Cross-listed courses often present instructional challenges due to the varying student academic backgrounds and experiences, especially in classroom engagement and teamwork performance. This observation is especially true for cross-listed mathematical data science courses due to their unique audience with diverse learner technical skills and expectations from multiple academic majors, educational cultures, and career stages. To enhance student engagement and improve teaching quality, team-based learning (TBL) was integrated into the course and then student-instructor perceptions via the Class-Level Survey of Student Engagement (CLASSE) surveys were assessed. The results from two introductory mathematical data courses demonstrate that team-based learning, guided by CLASSE data as well as reflective instruction prove an effective and engaging pedagogical experience for both student and instructor..