Arts and literature could be skills

Some personal curriculum should be added

Cultural canon varies

Maybe create sectors or areas/regions where there is a home-schooling counsel whereby other parents observe the skills and abilities....;-)

Thank you Camille, a group for evaluation will be really useful and parents can help each others.

I think that a creation of group meetings between students where they can debate about certain subjects, as a base to evaluate their knowledge and performance when exposed to other people and different way of thinking and ideologies.

There are many options, depending on the type of education from which you feel your child would benefit best. Most of the successful homeschool experiences I have seen begin with a mix of structured and unstructured learning. The parent develops a curriculum for the child and enhances that curriculum with problem-based learning, real world experience, and time for the child to follow an individual interest. The reason homeschooling can be very successful is because the learning is individualized and one on one. The child learns to love learning because it is less of an independent part of his or her lives, but rather an integration of learning, experience, nurturing, family, and personalization. For many homeschooling parents, there comes a time when they do not have the resources to continue the curriculum (e.g., they may need a science lab, a foreign language course, or an expert in the field -- such as robotics). At this point, parents often choose to bring in experts or send their child to community college.

There are many online and purchase-able homeschool curriculum materials for younger aged children. And many homeschooling families who can share their resources and their successful ideas. The beauty of homeschooling is that the curriculum can start with a canned curriculum and be enhanced and constructed to meet the talents and interests of the child.

Choose an internationally recognised examination to work towards?

you may find something useful here:

https://www.homeschool.com/resources01/curriculum.asp