Better conversational alignment can lead to shared understanding, changed beliefs, and increased rapport. We investigate the relationship in peer tutoring of convergence, interpersonal rapport, and student learning. We develop an approach for computational modeling of convergence by accounting for the horizontal richness and time-based dependencies that arise in non-stationary and noisy longitudinal interaction streams. Our results, which illustrate that rapport as well as convergence are significantly correlated with learning gains, provide guidelines for development of peer tutoring agents that can increase learning gains through subtle changes to improve tutor-tutee alignment.