DISCOVERING THE DERIVATIVE CAN BE “INVIGORATING:” MARK’S JOURNEY TO UNDERSTANDING INSTANTANEOUS VELOCITY

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DISCOVERING THE DERIVATIVE CAN BE “INVIGORATING:” MARK’S JOURNEY TO UNDERSTANDING INSTANTANEOUS VELOCITY

Abstract

This is a case study using qualitative methods to analyze how a first semester calculus student named Mark makes sense of the derivative and the role of the classroom practice in his understanding. Mark is a bright yet fairly average student who successfully makes sense of the derivative and retains his knowledge and understanding. The study takes place within a collaborative, student-centered, task-based classroom where the students are given opportunity to explore mathematical ideas such as rate of change and accumulation. Mark’s sense making of the derivative is analyzed in light of his use of physics, Mark as a visual learner, the representations he used to make sense of the derivative using Zandieh’s (2000) framework for representations of derivatives, and his conceptions of the limit over time. Classroom practice allowed Mark to exercise his agency and explore tasks in ways that were personally meaningful. The findings in this study contribute new details about how calculus students might solve tasks, develop strategies, and communicate with each other.

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