A Cognitive Cascade Analysis of High School Students’ Problem-Solving Difficulties in Algebraic Derivatives - Yuliani Yuliani; Sudianto Sudianto; Mohamad Gilar Jatisunda (Department of Mathematics Education, Universitas Muhammadiyah Purwokerto, Indonesia, 2026)
Mathematics instruction at the high school level generally continues to emphasize procedural mastery, so students’ problem-solving abilities are often assessed based on the accuracy of their final answers. Previous studies have tended to focus on procedural errors or students’ success rates, while studies that reveal the complete and meaningful process of students’ mathematical problem solving remain limited. Therefore, this study aims to explore students’ mathematical problem-solving processes in the topic of algebraic derivatives. This study employed a qualitative case study design with 32 twelfth-grade students. Data were collected through a written mathematical problem-solving test administered to all participants, followed by semi-structured interviews with a purposively selected group of students representing different problem-solving profiles. The data were analyzed thematically using NVivo to identify patterns in problem interpretation, mathematical modeling, solution strategies, mathematical communication, and the meaningful use of mathematics. The results showed that students’ main difficulty occurred at the mathematical modeling stage, where many students were unable to translate contextual information into appropriate algebraic representations before applying differentiation procedures. This difficulty triggered a chain reaction in subsequent stages, leading to the use of mechanical problem-solving strategies and affecting students’ mathematical communication and meaningful use of mathematics. This study confirms that mastery of derivative procedures does not guarantee meaningful problem solving. The findings imply the need for learning approaches that emphasize conceptual understanding, mathematical modeling, and reflection. They also open opportunities for further research based on learning interventions.