Design-based research on instructional lessons for differential calculus incorporating Desmos

Malaysian students have experienced considerable challenges in mastering calculus in recent years, with over 40% failing to attain a credit grade in mathematics. While technology like Desmos can enhance understanding, educators need insights into how students develop conceptual knowledge in technology-based environments. Therefore, this study investigated the pre-university science students’ understanding of differential calculus using the Action-Process-Object-Schema (APOS) theory through a Desmos instructional lesson. A design-based research (DBR) strategy was employed to facilitate the real-time design, implementation, and refinement of the intervention. Classroom observations and document analysis revealed that most students achieved the Process phase of understanding based on APOS. The students’ interviews also indicated that they found the Desmos-based lesson engaging and valued the opportunity for group discussion. Nevertheless, some students still encountered difficulties entering equations in Desmos. Further refinements of the instructional design were then conducted through a comparative retrospective analysis between the hypothetical learning trajectory and actual learning outcomes. Overall, this study contributes to the existing literature by providing detailed, stage-specific analyses of the design, implementation through a teaching experiment, and retrospective analysis and refinement processes within the DBR framework, which are often underreported in previous research.