A Christian worldview isn't possible with the separation of intellect and spirit. Attending a secular school during the week with Bible class on Sunday compartmentalizes religion.
Many private schools offer thorough Bible teaching, but it's a completely separate class and curriculum. The result is categorical thinking—young people think of their spiritual lives as separate from moment-to-moment decisions. It's a mental conflict that results in a dysfunctional worldview and drives them everywhere but to a close relationship with God.
In a Classical, Christ-centered environment, intellect and spirit are one. For example, the Bible may be used as reference in the study of world History or Biology.
To trace the origins of a Christian worldview in education, we again look to History. The Greco-Roman praxis of Paideia—meaning perfection, or the process of educating man into his true form, is not considered Classical until the Middle Ages (201-300). Shortly after the 3rd century, a Christian worldview was introduced into Classical Education when Christianity was declared as the state religion of the Roman Empire. Augustine also believed it was essential for Christians to be literate since Christianity was a religion of the Book.
For more information on Classical Education with a Christian worldview please reference the recommended reading list.