Abstract: To cultivate creative talents is one of the main aims of education in mathematics major;the teaching is a key factor to realize the goal.In this work,we investigate the methods by which the teaching is organized effectively to train students’ innovative abilities.We point out that the mathematical qualities of teachers and the learning interest of students are premises to develop students’ innovative abilities.We further analyze the functions of the teaching methods for cultivate students’ innovative abilities;and the methods involve analogy and  conjecture and induction,the problem-oriented ideas and the integration of modeling thinking into the teaching process;and some concrete examples are given to demonstrate that the methods discussed are advantageous to training students’ innovative abilities.

Key words: mathematics major, students；teaching, innovative abilities