Recommendations for a “Target Understanding” of the Derivative Concept for First-Semester Calculus Teaching and Learning

Abstract

The derivative framework described by Zandieh (2000) has been an important tool in calculus education research, and many researchers have revisited the framework to elaborate on it, extend it, or refine certain aspects of it. We continue this process by using the framework to put forward a suggestion on what might constitute a “target understanding” of the derivative concept for first-semester calculus teaching and learning. We draw on empirical results from psychological research into analogical reasoning in order to create a guideline for such a “target understanding,” which includes a process-object comprehension of the ratio-limit-function layers in three distinct graphical-symbolic-verbal/rate-physical contexts. Our recommended target understanding creates a testable hypothesis, in that obtaining this target may allow students to apply their derivative understanding to additional contexts, as needed. We provide the results of an empirical study regarding this hypothesis and show that they support our recommendation.