Constructivist learning theory suggests that learners must construct their own understandings, rather than have understanding passively dumped into their brains. These findings support the US National Research Council's recommendations for the adoption of active learning pedagogies in the classroom. However, the "classroom lecture" is only one of the resources students commonly have for learning in higher education. In this paper, we present exploratory homeworks -- a tool to support active learning for teaching programming languages. By leveraging the opportunity for the student to interact with the computer/compiler, we seek to provide a model for students of how to explore and understand programming language constructs and concepts. We report on the use of 15 exploratory homework assignments used in a CS0 course with 440 students in Winter 2011. We provide a model and advice for others wishing to develop exploratory homeworks for their programming courses and present quantitative and qualitative evidence regarding students' positive valuation of the homeworks.