Actionscript 3.0 :: Good Algorithm To Move Along A Path?

I have finished a little game called "math match". The idea of the game comes from "math mountain", a game is for the player who must caculate some kind of mathmatic questions, if the answer is correct, the player will move along a predefined path in several steps. I am newbie for programming games, so I am not sure what I have done in moving the role is the correct one, although it works okay. I know in Flash CS3, I can use motion guid layer to make the role move along a predefined path, but it seems it's not good in the game, or I don't know how to control it in actionscript 3.0. So I used many 'marks'(little movieclip) along the path. That divide a path into small pieces of lines, so I can move the role along the lines. If the 'marks' is enough, the precise is enough, the movement works okay.

But I think it's quite not a good method. I don't know if there is any good algorithm to move the movieclip along a predefined path, and this path is random, is hardly to be described by any math equation. I think in Flash CS3, we can draw a path by author tools, indeed Flash CS3 use some algorithm to do that. If we can get that math equation, we can simulate the movement very precisily, but is it possible? I don't know.