To answer "Yes" would be to assume that the Scriptures give specific detail on what method we must use, or how we must educate our children. That we must educate them in the Scriptures is true of course, but after that I think the Bible allows for a fair amount of liberty in this regard. Although we generally prefer a classical model in educateing our children, I've seen an almost blind devotion to it from others. I'm sorry, but as cool as it is to tell my Reformed friends that my kids speak Latin, I'd rather they learn Spanish, French and Chinese. And many of the classical works are only marginally beneficial to most people.
Bottom line, the Scriptures give us a broad outline, we have to fill it in and we need to be careful not to bind the consciences of other believers with how we've decided to fill in those blanks.