Abstract:Research methods concerning limit concept teaching are plentiful and rich in content. The discovery of laws in the development history of the limit concept and using it as the teaching guidance is not only an important part of HPM but also an innovative attempt. The history of the limit concept development shows that mathematicians’ knowing about limit is not at all a straight, but a gradual tortuous process. The setbacks and puzzles that students encounter in the learning of limit are just what the mathematicans in history had experienced, which confirms what M. Klein, the great mathmatician, had once pointed out: history is the guide for teaching. And it also dawns on us that the teaching of limit should abide by the law governing cognition and must be based on students’ mathematical level thus to promote a developing process like the growth of embryo in students.