Integrating role-play and STEM-based collaborative learning in understanding permutations and combinations

This article presents a STEM-based instructional approach for teaching combinatorics to 95 s-year students (72 IT engineering and 23 engineering management students) at a Serbian university of applied sciences. Although students had prior exposure to combinatorics, many relied on memorized formulas without conceptual understanding. To address this issue, we implemented a collaborative, constructivist learning design in which students collaboratively constructed combinatorial formulas through role-play, multiple representations, and real-world problem scenarios rather than receiving them in finalized form. Activities were connected to applications in computer science, reinforcing interdisciplinary relevance. Classroom data were collected through structured field notes, analysis of students’ written solutions, and follow-up interviews when necessary. Qualitative analysis focused on students’ reasoning processes and conceptual development, complemented by statistical comparison of individual test results with a previous cohort taught through traditional lecture-based instruction. The experimental group achieved significantly higher performance. The findings indicate that interdisciplinary, constructivist learning environments can foster deeper conceptual understanding and improved application of combinatorial reasoning. The study contributes to mathematics education literature by illustrating how collaborative knowledge construction in STEM contexts supports the transition from experiential activity to formal symbolic generalization in tertiary combinatorics instruction.