The Community of Inquiry framework has become a useful instrument for exploring learning in online classes; however, the interactions between the constructs of teaching presence and cognitive presence remain relatively unexplored. This study investigated student perceptions of cognitive presence as explained by three teaching presence elements; instructional design and course organization, direct instruction, and facilitated discourse, in both online and face-to-face classes. Results indicate that student perceptions of cognitive presence and teaching presence do not differ between face-to-face and online classes and that discourse facilitation is a key to engendering critical thinking or cognitive presence. Qualitative data indicated certain aspects of teaching presence that students felt related to critical thinking. Students felt critical thinking was positively influenced when an instructor designed an organized course with clear goals and relevant assignments, provided direct feedback that was encouraging, timely, and specific, and actively facilitated discussions that kept everyone focused and participating at a meaningful level. (Contains 1 figure and 2 tables.)