Historically, in the US we have a long lineage of classically-influenced public schools, starting with Boston Latin in 1635. What you might not be aware of, I wasn't a week ago, is that there is a contemporary "classical education movement" with a distinct history and perspective. The seminal text here is The Lost Tools of Learning by mid-20th century British author and classicist Dorothy Sayers. In particular this text is the source of the framing of the trivium as stages in the intellectual development of a child and adolescent.
These ideas, combined with some Adler and other sources, have been formed into an approach to classical education popular with Christians, conservatives, homeschoolers, and Christian conservative homeschoolers. As with all education movements, there's a lot of internal variety in theory and implementation. One of the intellectual leaders of the movement is the CiRCE Institute.
I started looking at contemporary "classical education" after reading a post over at Core Knowledge on the subject and having the distinct impression I was reading a lot of coded signs whose meaning eluded me. If you look at the CiRCE What is Classical Education page, they make a point of confirming my suspicion:
We use a different vocabulary.
Different words are used and emphasized (e.g. trivium, quadrivium, virtue, etc.), while some of the words that are common to classical and contemporary education carry significantly richer meanings (e.g. science, liberal arts, etc.).
Not that there's anything wrong with that.
On the other hand, my post-modern worldview isn't exactly sync with their pre-modern one. Nor does it seem to me like anything Jesus Christ would actually be interested in.
What all this means in practical terms, I don't know. Certainly you could conclude by looking at ed school syllabi that America's classrooms are dominated by Paulo Freire's liberation pedagogy. You'd be wrong about that. All this "trivium" stuff may be just be the consultant and administrator edubabble of the conservative world. Who knows?
I can't actually parse, say, a 9th grade literature syllabus which says:
Throughout the course, we will revisit the virtue of temperance and judge the personalities we meet based on their ability (or inability) to evince this virtue...
The poet Horace might be the greatest voice for the lessons Ridgeview purports to teach: living life to its fullest, pursuing the good life, enjoying good conversation among good friends, simultaneously realizing our mortality and striving to transcend it.
Just be aware, gentle reader, that Classical Education movement has its own discourse community, and shift your frame of reference as needed.