Many churches do have a separate children's service which runs simultaneously with the adult service. Since children have a different frame of reference than adults, along with a shorter attention span, their intellectual, emotional and spiritual needs are met by a service specifically geared for them.
The Bible does commission parents and the church to teach children:
Train (includes teaching by precept and example) up a child in the way he should go, And when he is old he will not depart from it (Prov. 22:6).
Therefore you shall lay up these words of mine in your heart and in your soul, and bind them as a sign on your hand, and they shall be as frontlets between your eyes. You shall teach them to your children, speaking of them when you sit in your house, when you walk by the way, when you lie down, and when you rise up.When a church has a separate service for children, they are attempting to impart the Word of God into the children at a level that the children can receive.
And you shall write them on the doorposts of your house and on your gates, that your days and the days of your children may be multiplied in the land of which the LORD swore to your fathers to give them, like the days of the heavens above the earth.
(Deut. 11:18-21)
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