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

To cultivate the mathematical thinking is an important goal for mathematics teaching. Through the illustra-
tion 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.