My ex's ex (got that?! *lol*) does not have this many children, 'only' 6, but is of a similar faith and has a similar ideology to the Duggars. She had to have emergency surgery that rendered her sterile or she would have many more than 6.
It's called 'quiverfull' taken from Psalm 127 verses 3-5: 'Sons are a heritage from the LORD, children a reward from him. Like arrows in the hands of a warrior are sons born in one's youth. Blessed is the man whose quiver is full of them. They will not be put to shame when they contend with their enemies in the gate.' Most believe having a quiverfull family is not using bc of any kind, even natural family planning, and 'letting God decide' how many children you will have.
My ex-stepchildren have always done the bulk of the household work once they were of a certain age. Chores like washing the entire family's laundry or cooking lunches & dinners for a week were rotated between children, and care of their youngest sibling fell mostly on the oldest who would get up in the middle of the night to change diapers and feed her a bottle when she was a baby. Their mother mostly supervised to be sure the chores were being done correctly and helped them with their homeschool studies when they couldn't figure it out for themselves from the textbooks they used.
They have lived this way for the last five years, so this lifestyle is all the youngest ones really know or remember. While they are, without question, the most obedient and self-sufficient children I have ever met, they are also so starved for attention and so hungry for peer-to-peer relationships that it makes my heart hurt.
The oldest emailed me this past week to tell me that her mom doesn't want her to go to college, and I have come to conclude this must be b/c her mom doesn't want to give up that extra pair of hands, especially now that she can drive the younger ones around and drive to town on errands. The oldest is brilliant, so I know it can't be b/c of grades. I just hope the Duggars are encouraging their older children to move up and out when they are of age so that they can experience a regular life, too.