Development of Mathematics Teaching Materials Using Didactical Design Research: A Study on Enhancing Pedagogical Content Knowledge in Quadratic Inequalities

Abstract

This study presents the development of mathematics instructional materials using the Didactical Design Research (DDR) framework, aiming to enhance the Pedagogical Content Knowledge (PCK) of prospective mathematics teachers in fractional number operations. The research adopted the ADDIE model and encompassed Analysis, Design, Development, Implementation, and Evaluation phases. The evaluation involved expert validators specializing in Didactical Design Research (DDR), subject matter, media, and educators. The resulting Semester Lesson Plan (RPS) assessment scores and teaching materials demonstrated a "Very Good" categorization, indicating their validity and suitability for field testing. Notable findings highlight epistemological, ontogenetic, and didactic obstacles in students' understanding of quadratic inequalities. The instructional materials showed incremental effectiveness during classroom implementation, as evidenced by increasing percentages of successful sessions. This research's implications for the future include the potential adaptation of the DDR framework across diverse educational contexts, exploring technological integration, and enhancing educators' proficiency in implementing DDR-based pedagogies. By bridging theoretical foundations with practical application, this study contributes to advancing mathematics education by fostering innovative instructional materials grounded in Didactical Design Research.