Mathematical Problem-Solving and Self-Efficacy in the Context of Algebraic Derivatives: A High School Study

The derivative of algebraic functions as a foundation for applications in mathematics, science, and engineering. Due to its complexity and contextual relevance, learning this topic demands not only strong problem-solving skills but also high levels of self-efficacy to support students’ confidence and persistence in mastering the material. Therefore, this study aims to analyze students’ mathematical problem-solving abilities and self-efficacy related to algebraic function derivatives. Conducted at a high school in Yogyakarta City, the study used a qualitative descriptive approach. Problem-solving was examined based on Polya’s steps: understanding the problem, devising a plan, carrying out the plan, and looking back. Self-efficacy was analyzed using Bandura’s dimensions: level, generality, and strength. The data was taken by self-efficacy questionnaire with Likert scale. The results elaborate students' problem-solving abilities in the topic of algebraic function derivatives fall into the good category. Students are also at a good level of self-efficacy. This study leads to the main conclusion that students’ problem-solving ability and self-efficacy in algebraic function derivatives are both categorized as good, and that there is a positive relationship between the two, indicating that higher self-efficacy corresponds to better problem-solving performance. These findings suggest that self-efficacy plays a significant role in supporting students’ success. Further research is recommended to explore this relationship more deeply, both qualitatively and quantitatively.