基于核心素养培养的平方差公式引入方式比较研究

Comparative Study on the Introduction Methods of the Difference of Squares Formula Based on Core Competency Cultivation

摘要: 本研究聚焦初中数学平方差公式的引入方式，对比分析复习引入与情境引入两种模式。通过梳理人教版等11个版本教材的引入设计，结合2022版数学课程标准要求，分别构建两种引入方式的教学设计。研究发现：复习引入以多项式乘法为基础，通过特殊算例引导学生归纳公式，侧重逻辑推理与抽象思维培养，适用于基础较好的班级；情境引入以校园文化墙改造为真实场景，通过面积计算抽象出公式，强化数学建模与应用能力，更适合激发基础一般学生的学习兴趣。研究为不同学情下选择合适的引入方式提供了教学参考，其核心思路与设计框架对初中数学其他知识点的教学也具有一定借鉴意义。

Abstract: This study focuses on the introduction methods of the difference of squares formula in junior high school mathematics, comparing and analyzing two models: review-based introduction and situational introduction. By sorting out the introduction designs of 11 textbook versions including the People’s Education Press edition, and combining with the requirements of the 2022 Mathematics Curriculum Standards, teaching designs for the two introduction methods are constructed respectively. The study finds that the review-based introduction is based on polynomial multiplication, guiding students to induce the formula through special calculation examples. It emphasizes the cultivation of logical reasoning and abstract thinking, and is suitable for classes with better basic knowledge. The situational introduction takes the renovation of the campus cultural wall as a real scenario, abstracting the formula through area calculation. It strengthens the cultivation of mathematical modeling and application abilities, and is more suitable for stimulating the learning interest of students with average basic knowledge. This study provides teaching references for selecting appropriate introduction methods under different student learning conditions, and its core ideas and design framework also have certain reference significance for the teaching of other knowledge points in junior high school mathematics.