In the popularization course of higher education, students entering into the higher colleges are not those excellent students with excellent achievements in the senior school, so the teaching of college mathematics in higher colleges should transform from the learning emphasis to popularization emphasis for traditional excellent higher education. In the transformation process, as a main basic course for the students of the engineering course, the calculus has many problems in the teaching. Based on many years' teaching practice and theoretic research, in this article, we first analyze the problems and antinomies faced by calculus teaching, demonstrate the feasibility of intuitive introduction method from the mathematical essential and the rule of human thinking, and finally explain the implementation method of the intuitive introduction combining with concrete teaching cases.