See my other comment here: https://news.ycombinator.com/item?id=14410788 There are many ways to punish children – taking away privileges is a good example – without denigrating them in front of their peers. (And even before reaching that point, talking with students who are acting out to understand what is causing them to do so often yields great results. But that's beside the point that humiliation is unnecessary.)
(Aside, consistently rewarding good behavior is not a great way to modify behavior either, as behavior reverts shortly after rewards stop. Inconsistent rewards are better; encouraging self-motivation is best.)
Some of those children acting out are doing so due to other trauma in their life. So, your suggestion of talking to them is a great one.
Offering up choices is good. "You cannot have another yogurt, but you can either read a book or go play outside." Children need to have some control over their lives and when they feel they don't have it, they act up.