The application of auxiliary element strategy in solving college entrance examination mathematics problems——taking 2024 college entrance examination questions as examples
运用辅助元素策略解高考数学题例析——以2024年高考题为例

摘要

辅助元素策略是高中数学中常见且实用的一种解题思路，能够帮助学生在解题过程中构建中间桥梁，将复杂问题逐步转化为清晰可解的步骤，降低思维负担。然而，许多学生对这一策略的理解仍不够深入，缺乏主动运用的意识。本文以高考数学题为例，围绕函数、几何、数列三类常见题型，选取具有代表性的题目进行分析，引导学生在实际解题过程中逐步形成构造辅助元素的思维方式，从而提升对题目结构的把握能力与整体解题的条理性。

Abstract

The auxiliary element strategy is a common and practical problem-solving approach in high school mathematics. It helps students build intermediate bridges during problem-solving, gradually transforms complex problems into clear and solvable steps, and reduces cognitive load. However, many students do not fully understand this strategy and lack the awareness to use it actively. Using college entrance examination mathematics problems as examples, this paper focuses on three common types of problems: functions, geometry, and sequences. It selects representative problems for analysis to guide students in gradually forming a way of thinking that involves constructing auxiliary elements during actual problem-solving. This enhances their ability to grasp problem structures and improves the overall coherence of their solutions.