Some researchers hypothesized that the development in executive function (EF) and mathematics is affected by the interrelation of resources in EF and mathematics. That is, EF is not a prerequisite to mathematics as had been known, but rather EF and mathematical skills are co-mutually supportive. Such hypothesis is referred to as developmental bidirectional associations (DBA) between EF and mathematics. Few longitudinal studies supported the DBA by showing how preschoolers’ beginning EF and math can predict EF and math at the end of pre-K. These results are limited to preschoolers with low socioeconomic status (SES). The literature is left with a question about whether the DBA can be generalized to upper grades and across children with different SES. Using longitudinal cross-lagged design may address the external validity issue by examining whether the DBA between EF and math continues across a nationally representative sample across the first three years of elementary school.