There is ample behavioral evidence that others' mere presence can affect any behavior in human and non-human animals, generally facilitating the expression of mastered responses while impairing the acquisition of novel ones. Much less is known about i) how the brain orchestrates the modulation of such a wide array of behaviors by others' presence and ii) when these neural underpinnings mature during development. To address these issues, fMRI data were collected in children and adults alternately observed and unobserved by a familiar peer. Subjects performed a numerosity comparison task and a phonological comparison task. While the former involves number-processing brain areas, the latter involves language-processing areas. Consistent with previous behavioral findings, adults' and children's performance improved in both tasks when observed by a peer. Across all participants, task-specific brain regions showed no reliable change in activity under peer observation. Rather, we found task-independent changes in domain-general brain regions typically involved in mentalizing, reward, and attention. Bayesian analyses singled out the attention network as the exception to the close child-adult resemblance of peer observation neural substrates. These findings suggest that i) social facilitation of some human education-related skills is primarily orchestrated by domain-general brain networks, rather than by task-selective substrates, and ii) apart from attention, peer presence neural processing is largely mature in children.