Dear Barb,
In the following paragraphs (from an IELTS exam sample, a very good article stated by IELTS), I can tell that "good members of society" should not be "a society", it sounds like an adjective to describe "good members". But in other sentences, I was told by my English teacher that "a society" is in general wrong.
A child’s education is never only about learning textbook theories and basic skills. It should also include how to educate the next generation to become good members of society. This cannot be the sole responsibility of parents.
In order to be a good member of any society, an individual must respect others and share the value system of their community. Educating children to obey rules and respect others always begins in home, and it is always thought to be the responsibility of parents as they are the first who can help children learn what is important in life, and how the children are expected to behave in a society.
However, learning how to share the value system of a society can hardly be achieved just at home. When a child goes to school, they are entering a bigger community where teachers and classmates will have significant influence on them. At school, children have to experience working and living with people from various backgrounds. The experience can teach them how to cooperate with each other, share the value system of the school and contribute to their community.
However, to be a valuable member of any society is not a simple skill that can be achieved within school and home. When a child grows up and enter society, they should continue to contribute to the community throughout life. As a good member of society, they should play a role model for others to follow to keep a society in tune so people can live together happily and the economy can prosper in the long term.