We present a computational model of language learning via a sequence of interactions between a teacher and a learner. Experiments learning limited sublanguages of 10 natural languages show that the learner achieves a high level of performance after a reasonable number of interactions, the teacher can produce meaning-preserving corrections of the learner's utterances, and the learner can detect them. The learner does not treat corrections specially; nonetheless in several cases, significantly fewer interactions are needed by a learner interacting with a correcting teacher than with a non-correcting teacher.