“5E”教学模式在初中几何证明教学中的应用研究——以“SAS判定定理”为例

Research on the Application of the “5E” Teaching Model in Junior High School Geometry Proof Teaching—Taking the “SAS Congruence Theorem” as an Example

摘要: 本文立足《义务教育数学课程标准(2022年版)》核心素养培养要求，针对传统初中几何证明教学“教师示范–学生模仿”的机械模式的局限性，探索“5E”教学模式在“SAS判定定理”教学中的应用。该模式以建构主义、学习迁移及“做中学”理论为支撑，通过引入、探究、解释、迁移、评价五个环节，构建以学生为中心的知识主动建构体系。研究结合人教版教材分析与初二学生学情特点，明确教学重难点与目标，设计递进式问题串激发认知冲突、动手操作建构定理、例题辨析澄清概念、变式训练强化迁移、全程评价落实“教–学–评”一体化的教学流程。实证检验显示，采用该模式的实验班在几何证明知识理解、过程规范及应用创新能力上显著优于对照班。研究表明，“5E”教学模式能有效突破几何证明教学难点，提升学生逻辑推理与空间想象素养，为初中几何证明教学优化提供实践参考。

Abstract: Based on the requirements for core literacy cultivation in the Compulsory Education Mathematics Curriculum Standards (2022 Edition), this study addresses the limitations of the mechanical “teacher demonstration, student imitation” model in traditional junior high school geometry proof teaching and explores the application of the “5E” teaching model in the instruction of the “SAS Congruence Theorem”. Supported by constructivist theory, learning transfer theory, and the “learning by doing” theory, this model constructs a student-centered system for active knowledge construction through five links: Engagement, Exploration, Explanation, Elaboration, and Evaluation. By analyzing the People’s Education Edition textbook and the learning characteristics of ninth-grade students, the study clarifies key teaching points, difficult points, and objectives, and designs a teaching process including progressive question chains to trigger cognitive conflicts, hands-on operations to construct the theorem, example analysis to clarify concepts, variant exercises to strengthen knowledge transfer, and whole-process evaluation to implement the integration of “teaching-learning-assessment”. Empirical tests show that the experimental class adopting this model significantly outperforms the control class in terms of geometric proof knowledge understanding, process standardization, and application innovation capabilities. The research indicates that the “5E” teaching model can effectively break through the difficulties in geometry proof teaching, improve students’ logical reasoning and spatial imagination literacy, and provide practical reference for optimizing junior high school geometry proof teaching.