We, as parents, have the responsibility to fully educate our children.
If we choose to we can delegate some of that responsibility to other teachers, mentors, and institutions, but particularly when our children are young the responsibility to see that education is happening still falls back onto the parents.
In the book A Thomas Jefferson Education Home Companion (Which IS a book on home-based education, but don't dismiss it because you aren't a homeschooling family because you'll completely miss where I am going with this conversation) it talks about creating a Master Plan for the education of your children, and I found it completely fascinating. Diann Jepson outlines nine key elements of an effective master plan. Take a look:
Academic Programs--Some people may immediately fill in "Public Schools K-12". But I think it is important to realize that that is a choice. As I've considered the education of my children I've found some of the complete resistance to doing anything differently very interesting. There is this idea that using the public schools is "just what you do" because that's why it exists. But there are other options for academic programs. There's online schools and private schools and home schools. As far as home schooling, some people might use full prepared curriculum that they purchase, Other people simply have a house full of good books that they open often with their children.
Classics: your list -- If you ever said "Oh I loved reading that book when I was little. I will definitely read that to my own children one day." That is where this list comes from. It's important to realize that classics exist in every field of study--who were the pioneers of that field and what did they produce? Art, music, writings, autobiographies. There's more to education than text books.
Cultural Literacy, Breadth and Depth -- Listing and considering all the topic areas that you find important in your children's cultural literacy can help you see where your personal list of classics, might need some supplementation. Art, citizenship, geography, philosophy, major fields of science, architecture, government, foreign language. Parent's all over put their children in "extra-curricular activities" Do we choose those based on how they are helping develop our children into more well-rounded people, or because it was the cheapest option or what their friends were doing?
Adult skills --There's always one freshman that gets to the college dorms without really knowing how to do their own laundry--I won't let that be my kid! There's also cooking, knowing how to sew a button back on, and perform first aid. Maintaining a car and bike, and basic household appliances and whatever skills might be important in your family situation. And most of this skills education should happen at home, by way of example and teaching from parents, or neighbors or grandparents.
Organizational Programs --These are programs in existence that you want to use to help your children develop skills and attributes you desire. Boy Scouts, and Girl Scouts, 4-H, Suzuki, dance/science/math camps, church youth achievement programs, continental congress simulation etc.
Experience -- Some experiences are things we just think our children should have experience with before reaching adulthood. Public speaking, a musical performance, lead a group, create a small business and similar things.
Places to Go -- Climbing mountains, visiting historical sites or other countries, a rafting trip or survival trek. All the places that going in person will help to round out your children's education.
God --Obviously our plan for the spiritual education of our children falls outside the responsibility of any state-run schools.
Family Relationships --How will you nurture the family environment you desire?
After you decide the "what" your children's education will consist of on the educational master plan, you outline the systems of "how" you will see to it. So "Enroll son in 4-H at age 7, support his activities in it" goes on the plan as well as, "Family read-aloud time for a half hour every night at 7:30," to get through your list of literature classics.
Reading through these elements of an Education Master Plan and how to create systems to implement it was so empowering for me. So much of it was the type of intuitive planning I did before I was married and before I was a mother.
I grew up in a rich learning environment. My mother had studied early childhood education, and was always providing learning opportunities for us. She loved learning herself and that came through in the household we grew up in. We went on hikes, visited museums, took classes, read books and I grew up desiring to do many of those same kinds of things with my own children.
It can feel like a burden but is very important to realize that we are responsible for the education of our children, and also to realize that even if we've chosen to put our children in public schools that that doesn't mean their whole education is covered. We, as parents, have work to do.