融合GeoGebra的线性代数探究式教学实践

Inquiry-Based Teaching Practice of Linear Algebra Integrating GeoGebra

摘要: 针对线性代数课程概念抽象、学生认知困难的问题，本文探索将数学软件GeoGebra与探究式教学相结合的教学路径，构建了以GeoGebra为支撑的“情境创设–探究实践–迁移应用”的实践教学模式。通过“空间平面位置关系的判断”与“平面向量的几何变换”两个典型教学案例，详细阐述了如何借助GeoGebra的可视化与动态交互功能，引导学生从直观感知出发，发现、提出并解决问题。实践表明，该教学模式能有效激发学生的学习兴趣与内在动力，促进学生空间想象能力、逻辑思维与创新能力的协同发展。

Abstract: Aiming at the problems of the abstract concepts of linear algebra and the cognitive challenges faced by the students in linear algebra courses, this paper explores a teaching path combining the mathematical software GeoGebra with inquiry-based teaching, and constructs a practical teaching model of “scenario creation - inquiry practice - transfer application” supported by GeoGebra. Through two typical teaching cases, “judging the positional relationships of spatial planes” and “geometric transformation of planar vectors”, this paper elaborates in detail how to utilize GeoGebra’s visualization and dynamic interactive functions to guide students to actively discover, propose and solve problems from intuitive perception. Practice shows that this teaching model effectively stimulates students’ learning interest and intrinsic motivation, and promotes the synergistic development of students’ spatial imagination, logical thinking and innovation abilities.