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Cognitive science offers rich theories of learning and communication, yet these are often difficult to operationalize at scale. We demonstrate how natural language processing can bridge this gap by applying psycholinguistic theories of discourse to real-world educational data. We investigate linguistic alignment - the convergence of conversational partners’ word choice, grammar, and meaning - as a measure of interactive alignment. Using a longitudinal dataset of real-world tutoring interactions and associated student test scores, we examine (1) the extent of alignment, (2) role-based patterns among tutors and students, and (3) the relationship between alignment and learning outcomes. We find that both tutors and students exhibit lexical, syntactic, and semantic alignment, with tutors aligning more strongly overall. Crucially, lexical alignment predicts student learning gains. As a lightweight, interpretable, metric, linguistic alignment offers practical applications in intelligent tutoring systems, educator dashboards, and tutor training.