基于弗赖登塔尔理论的高中圆锥曲线教学模型建构——聚焦现实情境的数学化与再创造

Construction of a High School Conic Sections Teaching Model Based on Freudenthal’s Theory—Focusing on Mathematization and Reinvention through Realistic Contexts

摘要: 针对高中圆锥曲线教学长期存在的抽象性强、模式僵化与学生认知困难等问题，本研究以弗赖登塔尔的数学化与再创造理论为框架，系统建构了一个以现实情境为驱动、以数学化与再创造为主线的教学模型。该模型将教学过程组织为现实情境启动、数学化探索推进、意义建构协同与反思深化延伸四个循环深化的阶段，并将动态几何软件作为贯穿全程的认知工具，引导学生亲历从几何直觉到代数模型的完整知识建构过程。文章详细阐述了模型的构成逻辑与操作要点，并以椭圆及其标准方程为例展示了具体应用。本研究为破解圆锥曲线教学困境提供了系统化、可操作的理论框架与实践路径，也为弗赖登塔尔理论在中国高中数学课程中的学科化应用提供了学科案例。

Abstract: Addressing the persistent challenges in high school conic sections instruction—namely, high abstraction, rigid teaching patterns, and students’ cognitive difficulties—this study draws on Freudenthal’s theories of mathematization and reinvention to systematically construct a teaching model driven by realistic contexts and centered on mathematization and reinvention. The model organizes the instructional process into four recursively deepening stages: realistic context initiation, mathematization exploration advancement, meaning construction collaboration, and reflection deepening extension. It employs dynamic geometry software as a cognitive tool throughout the entire process, guiding students to experience the complete knowledge construction from geometric intuition to algebraic models. The paper elaborates on the model’s constitutive logic and operational key points, and illustrates its concrete application through the example of the ellipse and its standard equation. This study provides a systematic and operable theoretical framework and practical pathway for addressing the instructional difficulties of conic sections, and also serves as a subject-specific case for the discipline-based application of Freudenthal’s theory within the context of Chinese high school mathematics curricula.