In novel situations, people need to repurpose past knowledge to guide behavior (generalization). How they do this remains a mystery in cognitive science. Moreover, building machines that can achieve this is a key goal in machine learning research. Here, we designed a paradigm that allowed us to study the circumstances under which people learn and generalize. We find that people generalize to new situations in ways that are not possible for standard neural networks. However, if networks are modified in a simple way, they can display the same sorts of generalization as people and the same costs and benefits from different training curricula. Our results are relevant to understanding how both biological and artificial agents can deal with novelty.