Computational Skills in Solving Application Problems Involving Basic Differentiation Rules in Differential Calculus: An Explanatory Sequential Study

Abstract

This study aimed to identify the level of computational skills and the challenges of students in solving application problems using basic differentiation rules in differential calculus. This study employed a mixed method explanatory-sequential design, which involves collecting and analyzing quantitative data first, followed by the collection and analysis of qualitative data. In the quantitative phase of this research, a simple random sampling method was utilized to administer a modified questionnaire (problem-solving examination type) to 50 calculus students. In the qualitative phase, purposive sampling was used to administer semi-structured in-depth interviews (IDIs) to a sample of 6 participants. Mean and thematic analysis with document analysis were utilized to examine the information that helped researchers identify problem about the subject matter. The study shows an overall high level of computational skills in basic differentiation, which means that the computational skills of students are often manifested. However, the computational skills of students in differential calculus in terms of chain rule are low, which is interpreted as rarely manifested. With this, this research had undergone an in-depth analysis of the challenges of the students in solving application problems using chain rule. The results reveal 3 challenges why the students’ computational skills in terms of the chain rule are low: the complexity of the composition of the chain rule, a lack of practice and exposure in using the chain rule, and uncertainty regarding its application. Effective teaching strategies are essential for breaking down complex concepts and enhancing students' computational skills in basic differentiation rules in calculus.