As an alternative to dominant cognitive-constructivist approaches to educational technology, this article makes the case for what has been termed a discursive, or postcognitive, psychological research paradigm. It does so by adapting discursive psychological analyses of conversational activity to the study of educational technology use. It applies these modified techniques specifically to discursive interactions with chatbots or intelligent agents, and to the theories commonly associated with them. In doing so, it presents a critique of notions of human-computer "indistinguishability" or equality as they have been articulated from Alan Turing to Reeves and Nass, and it sketches an alternative account of the potential and limitations of this technology. In divergence from Turing and Reeves and Nass, human discourse generated through encounters with natural language interfaces is seen as emphasizing the issue of conversation itself, foregrounding the achievement of common discursive aims and projects, rather than illuminating the internal states of either interlocutor. Mind and cognition, correspondingly, are revealed as phenomena "accomplished" through contingent social activity, rather than as computational processes concealed within or distributed between mind and machine. (Contains 1 figure and 2 footnotes.)