What is the Purpose of Public Education in a Democracy?

It has become clear to me that the purpose of public education in a democracy is to simply help children to be good open minded citizens. A public school should not just dump information into a kids head and say there you go you can leave now. A public school should take a child and do the best they can do to expand that child's way of thinking. Teach them the laws of our society and teach them how to work with others of all kinds. A child who has good critical thinking skills and can get along with other kids and people is a child who will grow up to be successful. A main part of life is the different interactions a person has with other people. A school needs to show kids that no one is better than anyone else and that they need to work and interact well with others in order to be successful in different tasks. If that can be taught along with allowing the kids to think through problems using each other as outlets for help then the kids in these school will grow up to be good citizens which is what the purpose of public education is. I feel everyone will have different views on what the purpose of public education is. I also feel there is no definite concrete answer, but i feel that if our society is going to survive and become stronger this is what public education has to do.