数学史视角下的高中数列性质探究及教学启示——以等差中项和等比中项为例

Exploration of the Properties of High School Sequences from the Perspective of the History of Mathematics and Teaching Implications—Taking Arithmetic Mean and Geometric Mean as Examples

摘要: 数学史作为数学文化的重要组成部分，可以帮助学生了解数学概念和思想的发展过程，更好地理解数学的抽象性和应用范围，在日常教学和教材上的体现也愈发明显。以等差中项和等比中项为例，从几何构造、函数特性与数列的前n项和这三个不同的历史视角，深入探析高中数列性质，旨在促进学生深度理解数列，实现核心素养落地。

Abstract: As an important component of mathematical culture, the history of mathematics can help students understand the development process of mathematical concepts and ideas, better comprehend the abstraction and application scope of mathematics, and its manifestation in daily teaching and textbooks is becoming increasingly obvious. Taking the arithmetic mean and the geometric mean as examples, this paper deeply explores the properties of high school sequences from three different historical perspectives: geometric construction, function characteristics, and the antecedent of a sequence, aiming to promote students’ in-depth understanding of sequences and achieve the implementation of core literacy.