement. At the same time, these individual differences are also determined by Working Memory (WM). The interrelationship between approximation, WM and math achievement has been largely unexplored. Also, the differential role of nonsymbolic and symbolic approximation in explaining math competencies is yet unclear. We examined an integrative theoretical model on the association between approximation (addition and comparison) and WM in 444 kindergarteners. As expected, approximation entailed two distinct abilities (nonsymbolic and symbolic). Both abilities correlated with mathematics achievement (i.e. counting and exact arithmetic), even when WM was taken into account. The association between nonsymbolic approximation and math achievement was completely mediated by symbolic approximation skills. These findings add to our understanding of the cognitive architecture underlying kindergarten math achievement.