Students’ Problem-Solving Behavior in Differential Calculus Based on Mathematical Prior Knowledge

Background/purpose. This study aims to analyze students' ability to solve differential calculus problems in relation to their prior mathematical knowledge (PMK).

Materials/methods. A qualitative research design method was employed. Participants in this study were 103 third-semester students at the university enrolled in the Differential Calculus course. They were divided into three groups, i.e., high, medium, and low, based on their PMK scores. They were given the same real-life problems to solve using differential calculus. In-depth interviews were conducted to identify and clarify things written and not written on the answer sheets. Data were analyzed using the Miles and Huberman model, while the process stages were analyzed according to the Bransford and Stein stages.

Results. The results showed that the real number course was the most mastered, indicated by the highest average PRK test score. The majority of students, namely 50.49%, were at the medium PMK level. Only the best group at the high PMK level could achieve correct final results and follow the Bradford and Stein stages. The group that excelled most at solving differential calculus problems was those with high limit course scores, not those with high real number course scores. It was also found that converting real-life problems into mathematical models was the most difficult stage.

Conclusion. Students who included problem scenario images during this phase performed better than those who did not. The most challenging problem was transforming a real-life problem into a mathematical model. Therefore, it is recommended to add a phase of transforming a real-life problem into a mathematical problem after the problem identification phase in Bransford and Stein's stages.

Keywords: Prior mathematical knowledge, problem-solving, differential calculus, real-life

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