I assume that you have a layer with your text and a layer ith your chalkboard.
One way to erase the text is to use the Brush tool (one of the Paint tools) to paint on just the alpha channel of the layer with the text, turning it transparent where your strokes are.
I would use an animated track matte. You can create the animation using stroke, paint, or a bunch of other tools. You could even grab some black tempera paint, a cheap bristle brush, and a piece of white card stock (or white paint on a black card) and film it. Then use the footage or the animated layer as a track matte for your text layer.
I cannot seem to be able to activate the brush tool so it will apply to the text layer, though. I can apply it to a solid, but not text. Do I need to turn something on to be able to apply it to a text layer?
Do you know of a tutorial by chance?
Apply it to a solid then use the solid as a track matte for the text layer.