利用一题多解培养大学生的数学思维能力

The Cultivation of Mathematical Thinking for College Students by Use of the Different Approaches in Solving the Same Maths Problem

以定积分及多重积分计算球冠面积为例,通过不同解题方法的训练及其对数学思维能力培养作用的分析,阐述如何引导学生用不同方法从不同角度思考问题,培养大学生的数学思维品质.这些具体做法与探讨注重实践性与可操作性.

To cultivate the mathematical thinking is an important goal for mathematics teaching. Through the illustration of calculating the area of a spherical cap via definite integral and multiple integral,the paper discusses about how to guide the students to adopt different methods to solve the same problem from different perspectives. It also discusses how to train the student's thinking ability and give some analysis of the relevant offects Such practices and explorations lay emphasis on the practicality and feasibility,which can serve as an invaluable referential source for college mathematics teaching.