Research in the social sciences and psychology has shown that the persuasiveness of an argument depends not only the language employed, but also on attributes of the source/communicator, the audience, and the appropriateness and strength of the arguments claims given the pragmatic and discourse context of the argument. Among these characteristics of persuasive arguments, prior work in NLP does not explicitly investigate the effect of the pragmatic and discourse context when determining argument quality. This paper presents a new dataset to initiate the study of this aspect of argumentation: it consists of a diverse collection of arguments covering 741 controversial topics and comprising over 47,000 claims. We further propose predictive models that incorporate the pragmatic and discourse context of argumentative claims and show that they outperform models that rely only on claim-specific linguistic features for predicting the perceived impact of individual claims within a particular line of argument.