人工智能赋能空间解析几何四重混合教学模式的构建与实施

Construction and Implementation of an Artificial Intelligence-Enabled Four-Fold Blended Teaching Model for Spatial Analytic Geometry

摘要: 空间解析几何是高校数学类专业核心基础课程，以向量法和坐标法为数形结合的工具，承载从初等几何直观向高等代数抽象过渡的桥梁功能。然而，课程内容的高度抽象性与对逻辑思维和空间想象能力的高要求，使教学长期面临沉默课堂、学生参与度低、空间思维培养不足等困境。本文针对上述痛点，结合混合式教学与人工智能赋能教育的研究现状，构建了“课前线上感知–课堂线下建构–课后线上强化–次课堂线下迁移”四重混合教学模式。该模式以“学习四遍”为认知主线，形成螺旋上升的认知闭环；普及化的人工智能技术以“计算引擎、可视化实验平台、即时诊断器和个性化资源生成器”的角色深度嵌入各环节，通过动态可视化突破空间想象瓶颈，通过即时诊断精准定位典型认知障碍。实践遵循“线下艰难思考属人的目的性活动，线上人工智能辅助属工具性活动”的边界原则，使学生在与人工智能的协作中完成从“被动接受”到“主动建构”的转变，为空间解析几何课程的智能化转型提供了可复用的实践范式。

Abstract: Spatial analytic geometry is a core foundational course for mathematics majors in colleges and universities. Using vector and coordinate methods to combine algebra and geometry, it serves as a bridge from elementary geometric intuition to higher algebraic abstraction. However, the course’s high abstraction and its demanding requirements for logical thinking and spatial imagination have long resulted in silent classrooms, low student participation, and insufficient development of spatial thinking. To address these issues, this paper proposes a quadruple blended teaching model—“online pre-class perception, offline in-class construction, online after-class reinforcement, and offline transfer in the secondary classroom”—based on current research in blended learning and AI-enabled education. The model follows a cognitive mainline of “learning four times” to form a spiraling cognitive loop. Popularized Artificial Intelligence technology is deeply embedded in various stages as a “computing engine, visualized experimental platform, instant diagnostic tool, and personalized resource generator”; dynamic visualization breaks the bottleneck of spatial imagination, while real-time diagnosis precisely identifies typical cognitive obstacles. The practice adheres to the boundary principle that offline difficult thinking is a human purposeful activity, whereas online Artificial Intelligence assistance is a tool activity. This enables students to transform from passive acceptance to active construction through collaboration with Artificial Intelligence, providing a reusable paradigm for the intelligent transformation of spatial analytic geometry courses.