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This article describes a practical approach to judging the nature and quality of critical discourse in a computer conference. A model of a critical community of inquiry frames the research. A core concept in defining a community of inquiry is cognitive presence. In turn, the practical inquiry model operationalizes cognitive presence for the purpose of developing a tool to assess critical discourse and reflection. The authors present encouraging empirical findings related to an attempt to create an efficient and reliable instrument to assess the nature and quality of critical discourse and thinking in a text‐based educational context. Finally, the authors suggest that cognitive presence (i.e., critical, practical inquiry) can be created and supported in a computer‐conference environment with appropriate teaching and social presence.