How we cite our quotes: (Book.Chapter.Paragraph)
Quote #1
Such teachers, though very well paid by their students, might be as much disposed to neglect them, as those who are not paid by them at all, or who have no other recompence but their salary. (5.1.71)
Again, Smith says that teachers would perform better if they had more financial incentive. That's why he thinks they should lose their salaries and be paid based on how many students they attract to their classes.
Quote #2
Force and restraint may, no doubt, be in some degree requisite in order to oblige children, or very young boys, to attend to those parts of education which it is thought necessary for them to acquire during that early period of life. (5.1.73)
Smith is willing to admit that some really young children should be forced to go to school because they're not yet capable of knowing what's good for them. But once they hit thirteen, he's cool with letting them do whatever.
Quote #3
Those parts of education, it is to be observed, for the teaching of which there are no publick institutions, are generally the best taught. (5.1.74)
Smith believes that the things that are best taught in society are the things that are taught outside the public school system. That's because these things are taught in direct connection with how badly people want to learn about them. This way, people learn more useful stuff.