For the achievement of mathematics learning at the primary education level, several authors have highlighted the importance of an adequate development of basic numerical skills (counting, comparing and estimating quantities) and of non-numerical cognitive functions (attention, memory, language and intelligence) in children between 3 and 6 years of age. Seventy-four children between 6 and 8 years of age participated in the study with the purpose of determining the influence of these variables on arithmetic skills. A coincidence analysis was performed between the scores of children with low performance in the subtest counting quantities and their long-term mathematical performance was observed. The results showed that counting quantities significantly explained the variability of arithmetic skills at the end of 1st and 2nd grade. Children with low performance on the counting quantities subtest also showed low performance in arithmetic skills at the same level. This finding is relevant for the early childhood education system (between 0 - 6 years), as it provides evidence that counting tasks could be important diagnostic markers for early detection of future difficulties in mathematics in the early school grade.