混合教学模式下中学数学分类讨论思想的渗透

Penetration of the Classification Discussion Method in Secondary School Mathematics under the Blended Teaching Model

摘要: 分类讨论思想是中学数学核心思想方法之一，逻辑性与系统性突出，广泛应用于代数参数分析与几何图形位置判断两大核心领域，对提升学生思维严谨性与综合解题能力意义重大。本文以混合教学模式为背景，聚焦代数与几何模块，探讨分类讨论思想的渗透路径。研究针对当前教学中存在的设计融合不足、评价反馈滞后、学生自主学习薄弱、分类思维不规范等问题，从教师教学与学生学习两个层面提出改进策略。通过线上自主探究、分类标准梳理与线下重难点精讲、思维互动相结合的方式，优化教学流程，强化过程指导。实践表明，混合教学模式可有效提升分类讨论思想的教学实效，帮助学生建立科学分类意识，形成不重不漏的解题习惯，进而培养逻辑推理、全面分析的数学核心素养，为中学数学思想方法教学提供实践参考。

Abstract: The idea of classified discussion is one of the core ideas and methods of middle school mathematics. It is logical and systematic. It is widely used in the two core fields of algebraic parameter analysis and geometric figure position judgment. It is of great significance to improve students’ thinking rigor and comprehensive problem-solving ability. Based on the background of mixed teaching mode, this paper focuses on algebra and geometry modules, and discusses the infiltration path of classified discussion ideas. In view of the problems existing in the current teaching, such as insufficient design integration, lagging evaluation feedback, weak students’ autonomous learning, and non-standard classification thinking, the research proposes improvement strategies from the two levels of teacher teaching and student learning. Through the combination of online independent inquiry, classification standard combing, offline key and difficult points intensive teaching and thinking interaction, the teaching process is optimized and the process guidance is strengthened. Practice shows that the mixed teaching mode can effectively improve the teaching effectiveness of classified discussion ideas, help students establish a scientific classification consciousness, form a problem-solving habit that does not leak, and then cultivate the mathematical core literacy of logical reasoning and comprehensive analysis, and provide practical reference for the teaching of mathematical thinking methods in middle schools.