To Common shaichel and The little i know:
I know this was done out of safety, it is the most safe place to spank. For little kids it was normal to get on the bottom over the pants both at home and in cheder, and in some homes and cheders even bigger kids. Regarding spanking on the raw skin i got once spanked like this at home as i mentioned before and it was very very effective and it is safe. I am sure that it is not acceptable for a melamed to spank a child on bare, but my question was if it is appropriate for parents. I think in the goyishe world where spanking is permitted they do it lecatchila on the bare.