高观点下高考数学数列的研究——以2021~2026年新高考全国I卷为例

Research on Sequences in Gaokao Math from a High-Level Perspective—Taking the 2021~2026 National Paper I of the New Gaokao as an Example

摘要: 新高考改革背景下，数列作为离散函数载体，是考查逻辑推理、数学运算、数学抽象核心素养的重要板块。本文以2021~2026新高考全国I卷数列真题为研究对象，立足高观点，即高等数学(数列极限、离散分析)、竞赛数学(序列构造、数论性质)、函数离散化视角，梳理试题考点与命题演变，挖掘试题背后的知识本源，剖析命题立意，总结命题规律，提出教学与备考建议。研究发现：新高考I卷数列命题从套路化求和转向新定义、递推变形、离散性质探究、多模块融合，试题以初等知识为基础，但背景蕴含离散数学思想，强调从函数视角理解数列，弱化机械题型训练，突出探究与迁移能力。

Abstract: Under the background of the new college entrance exam reform, sequences, as carriers of discrete functions, are an important part for testing logical reasoning, mathematical operations, and core mathematical abstraction skills. This article takes the sequence questions from the 2021~2026 National College Entrance Exam Paper I as the research object, based on a high-level perspective—that is, advanced mathematics (sequence limits, discrete analysis), competition math (sequence construction, number theory properties), and the discretization of functions. It sorts out the test points and trends in question design, explores the underlying knowledge behind the questions, analyzes the intention behind the questions, summarizes the patterns, and offers teaching and exam preparation suggestions. The research finds that the sequence questions in the new Paper I have shifted from routine summation problems to exploring new definitions, recursive variations, and discrete properties, as well as integrating multiple modules. The questions are built on basic knowledge but their context contains discrete math ideas, emphasizing understanding sequences from the function perspective, reducing mechanical exercises, and highlighting exploration and transfer skills.