Lexical alignment occurs when conversational partners converge on similar linguistic patterns. In collaborative learning settings, lexical alignment could indicate rapport, which can further predict learning and the collaborators’ evolving shared understanding. Traditional approaches to alignment computation often focus more on the summary statistics computed at the end of the conversation, which usually do not capture the conversational dynamics effectively. This work investigates how alignment evolves in a conversation by modeling lexical alignment trajectories between human dyads while interacting with a teachable robot. We find that, along with the summary statistics, the alignment curve parameters and the time taken to reach key alignment moments significantly predict rapport. We further see significant relationships between the early turns in the conversation and the overall alignment trajectories, indicating the importance of modeling conversational dynamics to plan real-time interventions in the robot, with the goal of altering the alignment trajectories and, consequently, learning outcomes.