Application of the “Constructor Function” method in high school mathematics fill-in-the-blank and multiple-choice questions
高中数学填空、选择题中“构造函数”法的应用

摘要

在高中数学填空题和选择题中，问题的解决往往不仅只依靠公式和定理的掌握与应用，更需要通过灵活变通的思想方法，如函数与方程思想、划归与转化思想等，将复杂的题目条件化繁为简，用一种全新的、更为直接的视角去厘清问题的本质。“构造函数”法在一些特殊的试题当中，可以引导学生通过观察题目条件的特点，或对条件进行适当的变形后，构造出新的函数关系，找到解决问题新的突破口，从而提高学生的数学解题能力与速度。

Abstract

Fill-in-the-blank and multiple-choice questions in high school mathematics often require more than just mastering and applying formulas and theorems to be solved. They demand flexible thinking approaches—such as the functional and equation approach, or the reduction and transformation approach—to simplify complex conditions and clarify the problem's essence through a fresh, more direct perspective. The “Constructing Functions” approach can guide students in certain specialized problems. By observing the characteristics of the given conditions or appropriately transforming them, students can construct new functional relationships. This process helps identify novel breakthroughs for solving problems, thereby enhancing both mathematical problem-solving skills and efficiency.