A “non-religious” curriculum with a long and honored history is Calvert School. I believe they started during the polio epidemic geared towards kids that had to stay hospitalized/in iron lungs etc.
The Calvert School goes back to the end of the 19th century, and has been used by folks who have had traditional schools unavailable to them, like missionaries in foreign countries, folks whose work requires extensive travel with family, etc.
We used the Calvert School curriculum with both our sons for a number of years.
My wife told me that they're planning to bring out a high school curriculum.
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