一道考研试题的多种解法与教学思考  

Multiple Solutions and Teaching Thoughts for a Postgraduate Entrance Examination Question

作　　者：何婧 Jing He(School of Mathematics and Statistics,Hunan University of Technology and Business,Changsha,Hunan 410205)

机构地区：[1]湖南工商大学数学与统计学院,湖南长沙410205

出　　处：《教育教学研究前沿》2025年第2期50-52,共3页Frontiers of Education and Teaching Research

基　　金：湖南省普通本科高校教学改革研究项目(编号:202401001100);湖南工商大学2024年度校级教学改革研究项目(编号:校教字〔2024〕34号)。

摘　　要：在高等数学教学中,鼓励学生探索问题的多种解法,不仅能拓宽他们的思维方式,还能提高其解决复杂问题的能力。本文通过极坐标、三角代换和对称性等方法,给出了2025年全国研究生入学考试数学试题的多种解法。文章比较了不同解法的应用,探讨了各自的优缺点,强调了解题过程中思维方式的多样性与灵活性。同时,结合自身的教学实践,提出了如何引导学生运用多种解法,促进他们数学思维的发展,并帮助学生在实际问题中灵活运用数学工具。In the teaching of advanced mathematics,encouraging students to explore multiple solutions to problems can not only broaden their thinking,but also improve their ability to solve complex problems.This article provides multiple solutions to the mathematics questions of the 2025 National Postgraduate Entrance Examination through methods such as polar coordinates,trigonometric substitution and symmetry.The article compares the application of different solutions,explores their respective advantages and disadvantages,and emphasizes the diversity and flexibility of thinking in the process of problem solving.At the same time,combined with its own teaching practice,it proposes how to guide students to use multiple solutions,promote the development of their mathematical thinking,and help students flexibly use mathematical tools in practical problems.

关 键 词：考研试题 一题多解 二重积分 对称性 

分 类 号：O172.1[理学—数学]