Abstract The emergence of dynamic geometry environments challenges researchers in mathematics education to develop theories that capture learner’s growth in geometric understanding in this particular environment. This study coordinated the Pirie-Kieren theory and instrumental genesis to examine learner’s growth in geometric understanding when solving problems in a dynamic geometry environment. Data analysis suggested that coordinating the two theoretical approaches provided a productive means to capture the dynamic interaction between the growth in mathematical understanding and the formation/application of utilization scheme during a learner’s mathematical exploration with dynamic geometry software. The analysis of one episode on inscribing a square in a triangle was shared to illustrate this approach. This study contributes to the continuing conversation of “networking theories” in the mathematics education research community. By networking the two theoretical approaches, this paper presents a model for studying learner's growth in mathematical understanding in a dynamic learning environment while accounting for interaction with digital tools.

中文翻译：

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解开学习者在动态几何环境中解决问题时几何理解的增长：协调两个框架

摘要 动态几何环境的出现对数学教育研究人员提出了挑战，以发展捕捉学习者在这种特定环境中几何理解增长的理论。本研究协调 Pirie-Kieren 理论和工具起源，以检查学习者在动态几何环境中解决问题时几何理解的增长。数据分析表明，在学习者使用动态几何软件进行数学探索期间，协调两种理论方法提供了一种有效手段来捕捉数学理解的增长与利用方案的形成/应用之间的动态相互作用。分享了对在三角形中刻出正方形的一集的分析，以说明这种方法。这项研究有助于数学教育研究界继续讨论“网络理论”。通过将两种理论方法联网，本文提出了一个模型，用于研究学习者在动态学习环境中数学理解的增长，同时考虑到与数字工具的交互。