Take a look at the Fish oil thread as deeyana suggests for more insight regarding the problem.
No one can make you test your child for ADHD (It's the law). It's the parent's or guardian legal decidtion. I agree that there could be a lot of others things going on. You mention that they 're doing writing . Is it possible that be can be having cramp when writing. You might want to read about dysgraphia and or check if he has any learning difficulties.
He might be doing better at home because mom is helping him. There could be many reasons your son could be acting this way. You might want to take a look at the fish oil thread in this forum.
That is exactly what is happening in exploding proportions,with schools all round the country, he has a behavioral problem which needs addressing by them at school, and you at home, how come they allow a child to throw pencils and kick? have they not heard of bounderies,so the teacher is not in control, and did they tell you a social worker would be observing him. It is possible your child is bored and is tuning out, it would be a good idea for you to talk to him and explain it is bad to throw and kick and ask him why he did that.as he doesnt do this at home the problem is at school and their way of handling any issue like this that comes up.Read the threads posted here it is a problem ,your child was at school a month some children are there for a few days and teachers are wottying parents with requeats they get their children evaluated. Go online to Breggin.com he has a lot to say on this subject