Although previous research has demonstrated that the acquisition of mathematical skills requires support from multiple cognitive abilities, the associations between cognitive precursors in different domains and mathematics at different hierarchical levels among primary school children are not well understood. This study explores the cognitive mechanisms underlying primary school children's mathematics learning by extending the original pathways model. A total of 409 children participated v.in the study. A battery of cognitive, symbolic number processing, and mathematics measures were performed on the participants. The cognitive pathways supported children's symbolic number skills, which in turn provided the foundation for formal mathematics. Different hierarchical mathematics skills were supported by different cognitive constellations. A hierarchical progressive development structure was found, from cognitive precursors, through symbolic number processing, to basic math fluency and complex numerical computation, and then, to problem-solving. The study also tried to divide children into two groups, grades 1-3 and 4-5. The exploratory results showed that there were commonalities and differences in the cognitive basis of mathematics learning in the two groups. These findings further explained the cognitive mechanisms underlying mathematical development in primary school children, with possible implications for the effective teaching and practice of mathematics knowledge and early identification and intervention of learning difficulties.