初中数学习题的“变式教学”研究

A Study of “Variation-Based Teaching” in Junior Middle-School Mathematics Exercises

摘要: 初中数学习题的变式教学在解题教学中有着重要作用，但也应该遵循一些相应的原则。通过分析，我们发现初中习题的变式教学以变条件的变式、变结论的变式、变解题过程的变式为基本类型。教师在掌握数学解题教学常用的变式策略的同时，学会运用条件特殊化、条件一般化、改变背景、联系实际以及变换条件和结论等方法指导教学。同时，在教学的过程中还应注意变式要适时、变式要适度、变式要注意纵向联系、变式要适量等问题，为以后的教育教学做好基础。

Abstract: Variation-based teaching of mathematics exercises plays a vital role in junior-middle-school problem-solving instruction, yet it must be guided by clearly defined principles. Analysis shows that such teaching rests on three fundamental types of variation: varying the conditions, varying the conclusions, and varying the solution process. Teachers should therefore master the variation strategies commonly used in mathematics instruction—such as specializing or generalizing the given conditions, altering the problem context, linking the task to real-life situations, and interchanging the conditions and conclusions—so as to guide their classroom practice effectively. At the same time, care must be taken to ensure that variations are introduced at the right moment, to the right degree, in the right amount, and with due attention to vertical coherence across the curriculum, thereby laying a solid foundation for future teaching and learning.