Problem-Based and Guided Discovery Approach in Developing a Differential Calculus Textbook

Abstract

This study was conducted with the primary objective of developing a problem- based differential calculus textbook designed through a guided discovery approach, while simultaneously examining its validity, practicality, and effectiveness. The research employed a research and development (R&D) framework, specifically the 4D model— Define, Design, Develop, and Disseminate—adapted in this study up to the Implementation stage. The participants comprised 20 third-semester students enrolled in the Mathematics Education Program at UIN Syahada Padangsidimpuan. Data collection instruments included validation sheets, response questionnaires, and conceptual understanding tests. Descriptive statistics were applied to evaluate validity and practicality, whereas inferential analyses, including t-tests and N-gain calculations, were performed to assess effectiveness. Findings revealed that the textbook achieved a “highly valid” category with an average expert validation score of 4.5. Practicality testing showed favorable responses from both students and lecturers, with a mean score of 4.4, also classified as “very practical.” In terms of effectiveness, the intervention produced a significant improvement in students’ learning outcomes: the mean pretest score of 58.2 increased to 82.6 in the posttest, yielding an N- gain value of 0.58, which falls within the medium-to-high category. These results suggest that the developed textbook is feasible, practical, and effective for use in differential calculus instruction. Moreover, the study highlights the potential for broader implementation and recommends further development to cover integral calculus and other mathematical topics.