The neurocognitive basis of elementary academic skills varies with parental socioeconomic status (SES). Little is known, however, about SES-related differences underlying higher-order cognitive skills that are critical for school success, such as reasoning.Here we used fMRI to examine how the neurocognitive basis of deductive reasoning varies as a function of parental education in school-aged children. Higher parental education was associated with greater reliance on the left inferior frontal gyrus when solving set-inclusion problems, consistent with other work suggesting that these problems might more heavily rely on verbal systems in the brain. In addition, children who are at the lower end of the parental education continuum, but have higher nonverbal skills relied on right parietal areas to a greater degree than their peers for solving set-inclusion problems. Finally, lower parental education children with higher verbal or nonverbal skill engaged dorsolateral prefrontal regions to a greater degree for set-inclusion and linear-order relations than their peers. These findings suggest that children with lower parental education rely on spatial and cognitive control mechanisms to achieve parity with their peers with parents who have more education. Better understanding variability in the neurocognitive networks that children recruit as a function of their parental factors might benefit future individualized interventions that best match children's characteristics.