人工智能赋能工科高等数学教学——以“空间解析几何”为例

AI-Empowered Advanced Mathematics Teaching for Engineering Majors—A Case Study of “Space Analytic Geometry”

摘要: 在教育数字化战略持续推进的背景下，生成式AI为课程教学改革提供了新的技术路径。空间解析几何作为高等数学的重点与难点章节，涵盖向量运算、平面与空间直线、二次曲面等内容，是电磁场、天线原理和信号空间分析等专业课程的重要基础。该章节对学生的三维空间想象能力要求较高，而依赖静态PPT和板书的传统教学模式难以帮助学生形成完整的空间几何直观。为此，本文以空间解析几何整章为改革载体，构建了生成式AI支持的“课前–课中–课后–评价”全流程教学模式，并融入三维可视化演示、电子信息工程案例与课程思政元素。研究选取某高校电子科学与技术专业两届学生开展准实验对比，通过单元前测与后测考察教学效果。结果表明，在本研究样本范围内，生成式AI辅助教学有助于降低空间认知门槛、提高学生对本章知识的掌握水平。同时，教学实践仍需关注AI幻觉、工具依赖及教育数据伦理等问题。本研究可为高等数学抽象章节的数字化教学改革提供实践参考。

Abstract: Against the backdrop of the continuous advancement of educational digitalization strategies, generative artificial intelligence (AI) offers a new technological pathway for curriculum teaching reform. As a key and challenging chapter in Advanced Mathematics, Space Analytic Geometry covers vector operations, plane and spatial straight lines, quadric surfaces, and other topics, serving as an essential foundation for specialized courses, such as electromagnetic field theory, antenna principles, and signal space analysis. This chapter places high demands on students’ three-dimensional spatial imagination abilities; however, traditional teaching methods relying on static PPT presentations and blackboard writing often fail to help students develop a complete spatial geometric intuition. To address this issue, this paper takes the entire chapter of Space Analytic Geometry as the reform subject and constructs a full-process teaching model supported by generative AI, encompassing “pre-class - in-class - post-class - evaluation”. This model integrates 3D visualization demonstrations, electronic and information engineering case studies, and curriculum-based ideological and political education elements. A quasi-experimental comparison was conducted between two cohorts of students majoring in Electronic Science and Technology at a university, with unit pre-tests and post-tests employed to assess teaching effectiveness. The results indicate that, within the scope of this study’s sample, generative AI-assisted instruction contributes to lowering the threshold for spatial cognition and improving students’ mastery of the chapter’s knowledge. Meanwhile, teaching practice still requires attention to issues, such as AI hallucinations, reliance on AI tools, and educational data ethics. This study may provide practical references for the digital teaching reform of abstract chapters in Advanced Mathematics.