破解“消元困境”——转化思想在初中代数教学中的形成培养研究

Breaking the “Elimination Dilemma”: Research on the Formation and Cultivation of Transformational Thinking in Junior High School Algebra Teaching

摘要: 基于新课程标准对数学思想方法的培养要求，探赜转化思想在代入消元法教学过程中的应用价值和实践路径。分析转化思想以“化繁为简”的核心内涵，揭示二元一次方程组教学中的关键作用，就是将复杂问题转化为熟知的一元方程求解过程。并结合建构主义理论和数学认知理论，采用以学生为主体的教学设计，利用问题引导和活动探究，来理解消元原理，掌握转化方法。

Abstract: Based on the requirements of the new curriculum standards for the cultivation of mathematical thinking and methods, this paper explores the application value and practical paths of the transformation idea in the teaching process of the substitution elimination method. It analyzes the core connotation of the transformation idea, which is “simplifying the complex”, and reveals its key role in the teaching of systems of linear equations in two variables, that is, transforming complex problems into the familiar process of solving one-variable equations. Combined with constructivist theory and mathematical cognitive theory, a student-centered teaching design is adopted, using problem guidance and activity exploration to understand the principle of elimination and master the transformation method.