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Many young children go through a stage where they hit others. They often lack the words to express their frustrations appropriatly to the other children. They also may lack the skills to know how to handle their frustration with the other kids. It sounds like he is doing okay in the other areas of his life and only seems to react when irritated by other kids and not unprevoked. What the school and you are doing is right on at this time. The diary will help you and the teachers see when he is most provoked and how he reacts. This will give you the best information about how to prevent any more hitting. Also I would suggest role playing with him at home on how to react appropriatly such as telling the teacher when he is hit or asking the child to stop bothering him. Also if he has a bad day go over with him what happened, how he felt, and what he can do different the next time. It may also help to start a reward chart. So if he has a good day he gets a sticker and after so many he gets a reward. This will allow him to look forward to being good and not always focusing on what he is doing wrong.
Please let me know if I can assist anymore, I am here to help!
It may help to see if the teacher will help with the reward chart. She may be a presant motivator to help him not hit. If he does not she can send home a report or star that he had a good day and after maybe 4 or 5 he can do something fun with you such as the park, etc. It will make it for faster rewards.
A 2 week diary should be enough for you to begin to see a pattern on when and why he is hitting. It he tired,hungry, is it always the same kid,etc. This may give you some insight into what is happening.
I would also sit down with your inlaws and get them on the same page as you. It is not good when they are overriding your rules. Your son sees that and all the efforts you do are being unraveled.
If he continues to hit it probably wouldn't hurt to talk to his pediatrician or a child councelor to make sure nothing else is going on that needs to be addressed such as ADD, which can cause the poor impulse control. Or he may just need to work with a counselor for a short time to help him learn to control himself and they can work directly with him.