This paper reports the multimodal resources that attached to students’ reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we design a task (in ℝ²) referring to specific tools and functions of GeoGebra. Task-based interviews were conducted with a pair of linear algebra students, by way of a computer and a teacher. Data was collected using a video camera observing the students’ working environment, screen recorder software, student production and field notes. The data was analysed according to the multimodal paradigm focusing on all semiotic resources, such as gestures and artefact use, in addition to written signs. According to the findings, the artefact use, verbal and written mathematical expressions all interlaced with the emergence of gestures. The students mostly gestured when they faced a new reflection situation and when describing associated geometric actions. Finally, a shared environment with action, production and communication conveyed student reasoning and they managed to reinvent a number of geometric linear transformations.

本文报告了在动态几何环境中重新发明特定几何线性变换（如根据轴的反射、轴上的投影和反射的组合）中与学生推理相关的多模态资源。遵循现实数学教育的设计启发式，我们设计了一个任务（在ℝ ²) 指的是 GeoGebra 的特定工具和功能。通过计算机和教师对一对线性代数学生进行了基于任务的访谈。数据是使用摄像机观察学生的工作环境、屏幕录制软件、学生制作和现场笔记收集的。根据多模态范式分析数据，重点关注所有符号资源，例如手势和人工制品的使用，以及书面符号。根据调查结果，人工制品的使用、口头和书面数学表达都与手势的出现交织在一起。学生们在面对新的反射情况和描述相关的几何动作时大多会做手势。最后，一个有行动的共享环境，