Conceptual and Procedural Knowledge of Prospective Mathematics Teacher in Solving Derivative Problems

Abstract: Both procedural knowledge and conceptual knowledge are needed to solve derivative problems. This study aims to describe PMTs' conceptual and procedural knowledge in solving derivative problems. A qualitative with a case study as the research method was used. The research subjects were 63 prospective mathematics teacher (PMT) who attended Differential Calculus in the 2022-2023 academic year. The subject was chosen with purposive sampling. This study employed three problems from the derivative understanding test as the research instrument. The data analysis technique used in this study was the data analysis technique outlined by Miles & Huberman which began with data collection, then data reduction and drawing conclusions. The findings reveal that PMTs' lack of meaningful understanding of the definition of derivatives and their symbols may lead to algorithmic errors in finding the function f when the derivative of the function f at c is known. Of all the subjects, 82.5% found the derivative of a function without using the product rule. The procedural errors in finding the derivative of the product of functions stem from the subjects' misunderstanding of the rule that the derivative of a product is the product of their derivatives.Furthermore, 55.5% of the subjects determined the maximum and minimum values by first finding the stationary points. However, only 11% correctly found the minimum and maximum values. The results of this analysis highlight the importance of having a profound understanding of concepts when selecting and developing effective problem-solving procedures. Thus, the findings of this study are expected to assist lecturers in preparing teaching materials about derivatives effectively. Keywords: conceptual knowledge, problem solving, procedural knowledge.