Our traditional model of calculus instruction at a large public research university emphasized factual knowledge and procedural fluency with few realistic applications, leaving a chasm between classroom mathematics and disciplinary practice. Amid an ongoing effort by our department to improve undergraduate learning outcomes, we replaced recitations in Calculus II with computational team labs to bridge this divide. Interview, classroom observation, survey, and gradebook data suggest that the labs facilitated a rich learning experience while student grade outcomes were unchanged. Student engagement, however, was inhibited by institutional structural factors, whose remedy requires a shift in departmental culture concerning the purpose of mathematics instruction.