Children this age are learning how to control their frustrations and anger. You want to help him develop self-control. It sounds to me that your son is being more than just playful with his hitting. He may have initially simply wanted your attention and now has misinterpreted your efforts to discipline him. He thinks your tapping of his hand is O.K., even perhaps part of a game. After all, you did it to him, too. It surely seems to have gotten your attention. This prompts him to want to do it even more.

I would recommend several approaches. First, try to avoid repeating any disapproving behavior. This never works and actually serves as negative modeling. It often reinforces the very behavior you are trying to eliminate. Second, when he is doing something non-threatening that he should not be, it is always critical to remain calm. Losing your temper sends the wrong message. Third, even at this age, always explain what behavior is wrong, why it is wrong, and what the consequences will be if it continues. You and his other caretakers must be consistent with the explanations and the consequences of his actions. Toddlers learn quickly how much they can get away with and with whom. You may want to place him in "time-out". Lastly, be sure to give positive strokes when he does interact in socially acceptable ways. Limits need to be set and non-physical means of achieving them encouraged. You also may be able to anticipate certain behaviors and re-direct his energies before the hitting begins. Close supervision and involvement in other activities may make a difference. Realize this will take some time, so be patient.