Looking past the advent of modern education into the past there is found a foundation of education that has largely been neglected - the Trivium. The Trivium consists of Grammar, Dialectic (Logic), and Rhetoric. This already marks a stark contrast with modern education. These are not subjects as such, but rather the Trivium's goal is to give the student the tools of learning. Grammar is the stage that is primarily concerned with memorizing information - learning the vocabulary of a subject. It takes advantage of the child's ability to retain large amounts of information. They memorize a lot of rules and facts as the very foundation of their education. The next stage is the Dialectic stage. During this stage the student starts paying attention to cause and effect and how things are connected. That is they are beginning to understand the "Why" of the "What" they learned in the Grammar Stage and learning how to apply their knowledge to solve problems. Finally, there is the Rhetoric stage. This is where the students learn to take what they have learned and express it elegantly, both in writing and speaking.
When the Trivium is properly understood, then understanding the integration of subjects is much easier. If all subjects are understood within the framework of the Trivium then it is clear that every subject can be taught within these stages. Sayers goes through various subjects showing how the Trivium influences the teaching of them all. The Trivium itself integrates the subjects as the teacher sees that each subject is best taught through these stages. As this is done, the connection between the various subjects is also seen more clearly. As Sayers said, "The "subjects" supply material; but they are all to be regarded as mere grist for the mental mill to work ."
So that the students are taught in accordance with how God has made them to learn and in so doing they learn how to think as Christians, are taught to appreciate the good, the beautiful, and the wise, and are and are so equipped to better love and serve the neighbor.