<![CDATA[Mathematical representation is central to problem solving, especially in tasks requiring Higher-Order Thinking Skills (HOTS), as students’ ability to construct and coordinate symbolic, visual, and verbal forms strongly influences conceptual understanding and solution flexibility. However, students with different mathematical ability levels demonstrate distinct representational preferences and constraints that shape their problem-solving effectiveness. This study investigates how high-, medium-, and low-ability students employ symbolic, visual, and verbal representations when solving HOTS problems, while also examining the cognitive and affective factors underlying these representational choices. A mixed-methods design was adopted, integrating quantitative analysis of students’ problem-solving performance with structured interviews to capture reasoning processes, representational strategies, and encountered difficulties. Six students representing high, medium, and low ability levels were purposively selected as research participants. The findings reveal clear differences in representational use: high-ability students flexibly integrated multiple representations, medium-ability students relied predominantly on symbolic procedures with limited translation across forms, and low-ability students tended to depend on verbal explanations with minimal formal representation. Notably, procedural fluency did not always correspond to strong conceptual flexibility. These results underscore the need for scaffolded, multi-representational instruction that explicitly supports translation among representations through guided prompts, visual supports, and collaborative problem-solving. Such pedagogical approaches are essential for strengthening conceptual understanding, enhancing cognitive flexibility, and improving students’ performance in HOTS-oriented mathematical problem-solving.]]>
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