My professor gave us the following reason:
The screen is positively charged. When dust particles fly near it, the positive charges in the screen induce a charge in the dust particle, pulling the negative charges closer to it, and pushing the positive charges away. The screen then attracts the negative side, pulling the dust particle to it.
But why does the screen attract the whole dust particle? Its only attracting the negative charges so why does the "whole" dust particle go to the screen? Why doesn't the screen just rip out the electrons, and repel away the rest of the particle?