Despite agreement about the importance of executive function (EF) for children's early math achievement, its treatment in correlational studies reflects a lack of agreement about the theoretical connection between the two. It remains unclear whether the association between EF and math operates through a latent EF construct or specific EF components. Specifying the correct measurement model has important theoretical implications for the predicted effects of EF interventions on children's math achievement. In the current study, we tested whether associations between EF and math operate via a latent EF factor, or via specific EF components using data from a large, nationally representative sample. We then replicated these same analyses with a meta-analytic database drawn from ten studies that collected measures of children's EF and math achievement. Our results lend support to explanations that a single EF factor accounts for most of the EF component-specific associations with math achievement. We discuss theoretical and methodological implications of these findings for future work.