In this paper we address the important task of automated discovery of speech act categories in dialogue-based, multi-party educational games. Speech acts are important in dialogue-based educational systems because they help infer the student speaker's intentions (the task of speech act classification) which in turn is crucial to providing adequate feedback and scaffolding. A key step in the speech act classification task is defining the speech act categories in an underlying speech act taxonomy. Most research to date has relied on taxonomies which are guided by experts' intuitions, which we refer to as an extrinsic design of the speech act taxonomies. A pure data-driven approach would discover the natural groupings of dialogue utterances and therefore reveal the intrinsic speech act categories. To this end, this paper presents a fully-automated data-driven method to discover speech act taxonomies based on utterance clustering. Experiments were conducted on three datasets from three online educational games. This work is a step towards building speech act taxonomies based on both extrinsic (expert-driven) and intrinsic aspects (data-driven) of the target domain. (Contains 5 tables and 1 footnote.) [For the complete proceedings, "Proceedings of the International Conference on Educational Data Mining (EDM) (5th, Chania, Greece, June 19-21, 2012)," see ED537074.]