大学数学一题多解中发散性思维培养实例研究  

A Case Study on the Cultivation of Divergent Thinking in Multi-solution for One Problem in University Mathematics

作　　者：邱克娥 熊胜兰 欧阳建新 QIU Ke-e;XIONG Sheng-lan;OUYANG Jian-xin(School of Mathematics and Big Data,Guizhou Education University,Guiyang,Guizhou,550018;School of Mathematical Sciences,Guizhou Normal University,Guiyang,Guizhou,550025)

机构地区：[1]贵州师范学院数学与大数据学院,贵州贵阳550018 [2]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《贵州师范学院学报》2024年第6期76-84,共9页Journal of Guizhou Education University

基　　金：2024年贵州省“金课”《复变函数》(2024JKHH0155);贵州师范学院教改项目“《数学分析》课程教学与课程思政深度融合的探索与实践”(2022JG31);贵州师范学院教师科研课题研究成果“带瞬时脉冲的分数阶发展系统的解及可控性研究”(2024ZD001)。

摘　　要：数学创造性思维培养是核心素养培养目标下数学教育的重要任务,发散性思维是创造性思维的核心。在大学数学教育中,根据发散性思维的灵活性、流畅性和独创性等特点,以武汉大学2023年数学分析考研试题计算题第1题的解题教学为切入点,通过多种求解方法,如换元积分法、留数定理法、幂级数展开法等,探究大学数学教学中发散性思维培养的策略。The cultivation of mathematics creative thinking is an important task of mathematics education under the goal of core literacy cultivation,and divergent thinking is the core of creative thinking.It is an important task of higher education to train talents with innovative consciousness and creative ability.In college mathematics education,based on the characteristics of flexibility,fluency and originality of divergent thinking,this paper takes the first question of the 2023 mathematical analysis postgraduate entrance examination of Wuhan University as the starting point,and explores the strategies for cultivating divergent thinking in college mathematics teaching through a variety of solution methods,such as substitution integral method,residue theorem method,power series expansion method,etc.It is of great significance to improve the quality of mathematics education.

关 键 词：大学数学 一题多解 发散性思维 换元积分 留数 

分 类 号：O172.2[理学—数学]