<![CDATA[Background: Understanding students’ mathematical reasoning in solving quadratic function problems is important because it reveals how they construct and regulate their thinking during problem-solving activities. According to Dual-Process Theory, reasoning involves intuitive processes (System 1) and reflective processes (System 2). Aim: This study aimed to investigate how students engage System 1 and System 2 when solving quadratic function problems. Method: A qualitative descriptive approach was employed involving two tenth-grade students representing lower and higher mathematical ability levels. Data were collected through written tasks, video recordings, and semi-structured interviews. Data credibility was established through method triangulation. Results: The findings showed that both System 1 and System 2 were involved in solving quadratic function problems. Lower-ability students relied more frequently on System 1, resulting in automatic and less reflective reasoning. In contrast, higher-ability students demonstrated a more coordinated use of System 1 and System 2, leading to more systematic and accurate solutions. Conclusion: Quadratic function problem solving requires the integration of intuitive and reflective reasoning. System 2 plays a critical role in evaluating and validating initial intuitive responses, thereby supporting more effective mathematical reasoning.]]>
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