From Wikipedia:

... average of seven children per family.

Amish rules allow marrying only between members of the Amish Church.

They typically operate their own one-room schools and discontinue formal education at grade eight, at age 13/14.

Almost no Amish go to high school and college.

the educational authorities allow the Amish to educate their children in their own ways.

Desertion from the Amish community is not a long-term trend, and was more of a problem in the early colonial years.

Rumspringa notwithstanding, the Amish way of life has several built-in features that repel modern influences without needing physical fences to do so.