The essential principle of home schooling is to effectively EDUCATE your child in a manner adaptive to their personalities, rather than running them all through the same meat grinder with only one way of learning. Added bonus; teaching them actual facts and knowledge, and how to USE it, rather than the 'government approved' curriculum.
It is these things plus more.
We were teaching Tori to read, mathematics and to observe the science and world around her constantly.
While she was mastering +-*/, same age neighbor's daughter was learning how to glue glitter and pasta on a paper plate. While she was using Algebra to learn how to think logically, same age neighbor's daughter was failing two apples and you give one to the less fortunate how many are left? While the neighbor's daughter is trying to write sentences that are readable in English, Tori is a published poet and has chosen to learn Japanese as a second language because she likes Japanese animation.
And while maintaining a A average, she has earned a Second Degree Black Belt in American Karate, will test this fall for her third Degree, has successfully competed in tournaments around the Southeast, has earned the highest belt possible in Brazilian Jiu-Jitsu until she turns 16. She is also a paid instructor and mentors students as they work toward getting their Black Belt. She is also a fine marksman with multiple firearms. We expect she will complete her high school studies two years early and can then decide which mountains she wants to master. The only thing off the table is President of the United States, but then I'd just as soon she picked an honorable job.
As for the 'Ahh, what is "well-done home schooling," surely not the race card?' comment, beats me as to what you're referring. Tori is Chinese, her teachers, companions, fellow students and kids she teaches - literally span the globe in their origins.