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.

中文翻译：

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借助几何画板的复数函数导数的发展推理

在这项研究中，描述了两个本科生在面试序列中借助几何图形绘制板（GSP）进行的关于复值函数的导数的几何推理的发展，该访谈旨在帮助他们对几何导数进行表征。具体而言，在此采访序列末尾的特定GSP任务有助于参与者将衍生产品视为本地财产。这项进步是显着的，因为以前的参与者在很大程度上无法精确地进行这种表征，而本研究的参与者只是在完成采访序列的最终任务时才这样做。该任务要求学生仅通过GSP确定仅给出几何数据的代数公式。特别，