People learn in fast and flexible ways that have not been emulated by machines. Once a person learns a new verb “dax,” he or she can effortlessly understand how to “dax twice,” “walk and dax,” or “dax vigorously.” There have been striking recent improvements in machine learning for natural language processing, yet the best algorithms require vast amounts of experience and struggle to generalize new concepts in compositional ways. To better understand these distinctively human abilities, we study the compositional skills of people through language-like instruction learning tasks. Our results show that people can learn and use novel functional concepts from very few examples (few-shot learning), successfully applying familiar functions to novel inputs. People can also compose concepts in complex ways that go beyond the provided demonstrations. Two additional experiments examined the assumptions and inductive biases that people make when solving these tasks, revealing three biases: mutual exclusivity, one-to-one mappings, and iconic concatenation. We discuss the implications for cognitive modeling and the potential for building machines with more human-like language learning capabilities.