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In online learning research, the theoretical community of inquiry framework has been used extensively to analyze processes of inquiry among learners and instructors within a community. This paper examines a special case of community of inquiry consisting of only one learner and one instructor. Together they engage in an online coaching discourse to form a relationship of inquiry. Within these relationships, coachees pass through processes of practical inquiry process while a coach supports the process. In this study, a framework and coding scheme were developed for use in a transcript coding procedure including 3,109 messages from an online coaching case in math for K-12 students. It is found that the elements of cognitive, teaching, and social presence, as well as the newly proposed emotional presence, which outlines a community of inquiry, comprise an effective structure for the analysis of one-to-one online coaching environments. The findings of this exploratory study suggest that a relationship of inquiry framework has the potential to support development of one-to-one online learning.