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Developing Reasoning about the Derivative of a Complex-Valued Function with the Aid of Geometer’s Sketchpad

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Abstract

In this study, a description is provided for the development of two undergraduate students’ geometric reasoning about the derivative of a complex-valued function with the aid of Geometer’s Sketchpad (GSP) during an interview sequence designed to help them characterize the derivative geometrically. Specifically, a particular GSP task at the end of this interview sequence aided the participants in viewing the derivative as a local property. This advancement is notable as previous participants had been largely unable to make this characterization precisely, and the participants of this study only did so while working on the final task of the interview sequence. This task required students to determine an algebraic formula given only geometric data through GSP. Particularly, they recognized that their disks constructed in GSP needed to be small to accurately identify points where the function is non-differentiable, and to stay away from the “bad points” when determining differentiability.

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  1. University of Oklahoma, Norman, OK, USA

    Jonathan Troup

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  1. Jonathan Troup
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Correspondence to Jonathan Troup.

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Troup, J. Developing Reasoning about the Derivative of a Complex-Valued Function with the Aid of Geometer’s Sketchpad. Int. J. Res. Undergrad. Math. Ed. 5, 3–26 (2019). https://doi.org/10.1007/s40753-018-0081-x

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  • DOI: https://doi.org/10.1007/s40753-018-0081-x

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