Argument mining systems often consider contextual information, i.e. information outside of an argumentative discourse unit, when trained to accomplish tasks such as argument component identification, classification, and relation extraction. However, prior work has not carefully analyzed the utility of different contextual properties in context-aware models. In this work, we show how two different types of contextual information, local discourse context and speaker context, can be incorporated into a computational model for classifying argument components in multi-party classroom discussions. We find that both context types can improve performance, although the improvements are dependent on context size and position.