Gamifying a first-year calculus course: a structured framework for engagement and persistence

The transition to higher education is particularly challenging in mathematically intensive courses such as first-year calculus, where low engagement and high dropout rates are persistent concerns. This study presents the design, implementation and evaluation of a structured, narrative-driven gamified learning environment, ‘Calculus of Thrones’, introduced in a first-semester undergraduate calculus course at a European business school. Grounded in self-determination theory and gamification literature, the intervention integrated collaborative team structures, role-based participation and continuous low-stakes challenges to foster sustained engagement and regular study habits. A comparative analysis across five academic years (approximately 600–680 per cohort) shows that, while average final grades remained broadly stable, the introduction of the gamified environment coincided with substantial improvements in student persistence and course completion. The approved-to-enrolled ratio increased from 61.07% to 74.92% (+13.85 percentage points), while student satisfaction rose from 4.17 to 4.57 on a 6-point scale. Response rates to course evaluations also increased from 29.6% to 55.5%. All differences were statistically significant (p < .001). These findings suggest that gamification can meaningfully enhance student engagement and support academic success, through improved persistence and course completion, without inflating performance, offering a scalable and transferable framework for demanding first-year courses.