To know his rights; to exercise with order & justice those he retains; to choose with discretion the fiduciaries of those he delegates; and to notice their conduct with diligence with candor & judgment.
The authors seem to emphasize the importance of understanding government and a free society a little more than the other objectives for education. Not only in this quote, but later in the objectives they discuss people becoming legislators and judges, the students being able to "expound the principles and structure of government" and for them to be able to participate in that kind of society by understanding "duties to his neighbors and country". This emphasis makes a lot of sense considering how young of a country the U.S. was and so understanding a more experimental form of government, one that hadn't been proven to work yet, was probably seen as incredibly useful for students to the authors of the Rockfish Gap.