一题多解发展数学思维——以一道中考数学题为例

Solving One Problem in Multiple Ways Develops Mathematical Thinking—Taking a Math Problem from the High School Entrance Examination as an Example

摘要: “一题多解”是发展数学思维及核心素养的载体，以2024年四川省成都市中考数学第22题引入，探究其本质与变式，详细研究了其中六种不同的解题方法，通过解法对比揭示数学思想的一致性，进一步通过探究本题的变式把握数学解题的本质，从而有效提升数学思维品质，进而推动数学思维的发展。

Abstract: “Solving one problem in multiple ways” serves as a carrier for developing mathematical thinking and core competencies. Taking Question 22 of the 2024 Chengdu High School Entrance Examination (HSEE) Mathematics Paper in Sichuan Province as the entry point, this study explores its essence and variations, conducts an in-depth analysis of six distinct solution methods, and reveals the consistency of mathematical ideas through comparative analysis of these methods. Furthermore, by investigating the variations of this problem, the inherent nature of mathematical problem-solving is grasped, thereby effectively improving the quality of mathematical thinking and further promoting the development of mathematical thinking.