Generalization (or transfer) is the ability to repurpose knowledge in novel settings. It is often asserted that generalization is an important ingredient of human intelligence, but its extent, nature, and determinants have proved controversial. Here, we examine this ability with a paradigm that formalizes the transfer learning problem as one of recomposing existing functions to solve unseen problems. We find that people can generalize compositionally in ways that are elusive for standard neural networks and that human generalization benefits from training regimes in which items are axis aligned and temporally correlated. We describe a neural network model based around a Hebbian gating process that can capture how human generalization benefits from different training curricula. We additionally find that adult humans tend to learn composable functions asynchronously, exhibiting discontinuities in learning that resemble those seen in child development.