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Background The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children. Methods The current study recruited 6- and 7-year-old children ( N  total  = 505,  n  6yrs  = 238, and  n  7yrs  = 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses. Results The current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.

Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling