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

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.