In general, three approaches have dominated education from the beginning of time and I’m not sure there can be any more that are not combinations, parts, or permutations of these three.
The sophist does not believe in a knowable universe, so he focuses on adapting to change. The modern version of this approach is progressivism.
The traditionalist believes that knowledge is embodied in a tradition, so he focuses on absorbing and perpetuating that tradition. Many variations of this approach are followed in contemporary schools, but the best of the traditional theorists is probably ED Hirsch with his Core Knowledge approach.
The classicist believes in a knowable world in which knowledge is perception and relationship.
Individual Christians hold to any of these views, though Christianity is obviously a tradition in that its truths reside, not in the discoveries of the student, but in the wisdom of the fathers.
I find that Christian teachers trained in conventional colleges are strongly influenced by Progressive approaches, which discourage, by their nature, philosophical reflection on what you are doing.
For the most part, accepting these Progressive approaches without reflection undercuts the work and claims of the Christian school.
I don’t believe any of these approaches aligns with the teachings of scripture at a high level except for the classical approach.
At the root of the classical approach is a commitment to the belief that things have a nature and that we can know them according to their natures and treat them in ways fitting to their natures.
In addition, things have a purpose, and love enables its object to fulfill both its purpose and its nature.
In the classical tradition, the object of a science is to know the nature of a thing. The object of an art is to refine one’s ability to know the nature of things.
The sophist or Progressive educator does not believe we can know anything.
The traditionalist believes that we can know only through the tradition.
The classicist believes that we can perceive the nature of things and relate to them according to their natures.
What does your teaching lead your students to? That will tell you which of these theories you hold.