Analysis of Students’ Mathematics Problem-Solving Ability: A Case on Derivative Function - Erliananda, Dinda; Lubis, Rahmad Mulia; Siregar, Rama Nida ((JIML) JOURNAL OF INNOVATIVE MATHEMATICS LEARNING, 2025)
Mathematical problem-solving ability is a basic competency that supports conceptual understanding and application of calculus concepts, especially derivatives, at the high school level. However, many students still experience difficulties in translating contextual problems into appropriate mathematical models and applying derivative concepts effectively. This study aims to investigate the mathematical problem-solving abilities of 12th-grade students on the topic of derivative functions. This study used a qualitative descriptive approach to gain an in-depth understanding of students' problem-solving processes. Participants consisted of 12th-grade students from SMA IT Al-Husnayain, who were purposively selected to represent high, medium, and low levels of problem-solving ability. Data were collected through a contextual essay test on derivative applications and semi-structured interviews. Test items were designed based on Polya's problem-solving indicators: understanding the problem, constructing a mathematical model, applying a solution strategy, and reviewing the results. Data analysis was conducted by examining students' written answers, triangulating with interview data, and categorizing students according to demonstrated abilities. The results showed that students in the high-ability category were able to systematically apply derivative concepts, construct accurate models, and verify their solutions. Students with medium abilities generally understood the basic concepts but made procedural errors and tended to neglect formal verification. Meanwhile, low-ability students experienced significant difficulties in understanding the problem context, constructing correct mathematical models, and interpreting the results. In conclusion, students' problem-solving abilities in derivatives varied significantly across ability levels. These findings highlight the importance of a problem-based learning approach that emphasizes conceptual understanding, modeling skills, and reflective verification to enhance students' mathematical problem-solving competencies.