School closures are one of the measures taken to combat COVID-19. By restricting social contact, closures contribute to the containment of infection chains. However, such measures have side effects that directly affect learners, since the loss of instruction time may lead to a reduction in learning outcomes. Our empirical analysis for primary school aged children shows that school closures could exacerbate inequalities relating to a child’s family-background. Some schools, and particularly dedicated teachers, are trying to provide alternatives to traditional classroom-based learning via online offerings and digital classroom instruction. However, it is precisely in these cases that non-school-related factors, such as the family environment, may become increasingly important once again and reinforce existing inequalities. School closures thus jeopardise the claim of equality in education made by education policymakers, particularly during the early years of primary school. It is therefore imperative to rethink the current approach to schooling. In light of digital progress, for the first time there exists the potential to bring professionalised, pedagogically tested interactions into the everyday life of school children while outside of the classroom environment. Rethinking schooling means doing justice to the need for equality even in times of school closures. This will be possible if age-appropriate high-quality instruction no longer needs to be tied to the school as a physical location.