新高考下利用竞赛思想解题的思路——以圆锥曲线和导数为例

The Approach to Solving Problems with Competitive Thinking under the New College Entrance Examination System—Taking the Conic Sections and Derivatives as an Example

摘要: 本文以圆锥曲线与导数两大核心知识模块为研究对象，探析竞赛思想在两大模块解题中的应用思路，并结合2021年至2025年的新高考真题进行分析，展示了竞赛思想与新高考数学考查导向的高度契合，其蕴含的以深刻性、简洁性和创造性为特征的高阶思维方法能够有效优化解题思路，简化运算，帮助学生提高解题效率和培养数学核心素养。

Abstract: This article takes conic sections and derivatives, two core knowledge modules, as the research objects, exploring the application of competition thinking in solving problems within these two modules. By analyzing real exam questions from the new college entrance examination in 2021~2025, it demonstrates the high alignment between competition thinking and the examination orientation of the new college entrance examination mathematics. The high-order thinking method characterized by profundity, conciseness, and creativity it embodies can effectively optimize problem-solving approaches, simplify calculations, and help students improve their problem-solving efficiency and cultivate core mathematical competencies.