We present the task of second language acquisition (SLA) modeling. Given a history of errors made by learners of a second language, the task is to predict errors that they are likely to make at arbitrary points in the future. We describe a large corpus of more than 7M words produced by more than 6k learners of English, Spanish, and French using Duolingo, a popular online language-learning app. Then we report on the results of a shared task challenge aimed studying the SLA task via this corpus, which attracted 15 teams and synthesized work from various fields including cognitive science, linguistics, and machine learning.