Analysis of Students’ Mathematical Understanding of Derivatives Algebraic Function on Islamic Boarding High School

Mathematical understanding is a critical component in learning mathematics, particularly in mastering the concept of algebraic function derivatives. This topic, included in the twelfth-grade curriculum at Islamic boarding schools, demands strong analytical thinking and the ability to apply mathematical concepts accurately. This study aims to analyze the mathematical understanding of grade XII students at Syahrani Bariah Zulkarnaen Islamic Boarding School in the context of algebraic function derivatives. The analysis focuses on three key indicators: the ability to apply mathematical objects, classify objects according to their properties, and select and use appropriate procedures or operations. The research was conducted in January 2025 and utilized qualitative methods, including observation, interviews, written tests in the form of problem-solving tasks, recordings, and documentation. The study involved three student respondents. The research process included several stages: preparation, consultation of questions with experts, implementation of data collection, result analysis, and conclusion drawing. Data were analyzed qualitatively by identifying errors and categorizing students' responses according to the indicators of mathematical understanding. The results indicate that students' mathematical understanding is generally low. This is evidenced by frequent conceptual and procedural errors, especially in the areas of selecting appropriate operations and classifying mathematical objects based on given concepts. These findings highlight the need for more adaptive and targeted instructional strategies in pesantren-based mathematics education. The study is expected to serve as a reference for educators in improving teaching methods and enhancing students’ conceptual and procedural understanding.