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Kindergarteners' numerical abilities are fundamental to their future academic development. The cognitive correlates of numerical abilities remain in debate. The present study examined whether non-verbal number sense and literacy could persistently predict kindergarteners' numerical abilities. A large-scale sample consisting of 930 children aged from 5.0 to 6.9 years were assessed for numerical abilities (addition and subtraction), non-verbal number sense (numerosity comparison), literacy (character reading), and general cognitive processing (word span, rapid automatized naming, mental rotation, figure matching and rhythm). The results showed that, after controlling for all other aspects of cognitive processing available, non-verbal number sense did not correlate with numerical abilities, while literacy was a stable cognitive predictor of numerical abilities in both age groups. And rapid automatized naming (RAN) was the most powerful cognitive predictor in the 6 years of age group. Further dominance analysis also showed that literacy was the most important predictor of numerical performance in the 5 years of age group and was next only to RAN in the 6 years of age group. The results suggest that literacy rather than non-verbal number sense is a unique cognitive correlate for kindergartener's numerical abilities. We argue that increased focus on natural language, especially literacy, may help to improve kindergarteners' math ability. Highlights: A large-scale sample consisting of 930 Chinese children aged from 5.0 to 6.9 years were assessed for numerical abilities, non-verbal number sense, literacy, and general cognitive processing. The link between non-verbal number sense and children's numerical abilities did not survive after controlling for other cognitive processing. Literacy rather than non-verbal number sense is a stable cognitive correlate for kindergartener's numerical abilities in 5.0–6.9 years old kindergarteners. [ABSTRACT FROM AUTHOR]