What does the Bible say about children in worhsip? Can they worship differently on their own level? Where is their place in worship?
The Bible is silent on the subject of children in worship. One reason for this may be that Jewish children were not required to attend assemblies at the synagogue. It was not until a boy became "bar mitzvah" at age 13 that he was obligated to observe the commandments. There was apparently no requirement for children to worship even among the gentile Christians. Either that or nothing is said because the practice of children participating in worship was so common that it did not merit special mention. I tend to think that they were not required to participate in the assembly until they became Christians.
There are a number of congregations that hold separate "children's worship" either during the sermon or during the whole assembly of the church. The congregation I attend holds one for ages three through third grade during the sermons. The thinking behind this is that the sermon is usually above their level of the child's understanding, so a special assembly is held with teachings at their level. The theory sounds good. I have, however seen studies (and I don't remember where I saw the data) that seem to show that children who participate in these assemblies are not as well behaved when they do join the "adult" assembly as those who have remained in the main assembly throughout their lives. Since I can't give the exact source of that, don't take my objection as absolute.
I also read one individual who said that children should be in the general assembly based on 1 Corinthians 11:20-34 which repeats instructions for when you "come together in one place." This, however, was addressed to Christians and not necessarily to their children.
Another argument is that children, not being baptized believers, do not actually participate in worship because they can not worship "in spirit and in truth" (John 4:24). While there may be some validity in the argument, it leads to the idea that children are sinners from birth.
Although I personally object to children's worship because they lose the opportunity to observe their parents in worship, I can find no clear scripture that can be used either to support or condemn the practice.