They are part of it as they are frequently taught as Christian doctrine. So basic Christian ethics in virtually all Christian disciplines do include the content of the Ten Commandments in some form. The Ten Commandments are Jewish, not Christian, but Jesus, a Jew himself, expressed them as God's law and they were quite easily incorporated into Christian doctrine as the Church formed and grew.Numerous people, in numerous threads, have said the 10 Commandments are the basis for our laws.
In a school, posting of things like this are most certainly coercive. A 4th grade child does not understand why his family believes differently than other families. They just want to fit in.
Islam also adopted the basics of the 10 Commandments into their doctrine with the exception of keeping the Sabbath.
The Ten Commandments are certainly not the whole of the Law in Judaism, Christianity, or Islam but they have been critical in religious theology for 3000+ years and a very large majority of us believe in the God who historically provided them to us. You don't get any more historical than that.
Can the government dictate we follow the 10 Commandments as they are written? No. And it should never have the power to do that. Can the government forbid the citizens from respecting the 10 Commandments and following them? No and it should never have the power to do that.