Worshiping God with the people of God is a privilege, a powerful, beautiful, and uniqueopportunity. We do a disservice to our children if we treat the time of worship as something they are to endure with trivial time-wasters while the adults "really" join in worship. When we treat our children this way, it usually betrays how we think of our own participation in worship. We may have the self-control to put on a smile, or other socially acceptable mask, to not draw attention to ourselves during the service. But our children may not have such social awareness, or self control, so we give them busy work to pass the time during the service.
If instead we understood the unique and amazing opportunity we have to join with other believers in worshiping the one true God, and prepared ourselves before, and focused ourselves during, this special set-aside time, surely as that vision took root within us more and more deeply, its effect would spill over into how we guided our children within the service.
Throughout the worship service, in Word, Table, song, and community, we are being fed the bread of Heaven. When we allow our children to be distracted during the service, we allow them to ignore, and be starved from, the tremendous gift and nourishment being put in front of them.
Additionally, I think of people in closed or oppressed countries and cultures. They know, to a greater and more immediate degree, the cherished value of community worship. They are much more keenly aware of what life is or would be without that gift of corporate worship. They know what it is to be starved of that bread of Heaven, and might see, more clearly than us, what our children miss when they are distracted during worship.