PME-NA

Representations of Derivatives for Teaching Calculus: Extending Beyond Traditional Frameworks

• In Event: Poster Session #2

Description

While extensive research exists on how students learn and understand derivatives across various contexts, there has been limited focus on how derivatives are taught and how different representations are used in instruction. Many researchers have relied on Zandieh's (2000) framework or its extensions to discuss derivative representations through graphical, symbolic, rate, and kinematic approaches. However, our recent study of eight calculus instructors' teaching methods revealed that they frequently use representations beyond those captured in Zandieh's framework, particularly when teaching with infinitesimals. This finding led us to develop the Representations of Derivative (RoD) framework, which aims to provide more comprehensive language for analyzing how instructors use different representations in derivative instruction. Our framework expands the existing literature by examining how these representations engage students' cognitive processes, offering new insights into effective calculus pedagogy.

Authors

• Saba Gerami, Cal Poly - San Luis Obispo

• Chris Liu, Cal Poly - San Luis Obispo

• Hannah Freund, Cal Poly - San Luis Obispo