\triv•i•um\, n. The three "liberal" arts, grammar, dialectic, and rhetoric; -- being a triple way, as it were, to eloquence.

The Trivium is based on three stages of learning:

The Grammar Stage:

  In the Grammar stage, the student has a natural affinity for storing up information on a wide range of topics and recalling that information at will. This may seem tedious to adults, but is delightful to children who find it easy and discover fun ways to memorize the basic facts of a subject. The Grammar stage is the time to establish foundational building blocks for future learning.

The Dialectic Stage:

  In the junior high years, which correlate roughly with the Dialectic stage, the student's ability to reason is honed and sharpened. He begins thinking about relationships between ideas and evaluating arguments. Discussion and debate in a small classroom setting complement the formal study of deductive and inductive logic. Thus this stage is often called the Logic Stage.

The Rhetoric Stage:

  In the Rhetoric stage, the high school student gains command of language through written and oral expression and develops cognitive abilities. His studies represent the culmination of a sequential and orderly process of acquiring, evaluating, processing, and truly understanding ideas, information, and truth about the world around him. Using the tools of the Rhetoric Stage, students participate in formal debate, persuasive speeches, plays, elocution, research writing, and essay competetion.

For further information on this and related topics, you might want to check these links.

Dorothy L. Sayers essay - The Lost Tools Of Learning

John Milton Gregory - The Seven Laws of Teaching

St. Augustine - On Christian Doctrine

Amazon.com reviews of Douglas Wilson's book The Case for Classical Christian Education

Canon Press - Web Site