The bible does say that if we spare the rod we spoil the child. This is a reference to punishment (not brutality) we all know that children can be punished in plenty of ways without violence. Sparing a child refers to when we tell a child that we will punish them for the wrong they are doing and don't follow through with it. Then the child will be spoiled, they'll walk all over their parents with no repercussions. Using the rod doesnt mean we need to beat kids, it means we must punish and in modern day language thats: timeout, going to bed with no dinner, no cell phone, no television, maybe a spanking etc. I'm totally against the idea of teachers hitting children, I think they should make them clean the school, do more homework and do community service. Usually physical labor is enough punishment for them.
"And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him." Hebrews 11:6