In this article, we focus on the cognitive presence element of the Community of Inquiry (CoI) framework. Cognitive presence consists of four categories: Triggering Event, Exploration, Integration, and Resolution. These categories have been described as phases following an idealized logical sequence, although the phases should not be seen as immutable. Few studies have empirically examined how the four categories develop over time during the inquiry process. This article uses learning analytics methods to study transitions between the categories in K-12 online mathematics tutoring. It was statistically most probable that the tutoring sessions started with Triggering Event (95%) and then transitioned to Exploration (51%). The transitions from Exploration to Integration (18%) and Integration to Resolution (21%) achieved statistical significance but were less likely. In fact, it was more likely that the tutoring sessions transitioned from Integration to Exploration (39%) and Resolution to Exploration (36%). In conclusion, the findings suggest that the idealized logical sequence is evident in the data but that other transitions occur as well; especially Exploration recurs throughout the sessions. It seems challenging for students to reach the Integration and Resolution categories. As the CoI framework is commonly adopted in practice, it is important that tutors and educators understand that the categories of cognitive presence will often not play out in idealized ways, underlining their role in supporting how the inquiry process unfolds. In order to gain an improved understanding of the inquiry process, future research is suggested to investigate how the presences and categories of the CoI framework develop over time in different educational settings. [Note: The page range (252-271) shown on the PDF is incorrect. The correct page range is 252-270.]