AI Teaching Assistants at Scale: Cross-Disciplinary Patterns of Adoption and Cognitive Engagement Across Hundreds of University Courses

Generative AI-powered teaching assistants are increasingly adopted in higher education, yet most existing research examines their use within single courses or controlled experimental settings. Little is known about how AI teaching assistants are adopted across diverse disciplines at an institutional scale, how cognitive engagement in student-AI interactions varies across academic contexts, and whether the quality of cognitive engagement matters more than usage frequency for learning outcomes. We present findings from a large-scale deployment of an AI teaching assistant platform across hundreds of course sections at four universities over four academic semesters, with over 2,400 active users who generated over 250,000 conversation messages. We address three research questions. First, what are the adoption and usage patterns of AI teaching assistants across this multi-institutional deployment? Second, how do student-AI interaction patterns and cognitive engagement levels---measured by Bloom's Taxonomy through automated LLM-based classification---differ across academic disciplines and institutions? Third, in a multi-semester programming course with pre- and post-assessments (? ≈ 200), how do students' cognitive engagement levels shift in response to different assessment designs, and what is the preliminary relationship between cognitive engagement and learning outcomes? Our analysis reveals distinct adoption patterns and interaction behaviors across disciplines, with meaningful variation in cognitive engagement levels across academic fields. In the programming course, week-by-week analysis reveals a gradual, progressive shift in cognitive engagement that mirrors the evolving course demands: higher-order interactions increased from 32\% in Week~1 (basic syntax) to 80\% by Week~16 (project work), with a strong monotonic trend (? = .884, ? < .0001). Preliminary regression analysis (? = 87) reveals that interaction frequency, rather than cognitive depth, predicts written exam performance---highlighting that the relationship between AI engagement and outcomes depends critically on assessment alignment. These findings contribute empirical evidence on AI teaching assistant deployment at scale, demonstrate how assessment design shapes cognitive engagement patterns, and offer practical implications for institutions planning large-scale adoption across diverse academic contexts.