学习进阶导向的高中数学概念教学设计——以“椭圆的定义”为例

Learning Progression-Oriented High School Mathematics Concept Instructional Design—Taking “Definition of an Ellipse” as an Example

摘要: 为突破高中数学概念教学的难点，本研究将学习进阶理论应用于“椭圆的定义”教学。研究首先界定了核心概念，构建了包含“经验、映射、关联、系统、整合”五个进阶水平的教学模型，并设计了相应的教学过程与测评工具。为检验模型有效性，研究实施了准实验，结果显示：与常规教学相比，实验班在即时测试与延迟测试中成绩均显著优于对照班，且效应量巨大。这表明，基于学习进阶的教学模型能有效促进学生认知的逐步深化与知识的长期保持，为高中数学概念教学提供了实证支持与可操作的路径。

Abstract: To overcome challenges in teaching high school mathematics concepts, this study applied learning progression theory to the instruction of “Definition of an Ellipse”. The research first defined core concepts, constructed a teaching model comprising five progression levels—“experience, mapping, association, system, and integration”—and designed corresponding instructional processes and assessment tools. To validate the model’s effectiveness, a quasi-experimental study was conducted. Results revealed that compared to conventional instruction, the experimental class demonstrated significantly superior performance in both immediate and delayed assessments, with substantial effect sizes. This indicates that the learning progression-based instructional model effectively promotes gradual cognitive deepening and long-term knowledge retention, providing empirical support and actionable pathways for high school mathematics concept teaching.