Early number knowledge and cognitive ability affect early arithmetic ability

• Number knowledge was modeled without including arithmetic skills in the construct.
• Number knowledge has a long lasting effect on to future arithmetic ability.
• Verbal working memory had an indirect effect on to arithmetic ability.
• Early number knowledge had a direct impact on the growth of arithmetic ability.

Previous literature suggests that early number knowledge is important for the development of arithmetic calculation ability. The domain-general ability of verbal working memory also has an impact on arithmetic ability. This longitudinal study tested the impact of early number knowledge and verbal working memory on the arithmetic calculation ability of children in preschool (N = 315) and then later in Grade 1 using structural equation modeling. Three models were used to test hypotheses drawn from previous literature. The current study demonstrates that both early number knowledge and the domain-general ability of verbal working memory affect preschool and Grade 1 arithmetic ability. Early number knowledge had a direct impact on the growth of arithmetic ability, whereas verbal working memory had only an indirect effect via number knowledge and preschool arithmetic ability. These results fit well with von Aster and Shalev’s developmental model of numerical cognition (Developmental Medicine & Child Neurology, 2007, Vol. 49, pp. 868–873) and highlight the importance of considering arithmetic ability as independent from early number knowledge. Results also emphasize the importance of training early number knowledge before school entry to promote the development of arithmetic ability.