Analysis of Students’ Mathematical Problem-Solving Ability on Senior High School – Case on Function Derivative Material

Abstract

Derivative functions are a fundamental concept in high school calculus and serve as a crucial indicator of students’ mathematical problem-solving abilities. However, many students face challenges in applying derivative rules, especially when the complexity of problems increases. This study aims to analyze the problem-solving abilities of eleventh-grade students on the topic of function derivatives. The research employed a descriptive qualitative method involving students from class XI as participants. Data were collected through a problem-solving ability test consisting of 10 essay questions based on indicators of mathematical understanding, followed by interviews to gain deeper insights into students’ reasoning processes. The analysis focused on students’ ability to apply differentiation rules, including the power rule, product rule, quotient rule, and chain rule. The findings revealed that students performed well on low to moderate difficulty problems, mainly due to routine practice and familiarity with basic differentiation procedures. However, performance significantly declined on more complex problems involving root functions and fractional exponents. Errors were commonly observed in the simplification process and the application of advanced differentiation techniques. This suggests that while procedural knowledge is somewhat developed, conceptual understanding remains limited. The study concludes that innovative teaching approaches are needed to bridge this gap, particularly in fostering deeper conceptual comprehension and critical thinking skills related to calculus problem-solving.