The Trivium is an educational method which conducts a student through his course of learning in a way which correlates systematically with his natural developmental stages.
The word "trivium" literally means "three ways."
The first phase of the Trivium is the grammar stage, during which time young students are most able to memorize the many facts and particulars of each subject area. The grammar stage corresponds approximately with the elementary school years. Students learn and memorize the grammar of math (addition and subtraction facts, multiplication tables, the ordering of time and money), geography (mountains, rivers, state capitals), science (formulas, definitions), history (wars, kings, dates), and so on.
At around the time of the middle school years, students then proceed to take the facts and knowledge they've accumulated, and begin to study their relationships during what is known as the dialectic (or logic) stage. Students analyze how the many pieces of what they've learned affect one another, and they learn to reason using the laws of formal logic and correct argumentation.
In the third phase of the Trivium, students focus on learning to express themselves with excellence. The material which they've accumulated in the grammar years, and learned to analyze and understand in the dialectic, is now polished and presented in rhetoric. The later high school years, which correspond with the rhetoric stage, are a time of learning to communicate and present knowledge in a manner which is worthy of the excellent education our students have received.
These three stages, grammar, dialectic, and rhetoric, compose the Trivium and are the methodological backbone of a Rockbridge Academy education.
For a more in-depth examination of the the Trivium, read Dorothy Sayer's article, The Lost Tools of Learning.