高中数学教学中的数学文化融入——以定积分的微元法为例

Integration of Mathematical Culture of Infinitesimal Method in Senior High School-Take the Infinitesimal Method of Definite integrals as Example

导数相关内容被引入高中数学拉近了初等数学与现代数学的距离。为使学生进一步感受极限的思想,提高其数学建模能力和科学的思维能力,培养其思辨和探索精神,针对高中导数应用内容,本文提出在此讲解定积分的微元法。课堂设计从定积分的思想和微元法介绍入手,展示立体几何中圆的面积、球的体积等常见公式的由来,渗透一般到特殊的哲学思想,探索中学数学课堂教学融入数学文化及思政元素的途径。

The contents of derivative in elementary mathematics make students more and more close with modern mathe⁃matics.In order to enable students to further feel the idea of limits,improve their modeling ability,and cultivate the spirit of innovation and exploration,and explore the setting of high school mathematics curriculum content,based on the content of derivative application,this article suggests imparting infinitesimal method(the micro element method)in this period,gives the premise of the definite integral and the basic steps of confirming definite integral.This article provides the strict proof to the common formulas,such as the area of a circle and the volume of a sphere in solid geometry,aiming at imparting the phil⁃osophical views from general to special,and mathematical culture.