<![CDATA[Combinatorial problems in discrete mathematics require systematic representation, reasoning, and problem-solving strategies. However, students often face difficulties in enumerating cases, understanding constraints, and managing the numerous possibilities that arise. This study aims to analyze students' thinking processes in using generating functions as a strategy for solving combinatorial problems based on Polya's stages. This qualitative descriptive exploratory research involved 10 Mathematics Education students from Universitas Tanjungpura who had studied basic combinatorics. Data were collected through written tests using the problem "From the word 'PONTIANAK', determine the number of ways to select k letters (with varying k) if each consonant must appear at least once, while vowels may appear at most 5 times," followed by semi-structured interviews. Data analysis employed the Miles and Huberman model, categorizing responses based on Polya's stages. The results showed varied understanding of generating functions (50% high, 40% medium, 10% low category). All subjects chose generating functions as their strategy, yet experienced difficulties in translating verbal constraints into mathematical representations (50%), complex algebraic manipulation (70%), and formal verification (70% did not verify). Conceptual barriers included procedural-conceptual gaps, relational thinking difficulties, and lack of consideration between OGF and EGF. Generating functions significantly contributed to strategy efficiency (100%), mathematical structure clarity (90%), and generalization capability (80%). This study recommends that combinatorics instruction be designed with scaffolding for verbal constraint translation, integration of conceptual understanding, symbolic skill training with computational support, and metacognition strengthening through reflective activities to bridge the gap between conceptual understanding and procedural skills in combinatorial problem-solving.]]>
