RUME 28
2026
Alexandria, Virginia
Targeting Conceptions of Derivative: Introducing Derivatives in Calculus With Inquiry
Page: 205
In this study, we leverage the Conceptions of Derivative (CoD) framework (Author et al., 2025) to analyze eight U.S. college calculus instructors’ instructional tasks for introducing derivatives. During four task-oriented interviews, each instructor proposed up to eight tasks for introducing derivatives with inquiry in their calculus I courses. Based on Zandieh's (2000) process-object model, the CoD framework was used to reveal derivative conceptions that instructors were targeting in their tasks. We identified four components of derivative conceptions targeted in the tasks: contextual framing, epistemological approaches (limit-based, infinitesimal/differential-based, and instrumental/rule-based), mathematical representations, and process-object layers. While pure contextual frames and limit-based approaches dominated early instruction of derivatives for these instructors, some targeted physics and biology contexts as well as infinitesimal/differential-based and rule-based epistemologies. We discuss implications for research on calculus teaching.