Formative assessment and emotional trajectories aiding investigation of flow in higher education

IntroductionFlow represents a psychologically optimal state characterized by deep engagement, intrinsic motivation, and a balance between perceived challenge and skill. While formative assessment is known to support self-regulated learning through feedback and reflection, its relationship with students' emotional trajectories toward flow in higher education remains insufficiently explored. This study investigates how formative assessment practices are associated with the development of emotional states consistent with progression toward flow in university mathematics courses.MethodsThe study was conducted over three academic years (2020-2022) with 70 undergraduate students enrolled in mathematics-related courses. A design-based research approach was implemented in a feedback-rich instructional environment combining project-based learning, weekly formative feedback cycles, co-assessment activities, and a two-day hackathon. Students reported their emotional states weekly using a structured self-report instrument based on Csikszentmihalyi's eight-state model. Longitudinal changes were analysed using cumulative link mixed models and transition-probability analyses.ResultsStudents' emotional states showed a significant upward progression over time, with the average category increasing from 4.19 in week 1 to 7.31 in week 12. Negative emotional states such as worry and anxiety were more frequent at the beginning of the course, whereas activating states (arousal and flow) peaked during the intermediate phase, with flow reported by 60% of students in week 10. Control and relaxation increased steadily toward the end of the semester, reaching 86% combined in the final week. Statistical modelling confirmed a strong positive effect of time on transitions toward higher emotional-state categories.DiscussionThe findings indicate that sustained formative assessment practices were associated with emotionally productive learning trajectories consistent with progression toward flow. Weekly feedback cycles and collaborative learning activities appeared to support gradual shifts from uncertainty to engagement and finally to confidence and stability. These results suggest that formative assessment can function as a pedagogical mechanism for fostering optimal learning experiences in higher education mathematics contexts.