Using excellent alumni as examples to demonstrate can serve as an effective way to ideological and political education for undergraduates in new situation.

Every top student who wants to seek a perfect platform for self-training on campus has gained a lot attention and love from the family,school as well as society.

Based on this, the thesis adopts the function of basic problems as tasks , and analyses the problem-solving process of top students and secondary students by using protocol analysis, By using quantitative analysis of oral code and qualitative analysis .

Psychological syndrome of the excellent students and the exercise prescription;

The excellent students, who are going to take the leadership in every walk of life in their future, are playing the role of the model in their classes as well, so their cooperation spirit cannot be overlooked.

Based on a wide-range review of literature, a case study was made on four excellent students in a key high school,.

The method of works analyzing is used to examine the 60 answering sheets of junior high school students in grade two of different achievements, such as students with excellent performance, students with moderate performance, students with low performance, and then the results is evaluated with the use of think-aloud method.

Data are collected mainly through three kinds of investigations:First, interviewing six high school top students in mathematics;Second, observing students mathematical behavior in their solution of six complex mathematical problems;Last, sampling top students in mathematics and average students from both top and average classes to survey their.