A slate in this case is a small chalkboard that you can carry - a little larger than your book. Before paper became so cheap, that is how students wrote their lessons.

Wow, that is old school.... yes it is literally slate (ie. the stone), used as a small chalkboard by students to write on. I'm imagining this story is set at least sixty years ago, if not over a hundred.

To abuse, To review unsparingly, To bait with dogs, To set on.