Phenomenological Hermeneutic Study on the Epistemological Obstacles of High School Students in Solving Combinatorics Problems

This study employs a hermeneutic phenomenological approach to explore students' epistemological obstacles in solving permutation and combination problems, with the goal of supporting the development of more effective teaching materials. The research involved 24 12th-grade high school students (14 males and 10 females) and used qualitative methods. Data were collected through five diagnostic essay questions and semi-structured interviews to identify epistemological obstacles in combinatorics. Students’ written responses and interview transcripts were analyzed and interpreted to uncover the underlying obstacles. The findings revealed several epistemological obstacles: (1) students were unable to identify all possible answers from a given problem; (2) students could not differentiate between problems requiring the concept of permutation and those requiring the concept of combination; (3) students struggled to solve problems that differed from the example problems provided; and (4) challenges in formulating a complete solution when faced with multiple conditions, despite being able to calculate partial results. These insights suggest that teachers and future researchers should consider students' epistemological obstacles when designing instructional materials, particularly for topics in combinatorics such as permutations and combinations. Developing learning resources based on these findings may enhance conceptual understanding and problem-solving skills among students.