Classifying the dialogue act of a user utterance is a key functionality of a dialogue management system. This paper presents a data-driven dialogue act classifier that is learned from a corpus of human textual dialogue in a task-oriented tutoring domain that involves tutoring in computer programming exercises. While engaging in the task, students generate a task event stream that is separate from and in parallel with the dialogue. To deal with this complex task-oriented dialogue, we propose a vector-based representation that encodes features from both the dialogue and the hierarchically structured task for training a maximum likelihood classifier. This classifier also leverages knowledge of the hidden dialogue state as learned by an HMM, which in previous work has increased the accuracy of models for predicting tutorial moves and is hypothesized to improve the accuracy for classifying student utterances. This work constitutes a step toward learning a fully data-driven dialogue management model that captures a user-generated task event stream.