Abstract: Two roles，bystander and participant，have been proposed in this paper according to the two stages of mathematical modeling，which are modeling construction and solution and modeling estimation and generalization．The outstanding mathematical modeling participant possessing the abilities to convert from bystander to participant and from participant to bystander again has been pointed out．At the same time．the characteristics of the excellent mathematical modeling paper has been discussed with two aspects，form and content．And the relationship of role conversion with the two stages and excellent paper has also been discussed．At last，some suggestion has been proposed