an advanced version of dynamic "proofs without word (PWWs) "in GPS is proposed in this paper. in addition to dynamic presentations, the student can observe the dynamic proofs under various situations simply by modifying those parameters of the graphs under consideration. the student can choose to show step either automatically or manually by themselves; moreover, the mathematical proof statements and related figures can be shown simultaneously on the screen on demanding. some elegant visual demonstrations are provided for pythagorean theorem, AG inequality, and cauchy inequality. to realize the geometric as well as the physical roles played by the parameters of functions. taking advantage of its ability of drawing and computing, dynamic environments are built in GSP so that the students can observe the interrelationship between the parameters and graphs of functions simply by modifying the parameters, or contrarily by dragging the graphs. special attentions are paid over lines and slopes, and over conic sections and eccentricities. all dynamic environments in a CD-ROM are also available on request.