Four, five, and sixes had to wear jackets that were buttoned down their backs. What was that to teach them?

From the text:

The little girl nodded and looked down at herself, at the jacket with its row of large buttons that designated her as a Seven. Fours, Fives, and Sixes all wore jackets that fastened down the back so that they would have to help each other dress and would learn interdependence.

The front-buttoned jacket was the first sign of independence, the first very visible symbol of growing up.

idk

interdependence